text:
When is the derived category of representations of a finite poset equivalent to its opposite? - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-23T00:01:09Z http://mathoverflow.net/feeds/question/108191 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/108191/when-is-the-derived-category-of-representations-of-a-finite-poset-equivalent-to-i When is the derived category of representations of a finite poset equivalent to its opposite? Sam Gunningham 2012-09-26T19:32:50Z 2012-09-26T23:50:41Z
If I have a finite partially ordered set $K$, I can look at its derived category of finite dimensional representations $D(K)$. Note that $D(K^{op}) \simeq D(K)^{op}$ by linear duality.

But when do we have an equivalence $D(K) \simeq D(K^{op})$?

The kind of thing I have in mind is in this paper of Justin Curry: http://www.math.upenn.edu/~jucurry/papers/co_sheaf_dereq.pdf

When the poset comes from a finite cell complex, there is such a duality which interchanges the standard injectives with skyscrapers.

Does this depend only on the poset, and can this always be done?
 http://mathoverflow.net/questions/108191/when-is-the-derived-category-of-representations-of-a-finite-poset-equivalent-to-i/108198#108198 Answer by David Treumann for When is the derived category of representations of a finite poset equivalent to its opposite? David Treumann 2012-09-26T23:50:41Z 2012-09-26T23:50:41Z
I don't know a very general answer. Your duality on cell complexes resembles Verdier duality and has a local nature, but some of these equivalences aren't like that. E.g. $K = (0 < 1 < 2)$ and $K^{op} = (2 < 1 < 0)$ are isomorphic as posets and so we get $D(K) = D(K^{op})$ from that, but I am pretty sure $K$ doesn't have a Verdier dualizing sheaf.

But here is an answer to a narrower question: when is there an equivalence $D(K) = D(K^{op})$ that is similar to the one on regular cell complexes? I mean an equivalence that is Verdier-like in the sense that it takes the standard injectives on $K$ to the skyscrapers on $K^{op}$, up to a shift.

For each $x \in K$, define $J_x:K \to \mathrm{Mod}_k$ by $$J_x(w) = \begin{array}{cc} k & \text{if w \leq x}\\ 0 & \text{otherwise} \end{array}$$ These are the indecomposable injective objects in the abelian category of functors $K \to \mathrm{Mod}_k$.

The $J_x$ have a simple Hom pattern: $\mathrm{Hom}(J_x,J_y) = k$ if $x \geq y$. All other Homs (and Exts) vanish. (They form an "exceptional collection" in $D(K)$.)

The simple objects are the skyscrapers $\delta_x$. You can compute the Homs and Exts between $\delta_x$ and $\delta_y$ by writing down an injective resolution of $\delta_y$ whose $p$th term is $$\bigoplus_{y = y_0 \geq y_1 \geq y_2 \cdots \geq y_p} J_{y_p}$$ The differentials have degree $+1$. Then $\mathrm{Hom}(\delta_x,\text{that injective resolution})$ is a complex whose $p$th term is $$\bigoplus_{y = y_0 \geq y_1 \geq y_2 \cdots \geq y_p = x} k$$ This is the cochain complex that computes something like the relative cohomology $H^*(N,\partial N)$ where $N$ is the nerve of the interval $\{p \in K \mid x \leq p \leq y\}$ and $\partial N$ is the subcomplex of simplices that don't contain the edge $[x < y]$. So a necessary condition is for this $\partial N$ to be a homology sphere.

I think this condition is sufficient too, except you have to worry a little bit about the dimensions of those spheres. You have to be able to choose integers $d(x)$ for each $x \in K$ so that the dimension of that homology sphere is $d(y) - d(x)$ or something.

Somebody once told me that this condition on the intervals in posets has a standard name, maybe "Gorenstein star posets" but I am not sure I am remembering that right.


text:
# Start a new discussion

## Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

## Site Tag Cloud

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

• CommentRowNumber1.
• CommentAuthorzskoda
• CommentTimeApr 8th 2010

New entry string topology, short sentence and several complete references, with links.

• CommentRowNumber2.
• CommentAuthorzskoda
• CommentTimeApr 8th 2010

Of course, respective changes at Dennis Sullivan and Behrang Noohi.

• CommentRowNumber3.
• CommentAuthorzskoda
• CommentTimeApr 8th 2010
• (edited Apr 8th 2010)

We still do not have Poincaré duality, so I created just a frame with one link. Too tired to think about how to write it. I hope somebody will write something about nPOV on string topoology. In topology department we also still miss entries for Thom space and Spanier-Whitehead duality, both of course related to Poincaré duality. I added still more references to string topology.

• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeApr 8th 2010

• CommentRowNumber5.
• CommentAuthorAndrew Stacey
• CommentTimeApr 8th 2010

Not quite sure how this happened, but we have 'Poincare duality', 'Poincaré duality', and 'Poinca%C3%A9 duality'. The second redirects to the first, but the third seems to be a page by itself. I presume that the first two are the ones that we should go with so I've replaced the third with a simple link to Poincare duality (renaming it doesn't seem too important, and there's no history or content to preserve there, so it could be deleted).

Hope this is okay.

• CommentRowNumber6.
• CommentAuthorzskoda
• CommentTimeApr 8th 2010

I probably messed it up, by copying and pasting the URL from wikipedia, hoping it does correct translation for the page name with é in the title, but our system did not accept it. However it somehow keeps in memory bad atttempts. Thanks.

• CommentRowNumber7.
• CommentAuthorMike Shulman
• CommentTimeApr 8th 2010

I guess the point being made here is not a vacuous one.

• CommentRowNumber8.
• CommentAuthorzskoda
• CommentTimeApr 8th 2010
• (edited Apr 8th 2010)

If the system sent me the message when I write nlab/new/weird+page+name that there is a system error and does not reply with the box to type the content, I assume that the page is NOT created. Then later Andrew says he finds the weird page name as one of the created pages and tries to help to clean the mess up. Why on Earth, the system remembers unsuccessful attempts to create a page in which the browser notified the actor with the message that there was an error in finding the web page with the entry box ? this is not about keyboards what Toby was talking about, but a bug in software. I should be able to try and change until I make a web page with the content and the title I am content with. Nothing else (apart from old versions saved after no activity in a descent amount of time) should remain in the database. I never created the page ’Poinca%C3%A9 duality’ as far as I could tell. Computer told me error and I did not type any content. If the computer possibly accepted and said OK, but with a bad outcome, I would change the name instantnly and would not keep the redirect to the old name if I did the change in few seconds and hence think that reasonably nobody cited it (what I can check in the meantime if somebody did). Then in the database you would see just possibly the redirects which were intentional and functional.

You see when one changes a name of the entry, the software automatically types the redirect line for the previous name in the entry box. But if I check that the old name was never cited in nlab and do the change very quickly afterwards, I feel free to erase the redirect line from the new version of the entry. This is about all kinds of changes, not only about accented characters but also things like BV-BRST quantization vs. BV theory and so on. But currently the system leaves the old name in the database, it seems to me, anyway. Even if I erased the redirect as unwanted. And then weird things happen. This is not, in my opinion, the way the things should be.

• CommentRowNumber9.
• CommentAuthorAndrew Stacey
• CommentTimeApr 8th 2010

What can I say, except that no system is perfect!

• CommentRowNumber10.
• CommentAuthorzskoda
• CommentTimeApr 9th 2010

But it looks very simple from logical point of view: if something is renamed, the old name is not treated as a name in the database unless it is explicitly a redirect. I do not see what is complicated here from the point of view of updating the database. I thought that it worked that way, at least in certain period.

• CommentRowNumber11.
• CommentAuthorzskoda
• CommentTimeApr 9th 2010

Oh my worries were addressed in another entry as too serious look at a temporary cache phenomenon. Never mind.

• CommentRowNumber12.
• CommentAuthorUrs
• CommentTimeNov 26th 2010

I edited the Idea-section at string topology

• CommentRowNumber13.
• CommentAuthorUrs
• CommentTimeMay 28th 2011

Added to string topology first details on the string product and the BV-operator.

• CommentRowNumber14.
• CommentAuthorUrs
• CommentTimeMay 28th 2011

added the pull-push charscterization of the string product

• CommentRowNumber15.
• CommentAuthorUrs
• CommentTimeMay 28th 2011
• (edited May 28th 2011)

expanded and corrected the list of references about who did what concerning the interpretation of string topology operations as extended TQFT

• CommentRowNumber16.
• CommentAuthorzskoda
• CommentTimeJun 8th 2011
• (edited Jun 8th 2011)

Yiannis Vlassopoulos and Maxim Kontsevich have a current collaboration on an approach to string topology via moduli spaces of marked Riemann surfaces; there is a growing preprint in statu nascendi.

• CommentRowNumber17.
• CommentAuthorUrs
• CommentTimeJun 8th 2011

Thanks, good to know. Do you have anything that one could look at?

• CommentRowNumber18.
• CommentAuthorzskoda
• CommentTimeJun 8th 2011

Talk to Yiannis, he sketched the approach very roughly to me at the board a year ago, and said that the article was only partly written and should be finished in few months, but he was changing places in the meantime (with few months at IHES and few away).

• CommentRowNumber19.
• CommentAuthorUrs
• CommentTimeJul 23rd 2011
• (edited Jul 23rd 2011)

Sander Kupers kindly points out to me this article which constructs string topology as an HQFT for target spaces that are classifying spaces of finite groups and compact Lie groups.

That’s interesting, I had not been aware before that this has been accomplished. As the authors remark (on p. 35), one would expect that the string topology of the classifying space of a discrete group $G$ is closely related to $G$-Dijkgraaf-Witten theory. That would be most interesting.

• CommentRowNumber20.
• CommentAuthorzskoda
• CommentTimeJul 11th 2014
• (edited Jul 11th 2014)

Slides by Ralph Cohen, Calabi-Yau categories, string topology, and Floer field theory, pdf from the 2014 topological conference this June (2014) in Dubrovnik. Quotes some results of the above mentioned collaboration of Vlassopoulos and Kontsevich.

• CommentRowNumber21.
• CommentAuthorUrs
• CommentTimeJan 10th 2020

have added these pointers, on the perspective of regarding string topology-operations as the TQFT of a topological string sigma model:

Haven’t managed yet to get hold of a copy of the first. If anyone has a pdf, I’d be grateful.

• CommentRowNumber22.
• CommentAuthorUrs
• CommentTimeJan 13th 2020

fixed the publication data for this item:

• Please log in or leave your comment as a "guest post". If commenting as a "guest", please include your name in the message as a courtesy. Note: only certain categories allow guest posts.
• To produce a hyperlink to an nLab entry, simply put double square brackets around its name, e.g. [[category]]. To use (La)TeX mathematics in your post, make sure Markdown+Itex is selected below and put your mathematics between dollar signs as usual. Only a subset of the usual TeX math commands are accepted: see here for a list.

• (Help)

format: plain


text:
# Cohens d effect sizes

I'm using Cohens d effect sizes as a means of providing a magnitude based inference in a study I'm conducting.

I just wanted to clarify if I'm correct here: Anything between .0 and .2 is small. Anything between .2 and .8 is moderate Anything above .8 is large

If anybody could let me know if this is correct that would be much appreciated.

Those values are largely arbitrary. I believe Cohen surveyed some published studies in his field and found that the mean $d$ was $.5$ with a standard deviation of $.3$. However, the means and SDs will vary by field. Moreover, they aren't necessarily the same thing as importance for anything. That is, people will naturally assume that a large effect is important and a small effect is not, but you will get a very large effect by comparing the heights of adults and 3 year olds, without having made an important discovery. In general, I think the only person who can say what is "large" in your research is you.


text:
# Weakly Sublinear Compact FE from Succinct FE and XiO

I'm confused about a problem these days and I decided to seek an answer here. The question is about the section 4.1 of the paper LPST16. Let me recall the weakly sublinear compact FE scheme $\textrm{FE}$ from succinct functional encryption scheme $\textrm{sFE}$ and XiO.

• $(msk, pk) \gets \textrm{FE.Setup}(1^\lambda)$: it runs $(msk,pk) \gets \textrm{sFE.Setup}(1^\lambda)$

• $\textrm{ct} \gets \textrm{FE.Enc}(pk, m)$: it samples a puncturable PRF key and outputs $\textrm{ct} \gets \textrm{XiO}(1^\lambda, G_{pk,K,m})$ where $G_{pk,K,m}$ is a circuit with input length $n = \log s$ and $s$ is the max output length of the circuit $C$, and circuit $G_{pk,K,m}$ works as follows $$G_{pk,K,m}(i) = \textrm{sFE.Enc}(pk,(m,i); \textrm{PRF.Eval}(K,i))$$

• $sk_C \gets \textrm{FE.KeyGen}(msk; C)$ outputs $\textrm{sFE.KeyGen}(msk,C')$ where $C'$ on input $(m,i)$ outputs the $i$th bit of $C(m)$

• $y \gets \textrm{FE.Dec}(sk_C, \textrm{ct})$: $\textrm{ct}_i \gets \textrm{ct}(i)$ and $y_i \gets \textrm{sFE.Dec}(sk_C, \textrm{ct}_i)$ for each $i$ and outputs $y_1,\cdots,y_{2^n}$

Now I have two questions:

1. The paper speficies the circuit size of $G_{pk,K,m}$ is bounded by $poly(\lambda, |m|, \log s)$, how can we get this? to the best of my knowledge, I thinks the size of a circuit should be only related to the elements that are hardwired, is that correct? If this is correct, why the size is also polylog in $s$? More broadly, I also want to know how to calculate a circuit size.

2. Assume that the circuit size is also related to $s$ and $\log s$ is because of the puncturing, the second question is from my imagination. What if the circuit $G_{pk,K,m}$ outputs two encryptions, where one is over $(m,i)$ and another one is over $m$, and what is the circuit size of $G_{pk,K,m}$ now?


text:
# [texhax] Boxes and indents

Stefan Björk stefan at raggmunk.nu
Thu Jan 27 18:25:51 CET 2005

I'd like to create a framed box right after a section header. The box
should use the entire column width (like \vbox do). The paragraph after
the box should have no indent, just like after a \section command. The
basic idea so far is something like:

\newcommand{\infobox}[1]{\fbox{\vbox{#1}}

\section{A new section}

\infobox{A short description\\forced on two lines.}

This is the section text...

The problems so far is (1) text inside \vbox is first-line-indented, (2)
the section text after the \infobox is also indented, and I would prefer
not to force this with \noindent.

For the moment, I have no clues and wonder if anyone could give me any
hints?

Stefan


text:
# Glicksberg's theorem

Not to be confused with Glicksberg theorem.

In the study of zero sum games, Glicksberg's theorem (also Glicksberg's existence theorem) is a result that shows certain games have a minimax value .[1]

If A and B are compact sets, and K is an upper semicontinuous or lower semicontinuous function on $A\times B$, then

$\sup_{f}\inf_{g}\int\int K\,df\,dg = \inf_{g}\sup_{f}\int\int K\,df\,dg$

where f and g run over Borel probability measures on A and B.

The theorem is useful if f and g are interpreted as mixed strategies of two players in the context of a continuous game. If the payoff function K is upper semicontinuous, then the game has a value.

The continuity condition may not be dropped: see example of a game with no value.

## References

1. ^ Sion, Maurice; Wolfe, Phillip (1957), "On a game without a value", in Dresher, M.; Tucker, A. W.; Wolfe, P., Contributions to the Theory of Games III, Annals of Mathematics Studies 39, Princeton University Press, pp. 299–306, ISBN 9780691079363


text:
# Thread: Prove each of the following by induction

1. ## Prove each of the following by induction

As the title says, prove each of the following by induction:

a) $\displaystyle \sum_{j=1}^nj2^j=(n-1)2^{n+1}+2$ for every positive integer $\displaystyle n$

b) $\displaystyle 4^n<n!$ for all integers $\displaystyle n>8$

c) $\displaystyle n^2-10n+8$ is positive for all $\displaystyle n\geq10$

d) $\displaystyle 3$ divides $\displaystyle n^3+2n$ for all positive integers $\displaystyle n$

Show your work, of course.

2. Hello Runty
Originally Posted by Runty
As the title says, prove each of the following by induction:

a) $\displaystyle \sum_{j=1}^nj2^j=(n-1)2^{n+1}+2$ for every positive integer $\displaystyle n$

b) $\displaystyle 4^n<n!$ for all integers $\displaystyle n>8$

c) $\displaystyle n^2-10n+8$ is positive for all $\displaystyle n\geq10$

d) $\displaystyle 3$ divides $\displaystyle n^3+2n$ for all positive integers $\displaystyle n$

Show your work, of course.
I'll leave all the peripheral bits of the proofs to you. But here are the algebraic proofs that $\displaystyle P(n) \Rightarrow P(n+1)$.

a) $\displaystyle P(n)$ is the propositional function: $\displaystyle \sum_{j=1}^nj2^j=(n-1)2^{n+1}+2$

Then $\displaystyle P(n)$
$\displaystyle \Rightarrow \sum_{j=1}^{n+1}j2^j=(n-1)2^{n+1}+2+(n+1)2^{n+1}$
$\displaystyle =2n.2^{n+1}+2$

$\displaystyle =([n+1]-1)2^{[n+1]+1}+2$
$\displaystyle \Rightarrow P(n+1)$
b) $\displaystyle P(n)$ is the propositional function: $\displaystyle 4^n<n!$

Then $\displaystyle P(n)$
$\displaystyle \Rightarrow 4^{n+1}<4.n!$
$\displaystyle <(n+1).n!$ for $\displaystyle n>8$

$\displaystyle <(n+1)!$
$\displaystyle \Rightarrow P(n+1)$
c) $\displaystyle P(n)$ is the propositional function:$\displaystyle n^2-10n+8 > 0$

Now $\displaystyle (n+1)^2 -10(n+1) +8=n^2 -8n -1$
$\displaystyle =n^2-10n+8 +2n -9$
$\displaystyle > n^2-10n+8$ since $\displaystyle 2n-9>0$ when $\displaystyle n \ge 10$
Hence $\displaystyle P(n) \Rightarrow (n+1)^2 -10(n+1) +8>0$
$\displaystyle \Rightarrow P(n+1)$
d) I'll leave this to you. It's rather similar to (c).

Expand and simplify $\displaystyle (n+1)^3 + 2(n+1)$. Then express the resulting expression in the form $\displaystyle n^3 + 2n + f(n)$, and you'll find that $\displaystyle f(n)$ is divisible by $\displaystyle 3$.

Can you fill in all the gaps?


text:
# Simplify _Elementary Calculus_ section 1.6 problem 33

Once again, I'm trying to simplify an expression from Elementary Calculus with hyperreals. Given that $H$ is infinite, compute the standard part of:

$$\frac{\sqrt{H+1}}{\sqrt{2H}+\sqrt{H-1}}$$

The answer in the back of the book is $\frac{1}{1+\sqrt{2}}$ or $\sqrt{2}-1$, which is consistent with what my calculator gives me if I compute: $$\lim_{x\to\infty} \left(\frac{\sqrt{x+1}}{\sqrt{2x}+\sqrt{x-1}}\right)$$

I see two ways to proceed: multiply the top and bottom by $\sqrt{H+1}$ to eliminate the radical in the numerator or multiply by the conjugate $\sqrt{2H}-\sqrt{H-1}$ but neither one seems to improve the situation.

Idea 1 (multiply by numerator):

$$\frac{\sqrt{H+1}\sqrt{H+1}}{\sqrt{H+1}(\sqrt{2H}+\sqrt{H-1})}$$ $$=\frac{H+1}{\sqrt{H+1}(\sqrt{2H}+\sqrt{H-1})}$$ $$=\frac{H+1}{\sqrt{H+1}\sqrt{2H}+\sqrt{H+1}{\sqrt{H-1}}}$$

Idea 2 (multiply by conjugate of denominator):

$$\frac{\sqrt{H+1}(\sqrt{2H}-\sqrt{H-1})}{(\sqrt{2H}+\sqrt{H+1})(\sqrt{2H}-\sqrt{H+1})}$$ $$=\frac{\sqrt{H+1}(\sqrt{2H}-\sqrt{H-1})}{2H-(H+1)}$$ $$=\frac{\sqrt{H+1}(\sqrt{2H}-\sqrt{H-1})}{H-1}$$

I don't think either of these are on the right path, but I don't know any other possibilities. Eventually, I suspect I will be multiplying the numerator and denominator by $\frac{1}{H}$ to convert some of these infinities to infinitesimals but I don't see a way to reduce it further (if these could be called reductions) before taking standard parts, and for some reason I feel like the algebraic manipulations should be complete before the standard part/hyperreal logic is used to eliminate infinitesimals.

-

Divide top and bottom by $\sqrt{H}$. That does not change the value of the expression.

On top we get $\sqrt{1+\epsilon}$, where $\epsilon=1/H$.

On the bottom, we get $\sqrt{2}+\sqrt{1-\epsilon}$. If $H$ is infinitely large, then $\epsilon$ is infinitesimal. (Note that $H$ cannot be infinitely large negative, since if it were then our square roots would not be defined.)

Now finding the standard part is easy. The answer is $\dfrac{1}{\sqrt{2}+1}$. If you prefer, you can write this as $\sqrt{2}-1$.

Remark: The same idea is useful in many other cases. For example, if we are interested in the behaviour of $$\frac{3x^3+100x^2+700}{7x^3-77x^2+x}$$ when $x$ has large absolute value, divide top and bottom by $x^3$.

-
$N$? You mean $H$? –  rotten Feb 2 '12 at 6:05
@rotten: Yes, I mean $H$. The name $N$ sounded like a good one for an infinitely big number, I didn't notice it was called $H$ in the post. Fixed. –  André Nicolas Feb 2 '12 at 6:09
Yeah, what gives? $H$ always goes to zero and $N$ always goes to infinity ;) –  rotten Feb 2 '12 at 6:23
@rotten: Not quite, it is $h$ (little aitch) that often goes to $0$. –  André Nicolas Feb 2 '12 at 6:31
Thanks again for your help! I am wondering though, is there a way to algebraically convert $\frac{1}{\sqrt{2}+1}$ into $\sqrt{2}-1$? –  Daniel Lyons Feb 2 '12 at 20:28


text:
# Non-Abelian statistics in one dimension: Topological momentum spacings and SU(2) level- k fusion rules

@article{Greiter2019NonAbelianSI,
title={Non-Abelian statistics in one dimension: Topological momentum spacings and SU(2) level-
k
fusion rules},
author={Martin Greiter and F. D. M. Haldane and Ronny Thomale},
journal={Physical Review B},
year={2019}
}
• Published 23 May 2019
• Mathematics
• Physical Review B
We use a family of critical spin chain models discovered recently by one of us [M. Greiter, Mapping of Parent Hamiltonians, Springer, Berlin/Heidelberg 2011] to propose and elaborate that non-Abelian, SU(2) level $k=2S$ anyon statistics manifests itself in one dimension through topological selection rules for fractional shifts in the spacings of linear momenta, which yield an internal Hilbert space of, in the thermodynamic limit degenerate states. These shifts constitute the equivalent to the…
6 Citations

## Figures from this paper

• Physics
• 2022
The quantum-mechanical description of assemblies of particles whose motion is conﬁned to two (or one) spatial dimensions offers many possibilities that are distinct from bosons and fermions. We call
• Physics
Journal of Statistical Mechanics: Theory and Experiment
• 2020
We construct a family of 1D and 2D long-range SU(2) spin models as parent Hamiltonians associated with infinite dimensional matrix product states that arise from simple current correlation functions
• Physics
Physical Review B
• 2020
The Haldane-Shastry model is one of the most studied interacting spin systems. The Yangian symmetry makes it exactly solvable, and the model has semionic excitations. We introduce disorder into the
• Physics
Quantum Information Processing
• 2019
The results can be justified with the current experimental capability and may be extended to an array of weakly coupled trapped-ion pairs for demonstrating the non-Abelian statistics of the quasiparticles and for encoding the topological qubits.
• Physics
• 2022
An external drive can improve the coherence of a quantum many-body system by averaging out noise sources. It can also be used to realize models that are inaccessible in the static limit, through

## References

SHOWING 1-10 OF 83 REFERENCES

• Physics
• 2016
We analyze the properties of a non-Abelian spin-1 chiral spin liquid state proposed by Greiter and Thomale [PRL 102, 207203 (2009)] using variational Monte Carlo. In this state the bosonic $\nu = 1$
• Physics
• 2011
We propose to use null vectors in conformal field theories to derive model Hamiltonians of quantum spin chains and the corresponding ground state wavefunction(s). The approach is quite general, and
• Physics, Mathematics
• 2008
We analyze the non-Abelian Read–Rezayi quantum Hall states on the torus, where it is natural to employ a mapping of the many-body problem onto a one-dimensional lattice model. On the thin torus—the
Anyons and fractional statistics are by now well established in two-dimensional systems. In one dimension, fractional statistics has been established so far only through Haldane's fractional
• Physics
• 2004
Some models describing unconventional fractional quantum Hall states predict quasiparticles that obey non-Abelian quantum statistics. The most prominent example is the Moore-Read model for the
• Physics
• 2000
We analyze pairing of fermions in two dimensions for fully gapped cases with broken parity (P) and time reversal (T), especially cases in which the gap function is an orbital angular momentum (l)
• Physics
• 1999
The Pfaffian quantum Hall states, which can be viewed as involving pairing either of spin-polarized electrons or of composite fermions, are generalized by finding the exact ground states of certain


text:
# Getting Post details when post is published

I would like to collect main info about post like Title etc. in moment when post was written and it’s going to be published and perform some actions on this data. What’s the hook for that?

Thanks!

#### Solutions Collecting From Web of "Getting Post details when post is published"

The function is wp_insert_post(), and as you can see there are some hooks you can use to modify data. wp_insert_post_data is a filter that gets all data right before it will be inserted into the database, so you modify it there and don’t need to do anything to get it saved. At the end of the function you can see the save_post action and its equivalent wp_insert_post, which are more appropriate if you want to do something (instead of change something).

These functions are fired when a post is saved, not only when it is published. For the publish action, look at wp_transition_post_status(), which has three hooks:

• transition_post_status, called with the new and old statuses, and the post data
• {$old_status}_to_{$new_status}, like draft_to_publish, called with the post data
• {$new_status}_{$post->post_type}, like publish_page, called with the post ID and post data

Also check here: WordPress prompt checklist before publish? “WordPress prompt checklist before publish?”


text:
# Non-orientable hyperbolic surface?

Define a hyperbolic surface $H$ as a metric space locally isometric to the Poincaré upper half-plane $\mathbb{H}^2$ with the appropriate metric. Note that the quotient $\mathbb{H}^2/\Gamma$ is a hyperbolic surface, where $\Gamma$ is a Fuchsian group acting properly discontinuously without fixed point on $\mathbb{H}^2$.

Every closed, connected Riemann surface $S$ of genus greater than $2$ admits the structure of a hyperbolic surface : this is a (fairly) direct consequence of uniformization. Indeed the universal cover $\tilde{S}$ is $\mathbb{H}^2$, and $Aut(\mathbb{H}^2)=PSL(2,\mathbb{R})$, so $S=\tilde{S}/\Gamma$ where $\Gamma$ is Fuchsian, and we conclude by the previous remark.

We have the following result:

Theorem : Let $H$ be a closed, connected, oriented hyperbolic surface of genus $\geq 2$. Then $S$ is isometric to $\mathbb{H}^2/\Gamma$ for some Fuchsian $\Gamma$. In particular, such hyperbolic surface carries the structure of a Riemann surface.

In the proof we do use the fact that $H$ is oriented to show that transition maps are holomorphic. However the following question arises : what are some interesting examples of non-orientable hyperbolic surfaces ? How much work is needed to find such a surface ? I cannot think of one just yet. Moreover, if every closed hyperbolic surface can be obtained by gluing pairs of pants, how do we even find one ? Where does the construction degenerate ?

Embed a surface $S$ of odd genus like in the picture: so that it is centered and symmetric with respect to the origin (in the obvious sense) Then the antipodal map $\sigma$ is a smooth self-diffeomorphism of order two which reverses the orientation of the surface. The quotient $S/\sigma$ is a non-orientable surface. If we put on $S$ a hyperbolic metric, then one can arrange to have $\sigma$ be an isometry, and then $S/\sigma$ inherits a hyperbolic metric.


text:
Calendar

Yesterday

Basic Notions Seminar, Jun Choi, Purdue University, REC 303

Thursday, Apr 19 10:30 am - 11:30 am

Hyperbolic polygons

Abstract: In this talk, I will talk about trigonometry of hyperbolic polygons and formulas for computing areas such as a law of sines. I will use these to get information about tiling of hyperbolic plane which gives arise to Fenchel-Nielsen coordinates for the moduli space for Riemann surfaces. No prior knowledge in Riemannian geometry will be assumed. Refreshments will be served as usual.

Mathematical Physics Seminar, Lara Anderson, Virginia Tech, REC 317

Thursday, Apr 19 1:30 pm - 2:20 pm

Calabi-Yau fibrations in string theory

I will describe recent efforts to systematically study fibrations within Calabi-Yau threefolds and their consequences for string compactifications. This includes a recent enumeration of all genus one fibrations in class of 7890 Calabi-Yau manifiolds defined as complete intersections in products of projective spaces (so-called CICY threefolds). This survey is a complete classification that depends only on topology and improves upon past approaches that probed only a particular algebraic form of the manifold. I will also describe K3-fibrations and so-called “nested" fibration structures (for example, K3 fibrations in which the generic fiber can in turn can be elliptically fibered in many distinct ways).

Automorphic Forms and Representation Theory Seminar, Dr. Cris Negron, MIT, UNIV 317

Thursday, Apr 19 1:30 pm - 2:20 pm

Cohomology for Drinfeld doubles of finite group scheme

Abstract: In the mid 2000's Etingof and Ostrik conjectured that the cohomology $H^\ast(A,\mathbb{F})$ of any finite dimensional Hopf algebra $A$ over an arbitrary field $\mathbb{F}$ is itself a finitely generated algebra, under the standard (Yoneda) product. This conjecture was motivated, in part, by fantastic work of Friedlander and Suslin from the 90's, in which they showed that any finite group scheme in characteristic $p$ has finitely generated cohomology. I will discuss joint work with E. Friedlander, where we return to the finite characteristic setting to provide a strong analysis of cohomology for so-called Drinfeld doubles of finite group schemes. I will discuss the central role such doubles play in the more general theory of finite tensor categories, and explain how the cohomology of such doubles can be understood via “classical" data.

Next Week

Gayane Poghotanyan - Thesis Defense

Monday, Apr 23 11:30 am - 1:00 pm

Title: The Effective Reproduction Number for a Class of Mixing Matrices in Meta-Population Models in Epidemiology

Automorphic Forms and Representation Theory Seminar, Prof. Helene Esnault, Freie Universität Berlin, REC 308

Monday, Apr 23 3:00 pm - 4:00 pm

Title of Talk: Companions

Abstract: We give some background on companions (a notion due to Deligne) for l-adic sheaves, and if time permits, for F-overconvergent isocrystals as well. (On the latter: joint work with Tomoyuki Abe)

Student Commutative Algebra Seminar, Mr. Cheng Meng, Purdue University, REC 313

Monday, Apr 23 3:30 pm - 4:30 pm

Monomial Resolutions

CCAM Seminar, Dr. Andrew Hill, Centers for Disease Control and Prevention, REC 308

Monday, Apr 23 4:30 pm - 5:30 pm

Striving for Realism in Mathematical Models of Infectious Disease: Two Cautionary Tales

The appropriate development of a mathematical model of infectious disease transmission begins with understanding the problem that is being represented. Thus, building a good model for use in public health policy and decision making generally requires consultation with subject matter experts. Examples of relevant factors that may be crucial to capture are demographic trends, contact patterns describing how individuals mix with each other, and underlying epidemiologic processes specific to the disease in question. In this talk, I look at two separate examples to illustrate what can go wrong if realistic assumptions are ignored. The first considers heterogeneity in mixing among sub-populations and demonstrates that this should be considered when evaluating public health interventions to prevent or control infectious disease outbreaks. Neglecting to do so can lead to under-estimation of reproduction numbers and control efforts. The second looks at the published modeling literature for tuberculosis and examines how progression from latent infection to disease has been modeled, and how closely different approaches taken agree with empirical evidence from epidemiologic and clinical studies. Given the long latency periods of tuberculosis infection, models which fail to replicate progression dynamics and latent period distributions may produce unreliable projections and run the risk of misinforming future policy.

Operator Algebras Seminar, Kyle Austin, Ben Gurion, REC 315

Tuesday, Apr 24 2:30 pm - 3:30 pm

A Functorial Approach to Groupoid Modeling of C*-algebras

Abstract: In joint works with Magdalena Georgescu and Atish Mitra, we have devised a way to do categorical modeling of c*-algebras using groupoids. Specifically, we have found morphisms of groupoids with Haar systems of measures that induce morphisms of maximal groupoid c*-algebras; moreover, our association of groupoid to maximal groupoid c*-algebra and our morphisms of groupoids to their induced morphisms is functorial and generalizes the Gelfand duality functor for spaces. We use this to construct explicit examples of lots of c*-algebras including the Jiang-Su and Razak Jacelon algebras. If there is time, I will also talk about our current project on finding an inverse functor from certain pairs of c*-algebras to groupoids.

Department Colloquium, Prof. Helene Esnault, Freie Universitat Berlin, MATH 175

Tuesday, Apr 24 3:30 pm - 4:20 pm

Rigidity and integrality

Abstract: We explain the general p-curvature conjecture, Simpson's geometricity conjecture and his integrality conjecture for irreducible rigid connections with finite determinant and quasi-unipotent monodromies at infinity. We give a sense of what is behind the proof of the integrality on cohomologically rigid connections. (Joint work with Michael Groechenig)

Algebraic Geometry Seminar, Prof. Helene Esnault, Freie Universität Berlin, MATH 731

Wednesday, Apr 25 3:25 pm - 4:25 pm

Rigidity and F-isocrystals.

Abstract: We explain that rigid connections yields F-overconvergent isocrystals (in the projective case) and discuss a few points concerning the p-curvature conjecture. (Joint work with Michael Groechenig)

Mathematical Physics Seminar, Rinat Kedem, U. of Illinois, Urbana-Champaign, REC 317

Thursday, Apr 26 1:30 pm - 2:20 pm

Q-systems: Discrete integrability and cluster algebras

I’ll introduce a family of remarkable recursion relations, originally found in the context of the Bethe ansatz of generalized Heisenberg modules and quantum groups. I will reconsider this system as a discrete integrable system in its own right, and show some of the remarkable properties it and its quantization, via a cluster algebra formulation, exhibit. This will be a basic talk with no prior knowledge of any of the above mentioned topics assumed, with the purpose of introducing some of these structures and showing why they might be useful in mathematical physics.

Automorphic Forms and Representation Theory Seminar, Dr. Fan Gao (Purdue University), UNIV 317

Thursday, Apr 26 1:30 pm - 2:20 pm

A glimpse of the history and some problems in the Langlands program for covering  groups

Abstract: The long-lasting significance of the Langlands program for linear reductive groups and its deep connection with number theory, arithmetic of variety etc are well-known. On the other hand, for finite-degree central coverings of a linear reductive group, the analogous framework has not been fully established despite many important works for special families of coverings, e.g,. the classical double cover of the symplectic group. In this expository talk, we will give a brief overview of the analogous Langlands program for covering groups. We highlight several concrete questions which pertain to a Langlands-Shahidi theory (yet to be developed) for covering groups.

Spring Math Awards, Lawson Commons

Thursday, Apr 26 3:30 pm - 4:30 pm

Two Weeks

Automorphic Forms and Representation Theory Seminar, Prof. John Bergdall, Michigan State University, UNIV 317

Thursday, May 3 1:30 pm - 2:20 pm

TBA

Andrew Ursitti - Defense

Friday, May 4 10:00 am - 12:00 pm

Sublaplacians on Real Flag Manifolds


text:
# Implementing a Sort for an Array

Yesterday, I gave an interview after a long time, and I was asked a question which I couldn't solve on the spot.

I had to implement a sort function for a Array of strings in JavaScript, with the following requirements:

• The Array will always contain Strings
• For sorting, Upper Case has higher priority than Lowe Case Letters, with Numbers having the Least.
• Assume that Array.sort() cannot be used
• The performance of the sorting is not a factor; i.e. Bubble sort is fine.

I was thinking of the solution today, and came up with this:

function sortArray(items) {
let itemcount = items.length;
for (var i = 0; i < itemcount; i++) { //number of passes
for (var j = 0; j < (itemcount - 1 - i); j++) { //for checking all pairs in a given pass
let a = items[j];
let b = items[j + 1];
if (compareCaseSenitiveStrings(a, b) < 0) {
console.log("Switch", a, b)
items[j + 1] = a;
items[j] = b;
}
}
}
//return
return items;
}

//Function to compare two given strings, and return the index of the higher priority one
function compareCaseSenitiveStrings(a, b) {

//Inner functions
function compareCharacters(a, b) {
//check the case first()
if (a.getFirstCase() == b.getFirstCase()) {
let charDiff = a.codePointAt(0) - b.codePointAt(0);
return -Math.sign(charDiff)
} else {
//different cases
//We need to pass the id of the one which is higher;
let requiredCaseOrder = ["NONE", "LOWER", "UPPER"];
return requiredCaseOrder.indexOf(a.getFirstCase()) - requiredCaseOrder.indexOf(b.getFirstCase());
}
}

function isNumeric(n) {
return !isNaN(parseFloat(n)) && isFinite(n);
}
//End of inner functions
//===============================================

//Start of function here

//First check if both are numbers
if (isNumeric(a) && isNumeric(b)) {
//return the index of smaller number (since it has higher priority)
return -Math.sign((parseFloat(a) - parseFloat(b)));
}

//Now check that lengths of both is greater than 0
if ((a.length > 0) && (b.length > 0)) {
//check the first elements of this string
let result = compareCharacters(a[0], b[0]);
if (result != 0) {
//this means one input has higher priority, lets return that
return result;
} else {
//both are equal
//get the result of remaining characters
return compareCaseSenitiveStrings(a.substring(1), b.substring(1));
}
} else {
//length of atleast one of these strings is zero.
//return the index of the longer element
let lengthDiff = a.length - b.length;
return Math.sign(lengthDiff);
}
}

String.prototype.getFirstCase = function() {
let caseEnum = ["LOWER", "NONE", "UPPER"];
var caseIndex = 1;
if (this == this.toLowerCase()) {
caseIndex--;
}
if (this == this.toUpperCase()) {
caseIndex++;
}
return caseEnum[caseIndex];
};

Is this code readable enough? Are there any other Design Patterns that could be applied? Any other points which could be improved?

• Lose the redundant comments – psaxton Jul 12 '16 at 22:02

Sorting is hard.

• console.log( sortArray([ '123', '9' , '1' , '11' ]) ); returns ["1", "9", "11", "123"], that does not sound good. After removing the numeric test I get ["11", "123", "1", "9"] which is better but not intuitive, I would have expected the 1 up front. This shows that you cannot just write the code, you need to build a set of tests to validate your code. Especially during interviews.

• String.prototype.getFirstCase is very cute, but it needs commenting for lesser readers.

• You are mixing var and let, I am not too excited about that

• If you remove the numeric test, then you no longer need isNumeric as well

• compareCaseSenitiveStrings should be compareCaseSensitiveStrings

• I would convert 2 line comments to 1 line comment for readability, and an overall review of what comments really add value

• Other than the code was very readable

• Thanks for your comments. Maybe I wasn't clear in the requirements, but the requirement, as I understood, was that pure numbers should be arranged in increasing order of their value; But I can see that something like '221B Baker' will be arranged with the least priority. – Devdatta Tengshe Jul 13 '16 at 3:37
function sortArray(items) {
let itemcount = items.length;
switches = 1 // dummy variable to enter the while loop
while (switches) { // while there were switches made in the previous iteration
switches = 0;

// this while loop will stop when there are no switches, i.e. the array has already been sorted
for (var j = 0; j < (itemcount - 1); j++) { //for checking all pairs in a given pass
let a = items[j];
let b = items[j + 1];
if (compareCaseSenitiveStrings(a, b) < 0) {
console.log("Switch", a, b); // semi-colon added
items[j + 1] = a;
items[j] = b;
switches += 1;
}
}
}
//return
return items;
}

(In the future, use !== to compare to 0). Personally, I would change the sorting algorithm as above, because I think this method would require fewer iterations, although I haven't timed it.

• I can't figure out two things in this code: 1) when does switches become zero? I can only see us incrementing it 2) What does i in line 6 represent? – Devdatta Tengshe Jul 13 '16 at 3:42
• Sorry - both errors have been corrected – codecademic800 Jul 13 '16 at 7:10


text:
## Chapter 3 - Day 5 - Lesson 3.4

##### Learning Targets
• Use simulation to approximate the margin of error for a sample proportion and interpret the margin of error.

• Use simulation to approximate the margin of error for a sample mean and interpret the margin of error.

##### Activity:

Students are expected to do the first page of this Activity in pairs.  The second page is done as a whole group.  On the first page, we are trying to get students to see the reason why we multiply the standard deviation by 2 in order to get the margin of error.  The reason is because a majority or our estimates will be within 2 standard deviations away from the mean  (should be around 95%).  Since our students have already seen the normal distribution and the 68-95-99 rule in their Algebra 2 class, we can also make this connection.

Mean – 2 * S.D. = 5.019 – 2 * 0.262 = 4.495

Mean + 2 * S.D. = 5.019 + 2 * 0.262 = 5.543

29 out of the 30 (97%) of the estimates are between 4.495 and 5.543 hours of TV.

On page two of the activity, we show students this calculation (which is really a 95% confidence interval…a preview of what’s to come!).  We felt that we needed the idea of a confidence interval in order to discuss the margin or error.  We worked as a whole group to take the students through the second example concerning the proportion of students who text during class.

##### Application 3.4

As an exit slip, students worked individually on the application.  The Application allows students a chance to try to write an interpretation of a margin of error on their own.  It also gives them their first chance to assess whether a claim is plausible (is the claimed value within the confidence interval?).  We like that students are already practicing inferential thinking before we have formally reached statistical inference.

##### Notes

We were very specific with how we wanted students to interpret the margin or error: “we expect the true proportion/mean (context) to be at most _______ away from our estimate of _________.”


text:
Register FAQ Calendar Mark Forums Read

 Global Atheist Convention Forum All discussions regarding the AFA's Global Atheist Conventions

#21
24th July 2011, 06:59 PM
 Podblack AFA Member Join Date: Jan 2009 Location: Perth Posts: 1,220
Re: GAC2012 Accommodation Discussion

#22
25th July 2011, 07:09 PM
 Onlyatheory? You can't be serious!!? Join Date: Apr 2010 Location: Everywhere that I am. Posts: 1,346
Re: GAC2012 Accommodation Discussion

Woohoo!! All booked at the grand mercure. My significant, grainy other suggests that packing is a little premature.
I am hoping to meet as many AFAers as possible. May even give Annie and 2Dogs a run for their money in the 'How many forumites have you met' stakes
__________________
Growing up means watching my heroes turn human in front of me.
#23
28th July 2011, 01:04 PM
 Linda Harris Junior Member Join Date: Jun 2011 Location: Perth Posts: 3
Re: GAC2012 Accommodation Discussion

I am looking to share accommodation at next years GAC in a hotel near the convention. If anyone is interested please email me.
#24
30th July 2011, 09:45 AM
 Praxis Here come the drums, here come the drums! Join Date: Jun 2009 Location: Melbourne Posts: 7,327

MOD NOTE:

I've just realised that this thread has taken somewhat of a derail into general chit chat so I am going to move some chit-chat stuff into the general discussion thread about the GAC, which is the Now It's Official thread.

We need to leave this thread for speciifc discussion about accommodation, such as Linda Harris's post (now shown above), which will otherwise get lost.

I'm just going to do this rather than tiptoe around the niceties of "I hope you don't mind if I..." because all of those involved (including me!) are grown-up enough to cop it sweet

Please continue the discussion re chocolate, the Annie/Two Dogs Race To Meet Every Forum Member, etc. in to the general thread.

Thanks everyone!

/END MOD NOTE
__________________
I've never been very good at knowing "my place". Well actually I have, it's just never been where you want it to be.
#25
18th August 2011, 12:25 PM
 OzAtheist AFA Member Join Date: Jan 2009 Location: Newcastle, NSW Posts: 254

Is the AFA going to organise cheap deals at some of the hotels like last time?
__________________
I think, therefore I'm not a sheep
#26
18th August 2011, 01:58 PM
 davo SIR Vacuous cunt Administrator Join Date: Jan 2009 Location: 3rd Planet from the Sun Posts: 8,767

Quote:
 OzAtheist said Is the AFA going to organise cheap deals at some of the hotels like last time?
Yes this information was up, then we had a server crash. I have been flat out with a myriad of stuff but will collate it all again asap.
__________________
Spearthrower: "There are words like vacuous & cunt that are applicable."

(delta p)*(delta q) >= h/(4*pi) ----- An explanation of Logical Fallacies : http://www.nizkor.org/features/fallacies ----- ferox deo vacuus vinco ----- How do I post video etc here?
#27
18th August 2011, 03:20 PM
 OzAtheist AFA Member Join Date: Jan 2009 Location: Newcastle, NSW Posts: 254

Quote:
 davo said Yes this information was up, then we had a server crash. I have been flat out with a myriad of stuff but will collate it all again asap.
You are a (over-worked) marvel Davo. Thanks, will postpone booking till then
__________________
I think, therefore I'm not a sheep
#28
18th August 2011, 06:44 PM
 Imperfectpeta Member Join Date: Aug 2011 Location: Ipswich, Australia Posts: 69

If people are very hard up on cash (as I am now!) I suggest looking through the options on www.hostelworld.com. Awsome site and you can look at hostels from location, quite a few around the area.

Prices range form $20 a night for a dorm to up to$100 a night for privates.
Stayed in plenty of places like this while travelling Japan and they are awsome, and for the broke among us, the place to be!
__________________
I've learned that evolution is not just a theory, religion is not the path to truth, and that there probably isn't a God.
Amazing what being able to research the internets can do to your personal world view, eh?
#29
18th August 2011, 07:03 PM
 Quark Junior Member Join Date: Aug 2011 Location: West of Oz Posts: 29

Is Crown seriously fully booked out from the 13th to the 15th already?

Back to the drawing board.
#30
18th August 2011, 07:24 PM
 davo SIR Vacuous cunt Administrator Join Date: Jan 2009 Location: 3rd Planet from the Sun Posts: 8,767

Accommodation options and deals via the Accommodation page (under the FAQ menu as a drop down)

http://www.atheistconvention.org.au/accommodation/
__________________
Spearthrower: "There are words like vacuous & cunt that are applicable."

(delta p)*(delta q) >= h/(4*pi) ----- An explanation of Logical Fallacies : http://www.nizkor.org/features/fallacies ----- ferox deo vacuus vinco ----- How do I post video etc here?

 Bookmarks


text:
## Friday, February 10, 2006 ... //

### Hijacked faculty meetings

Incidentally, later I learned that The Crimson has used the very same word "hijacked" independently of your humble correspondent.

I had neither time nor the desire to attend the FAS faculty meeting that took place on Tuesday. Indeed, the meeting has become an opportunity for various anti-president elements to ventilate their strange emotions and strange opinions and to give Summers a hard time. If one wants to get a bit frustrated, it is enough to read the report in The Crimson. The article says, among other things:

• Capturing the sentiment of most professors who spoke at the meeting, English Department Chair James Engell appealed to Summers and Harvard’s governing bodies to recognize that the president has left the Faculty “divided, demoralized, and dispirited.”
Well, as far as I remember, it was not the president but rather various whining PC militias who have divided, demoralized, and dispirited the faculty. Some of them initiated highly controversial votes that had to end up something like 50:50; is there a better way to divide the faculty? Others - and sometimes the very same people - have threatened their colleagues for their insufficiently "politically correct" opinions which demoralized and dispirited many of their colleagues. And they have also transformed faculty meetings from rather efficient constructive (albeit arguably boring) meetings to an arena for spreading hatred and content-free criticism.

Nevertheless, I have personally been psychologically immune against these matters since July when I decided that one should not attempt to harmonize his opinions about these issues with the "politically correct majority" because they are just too far from something that could be considered as an acceptable starting point for a compromise. Also, one should never try to surrender or apologize to these people because the only conceivable result of such an approach is to strengthen their position. And the goal of many of them is nothing less than to push the whole society infinitely far in a rather weird direction. As far as I can say, the debates at the faculty meetings have been more or less hijacked by people whom I don't trust - and it is counter-productive to go into battles that are lost from the very beginning. Most well-known supporters of Summers skipped the last meeting and it is obviously good for their health.

Last night, we had a nice dinner at the Faculty Club and I was sitting next to a well-known senior biochemist who also supports Summers.

One of the new plans of the revolutionary committees is a "radical dean search plan". What does it mean? It means that in the "ideal" case they want to choose the new FAS dean themselves, with Summers having no influence whatsoever. They think about several alternatives how the new dean should be found - and neither of these alternatives is the correct one, namely that the dean should be chosen by the president. In other words, dozens of self-appointed "leaders of the people" - many of whom have little demonstrable experience and/or management skills - want to exclusively control some of the most important political decisions at this university. What do they exactly think about their qualification? Do they really think that they are better managers than Summers or that they have a better vision? Who is exactly encouraging them to think in this nonsensical way? Have they been the secretaries of treasury or the chief economists of the World Bank? And what do they think about their job description?

Unfortunately, many people indeed prefer puppets over of thinkers-in-chief, form over content, anarchy over leadership, political correctness over the truth, vacuous clichés over rational debates, and it's probably better not to think about these issues too much and avoid similar unconstructive meetings.

Prof. Andrei Shleifer

There is another line of attack against the president whose logic is completely beyond my understanding. The other "crime" that Summers apparently "committed" was that he is a personal friend with Andrei Shleifer. See a description of the affair here. Andrei Shleifer is a star economist at Harvard who was also active during privatization in Russia. He is an expert in price dynamics, market inefficiencies, corporate control, and transition to capitalism, among other things. No doubt, the emerging capitalism in the former Soviet bloc needed gifted economists, managers, experience, and capital from the West.

As far as I understand, Shleifer was caught into some of these weird regulations about the conflict-of-interest: the type of rules that if your wife drinks Danish beer, you must be very careful whether your business partners in Russia had Danish grandmothers. His problem was settled as he paid \$2 million dollars of compensations, to the full satisfaction of the courts. As far as I can see right now, Shleifer himself has been cleaned. Even an attack against Shleifer himself would probably lack any legal substance these days. How can Shleifer's situation be used as a weapon of mass destruction against Summers whose "sin" is to be a friend and have a respect for another star economist is simply beyond my comprehension. It reminds me of the plans to exterminate Denmark because a few Danish cartoonists drew a cartoon.

Confidence

Unfortunately, the president will face another lack-of-confidence vote. The person who proposed the motion is from comparative literature. Indeed, if you compare her literature and the literature from last spring, she only added the word "continues" to the previous lack-of-confidence resolution. This precious contribution of her to the humankind is a sufficient recipe for another blockbuster.

Finally, I must mention that what I wrote here is not terribly controversial in the physics department. Consider Melissa Franklin, the first tenured female physicist here and consequently one of the heroes of feminism. While she denies the crucial reponsibility of feminism for the current furore and she wants to emphasize that the issues have gone well beyond the feminist interests, she seems to agree completely that the situation is mess, and a hypothetical dismissal of Lawrence Summers would probably cause a rather devastating hit for the whole Harvard University. Needless to say, we would probably agree on a whole ensemble of other issues, too.


text:
# Diffusion capacity

Diffusion capacity
Diffusion capacity
Diagnostics
MeSH D011653

In biology, diffusion capacity is a measurement of the lung's ability to transfer gases. Oxygen uptake may be limited by diffusion in circumstances of low ambient oxygen or high pulmonary blood flow. Carbon dioxide is not limited by diffusion under most circumstances.

The "diffusing capacity" or "diffusion capacity" is part of a comprehensive test series of lung function called pulmonary function testing. In Europe, this is often called the "transfer factor". Critics of the term "diffusion capacity" argue that it may be misleading, and point out two problems with the term. The first is that the test measures not just diffusion across the alveolar-capillary membrane, but also takes into account factors affecting the chemical combination of a given gas with hemoglobin. The second criticism is that the test is typically measured under submaximal conditions and doesn't truly reflect a functional capacity. For these reasons the term "transfer factor" better reflects the physiological process being measured.

## Calculation

The rate of flow is directly proportional to the oxygen gradient (per Fick's law of diffusion), and the diffusion capacity (DLOO2) can be calculated as the ratio of oxygen flux (J^*) across the alveolar-capillary membrane over the oxygen partial pressure gradient between the alveoli ("A") and the alveolar capillaries ("a")

$D_L = \frac {J^*_{O2}}{P_{AO2} - P_{aO2}}$

(The asterisk should be read as a dot over the letter, which is used to denote rate in respiratory physiology.)

J*O2 is the uptake of oxygen (ml/min). PAO2 is the alveolar partial pressure of oxygen. PaO2 is the partial pressure of oxygen in the alveolar capillary. Thus, the higher the diffusing capacity DL, the more gas will be transferred across the alveolar-capillary membrane for a given gradient in partial pressure (or concentration) of the gas.

Because it is difficult to measure the capillary partial pressure of oxygen, carbon monoxide (CO) is used as the test gas to measure the diffusing capacity (Dlco). Because CO is so tightly bound to hemoglobin in the red blood cells, the partial pressure of CO in the capillaries is assumed to be zero. Thus,

$D_LCO = \frac {J^*_{CO}}{P_{ACO}}$

## Test Performance

In practice, the test is performed by having the test subject blow out all of the air that they can to reach residual volume. The person then takes a full vital capacity inhalation of a test gas mixture that contains a small amount of carbon monoxide (usually 0.3%) and some helium or other non-absorbed tracer gas. The test gas is held in the lung for about 10 seconds and then is exhaled from the lung. The first part of the expired gas is discarded and the next portion which represents gas from the alveoli is collected. By analyzing the concentrations of carbon monoxide and helium in the inspired gas and in the exhaled gas, it is possible to calculate how much carbon monoxide was taken up during the breath hold, and what the partial pressure of carbon monoxide was during the breath hold. This method is known as the single-breath diffusing capacity test.

Other methods that are not so widely used at present can measure the diffusing capacity. These include the steady state diffusing capacity that is performed during regular tidal breathing, or the rebreathing method that requires rebreathing from a reservoir of gas mixtures. A more sophisticated "three-equation method" which involves fast responding analysers for the carbon monoxide and a tracer gas such as helium has been developed. It monitors all parameters continuously and solves some of the technical problems of the traditional method but is more expensive to implement.

## Interpretation

Values between 75% and 125% of average diffusion capacity in the healthy population are considered normal.[1]

The diffusing capacity (DLCO) is a test of the integrity of the alveolar-capillary surface area for gas transfer. It may be reduced in disorders that damage the alveolar walls (septa) such as emphysema, which leads to a loss of effective surface area. The DLCO is also reduced in disorders that thicken or damage the alveolar walls such as pulmonary fibrosis. The DLCO is also reduced in interstitial lung diseases such as hypersensitivity pneumonitis (e.g. bird fancier's lung, farmer's lung) or dust-inhalation diseases such as asbestosis. Because the transfer of CO depends upon how much blood is present in the lung capillaries, the DLCO can be reduced due to anemia and raised in polycythemia. Some laboratories adjust or correct the DLCO for a serum hemoglobin to take into account the effect of anemia. Disorders of the pulmonary blood vessels such as chronic thromboembolic disease or pulmonary hypertension also reduce the diffusing capacity, as can any condition/disease which results in reduction in pulmonary capillary blood volume. The DLCO is not, however, a sensitive test for acute pulmonary embolism. Cigarette smokers tend to have lower DLCO, which is partly due to damage to the lungs (mild emphysema) and partly due to the retention of carbon monoxide from the cigarettes, which causes back pressure (decreasing the CO gradient). For these reasons, the DLCO is a sensitive test for disorders of the lung, but does not point toward a specific diagnosis. By calculating the dilution of the tracer gas, the test can also be used to estimate the total lung capacity. In the presence of poor gas mixing from obstructive lung disease it is used to measure the single breath total lung capacity.

## References

1. ^ LUNGFUNKTION - Practice compendium for semester 6. Department of Medical Sciences, Clinical Physiology, Academic Hospital, Uppsala, Sweden. Retrieved 2010.

Wikimedia Foundation. 2010.

### Look at other dictionaries:

• Capacity — is the ability to hold, receive or absorb, or a measure thereof, similar to the concept of volume.Capacity may also refer to: *Capacity (economics), the point of production at which a firm or industry s average (or per unit ) costs begin to rise …   Wikipedia

• Diffusion of technology in Canada — This article outlines the history of the diffusion or spread of technology in Canada. Technologies chosen for treatment here include, in rough order, transportation, communication, energy, materials, industry, public works, public services… …   Wikipedia

• diffusing capacity — diffusion capacity the ability of the alveolocapillary membrane to transfer gas: a reflection of the thinness and area of the alveolocapillary membrane. It is the amount of gas transferred per minute from the alveolar gas to the pulmonary… …   Medical dictionary

• Closing capacity — The closing capacity (CC) is the volume in the lungs at which its smallest airways, the alveoli collapse. The alveoli lack supporting cartilage and so depend on other factors to keep them open. The closing capacity is greater than the residual… …   Wikipedia

• Spirometry — TLC Total lung capacity: the volume in the lungs at maximal inflation RV Residual volume: the volume of air remaining in the lungs …   Wikipedia

• VO2 max — VO2 redirects here. For the chemical compound, see Vanadium(IV) oxide. VO2 max (also maximal oxygen consumption, maximal oxygen uptake, peak oxygen uptake or aerobic capacity) is the maximum capacity of an individual s body to transport and use… …   Wikipedia

• Oxygen–haemoglobin dissociation curve — The oxygen–haemoglobin dissociation curve (or oxygen–hemoglobin dissociation curve) plots the proportion of haemoglobin in its saturated form on the vertical axis against the prevailing oxygen tension on the horizontal axis. The oxyhaemoglobin… …   Wikipedia

• DLCO — (Diffusing capacity of the lung for carbon monoxide,[1]) is the extent to which oxygen passes from the air sacs of the lungs into the blood. Commonly, it refers to the test used to determine this parameter. It was introduced in 1909.[2] Contents… …   Wikipedia

• Respiratory system — See also: Respiratory tract Respiratory A complete, schematic view of the human respiratory system with their parts and functions. Latin …   Wikipedia

• Hypoxia (medical) — Hypoxia ICD 9 799.02 MeSH D000860 Hypoxia, or hypoxiation, is a pathological condition in which the body as a whole (generalized hypoxia) or a region of the body (tissue hypoxia) is deprived of adequate ox …   Wikipedia


text:
## Why I don’t use the term “fixed and random effects”

People are always asking me if I want to use a fixed or random effects model for this or that. I always reply that these terms have no agreed-upon definition. People with their own favorite definition of “fixed and random effects” don’t always realize that other definitions are out there. Worse, people conflate different definitions.

Five definitions

Here are the five definitions I’ve seen:

(1) Fixed effects are constant across individuals, and random effects vary. For example, in a growth study, a model with random intercepts a_i and fixed slope b corresponds to parallel lines for different individuals i, or the model y_it = a_i + b t. Kreft and De Leeuw (1998) thus distinguish between fixed and random coefficients.

(2) Effects are fixed if they are interesting in themselves or random if there is interest in the underlying population. Searle, Casella, and McCulloch (1992, Section 1.4) explore this distinction in depth.

(3) “When a sample exhausts the population, the corresponding variable is fixed; when the sample is a small (i.e., negligible) part of the population the corresponding variable is random.” (Green and Tukey, 1960)

(4) “If an effect is assumed to be a realized value of a random variable, it is called a random effect.” (LaMotte, 1983)

(5) Fixed effects are estimated using least squares (or, more generally, maximum likelihood) and random effects are estimated with shrinkage (“linear unbiased prediction” in the terminology of Robinson, 1991). This definition is standard in the multilevel modeling literature (see, for example, Snijders and Bosker, 1999, Section 4.2) and in econometrics.

The definitions are all different!

Of these definitions, the first clearly stands apart, but the other four definitions differ also. Under the second definition, an effect can change from fixed to random with a change in the goals of inference, even if the data and design are unchanged. The third definition differs from the others in defining a finite population (while leaving open the question of what to do with a large but not exhaustive sample), while the fourth definition makes no reference to an actual (rather than mathematical) population at all. The second definition allows fixed effects to come from a distribution, as long as that distribution is not of interest, whereas the fourth and fifth do not use any distribution for inference about fixed effects. The fifth definition has the virtue of mathematical precision but leaves unclear when a given set of effects should be considered fixed or random. In summary, it is easily possible for a factor to be “fixed” according to some of the definitions above and “random” for others.

Because of these conflicting definitions, it is no surprise that “clear answers to the question ‘fixed or random?’ are not necessarily the norm” (Searle, Casella, and McCulloch, 1992, p. 15).

In summary . . .

If you use a particular definition of fixed and random effects, don’t automatically assume that the other definitions apply also. For example, if an effect is interesting in itself (see definition 2), it is not necessary to estimate it using least squares (see definition 5).

(See also Kreft and De Leeuw, 1998, Section 1.3.3, for a discussion of the multiplicity of definitions of fixed and random effects and coefficients, and Robinson, 1998, for a historical overview.)

The paper

This is all taken from my paper, “Analysis of variance: why it is more important than ever” (with discussion), Annals of Statistics, 2005.

Or it may be more fun to start with my rejoinder to the discussion.

References

Kreft, I., and De Leeuw, J. (1998). {\em Introducing Multilevel Modeling}. London: Sage.

Searle, S. R., Casella, G., and McCulloch, C. E. (1992). {\em Variance Components}. New York: Wiley.

Green, B. F., and Tukey, J. W. (1960). Complex analyses of variance: general problems. {\em Psychometrika} {\bf 25} 127–152.

LaMotte, L. R. (1983). Fixed-, random-, and mixed-effects models. In {\em Encyclopedia of Statistical Sciences}, ed.\ S. Kotz, N. L. Johnson, and C. B. Read, {\bf 3}, 137–141.

Snijders, T. A. B., and Bosker, R. J. (1999). {\em Multilevel Analysis}. London: Sage.

Robinson, G. K. (1991). That BLUP is a good thing: the estimation
of random effects (with discussion). {\em Statistical Science} {\bf 6}, 15–51.

1. J. Levy says:

Do you have any idea which of the definitions is utilized by SAS(R) PROC MIXED?

2. Andrew says:

I'm almost sure SAS uses definition (5). Which is fine, as long as the user doesn't naively assume that definitions (2), (3), and (4) apply also. (For example, a bad thing (in my opinion) is to say "I'm interested in so-and-so [definition 2] and thus I'll include it as fixed effects in Sas [definition 5].")

3. Eric says:

Are any of these definitions consistent with the following definition:

1. An effect is fixed if the effect is correlated with the error term.

2. An effect is random if the effect is not correlated with the error term.

4. Andrew says:

Eric,

No.

Definition 1 distinguishes constant from varying coefficients. Constant coefficients are, by definition, not correlated with anything. varying coefficients can be correlated or not correlated, depending on the model.

Definition 2 is about whether coefficients are intersting in themselves. Coefficients can be individually interesting, or not interesting, whether or not their distribution is correlated with the error term.

Definition 3 is about whether the sample exhausts the population. This can occur, or not occur, with correlated or uncorrelated models.

And so forth.

5. Zhongyi says:

Perhaps Eric means:
1.An effect is fixed if it is correlated with the predictors

2.It is random if not correlated with the predictors.

I have seen such a definition in Econometric Analysis (William H.Greene).
But this definition seems to contradict Prof. Gelman's paper: Fitting Multilevel Models When Predictors and Group Effects Correlate, in which random effects are assumed to correlate with predictors.

6. D Seka says:

Predictor variables exhibit fixed effects. And the fixed effects (of the predictors) on the response variable(s) are the observations.

7. Joss says:


text:
# [OS X TeX] Page number appears with \pagestyle{empty}

Manuel libros at limay.de
Sun Feb 28 08:02:46 EST 2010

Am 28/02/2010 um 13:53 schrieb Themis Matsoukas:

> On Feb 28, 2010, at 5:10 AM, Manuel wrote:
>
>> bottom of the page, even with
>>
>> \thispagestye{empty}
>>
>> before or after \tableofcontents*. I didn't find any reference to
>> this in the mail archives or in other sources. Could somebody point
>> me in the right direction to solve this little problem?
>>
>
>
> The following works here;
>
> \documentclass[article,twoside,a4paper,12pt]{memoir}
>
> \begin{document}
> \tableofcontents*
> \thispagestyle{empty}
>
> \clearpage
>
> \chapter{Page numbers}
> text text text
>
> \end{document}
>
> Themis Matsoukas
>

Themis, what I'm trying to get is a document (a collection of ca.
5000 pdf-pages) completely without page numbers, with the toc at the
end (I'll use "pagecommand" later to numerate the pages).

Manuel


text:
# Linear algebra, reduced row echelon form

The code that I am sharing here for you to review today, is a segment of a JavaScript library that I am going to write as time goes by for fun. It is only the two functions in the following code:

/*jslint browser: true, indent: 8 */
/*global console */

/*
Sorts matrix like from something like this:
[
[0, 0, 0],
[0, 0, 0],
[0, 2, 1],
[0, 1, 3],
[1, 2, 3],
[0, 0, 3]
]
to this:
[
[1, 2, 3],
[0, 1, 3],
[0, 2, 1],
[0, 0, 0],
[0, 0, 0],
[0, 0, 3]
]

The reason why the [0, 0, 3] is last is because
the vector has the length of 3, so only
3 vectors are sorted and the rest (irrelevent vectors) are appended
later.
*/
function sort_reduced_matrix(matrix) {
'use strict';
var i, j, len, has_pivot, irrelevant, positions, new_matrix, count;

len       = {};
len.i     = matrix.length;    // matrix length (row)
len.j     = matrix[0].length; // vector length (column)
positions = [];

has_pivot = [];

// Find pivot positions
for (j = 0; j < len.j; j += 1) {
for (i = 0; i < len.i; i += 1) {
if (matrix[i][j] === 1 && has_pivot[i] !== i) {
has_pivot[i] = i;
positions[positions.length] = i;
break;
}
}
}

irrelevant = [];
count      = 0;

// Find irrelevant vectors positions
for (i = 0; i < len.i; i += 1) {
if (has_pivot[i] === undefined) {
irrelevant[count] = i;
count += 1;
}
}

new_matrix = [];
count      = 0;

// Sort positions
for (i = 0; i < len.i; i += 1) {
if (matrix[positions[i]] !== undefined) {
new_matrix[i] = matrix[positions[i]];
} else {
new_matrix[i] = matrix[irrelevant[count]];
count += 1;
}
}

return new_matrix;
}

function reduced_row_echolon_form(matrix) {
'use strict';
var i, p, tmp, len, mu, mv;

len = {}; // Length.
i   = {}; // Increment.
tmp = {}; // Temporary holder.
p   = {}; // Position.

len.r   = matrix.length;    // Row, length.
len.c   = matrix[0].length; // column, length.

i.r  = 0; // Row, increment.
i.r2 = 0; // Row2, increment.
i.c  = 0; // Column, increment.

tmp.v = []; // Vector, temporary holder.
tmp.p = 0;  // pivot value.

p.lp  = 0;  // Lead pivot, position.
p.rpd = []; // Reserved positions direct, position.

// Find lead pivots in matrix.
for (i.r = 0; i.r < len.r; i.r += 1) {

p.lp = null;
for (i.c = 0; i.c < len.c; i.c += 1) {
/* If position is not reserved nor is zero, then that is
if (matrix[i.r][i.c] !== 0 && p.rpd[i.c] === undefined) {
p.lp = i.c;
break;
}
}

if (p.lp !== null) {
p.rpd[p.lp] = p.lp;
// Reduce row such that the pivot is 1.
if (matrix[i.r][p.lp] !== 1) {
tmp.p = matrix[i.r][p.lp];
for (i.c = 0; i.c < len.c; i.c += 1) {
matrix[i.r][i.c] /= tmp.p;
}
}
/* Reduce other rows (i.r2) from row (i.r). */
for (i.r2 = 0; i.r2 < len.r; i.r2 += 1) {
/* Skip row (i.r) and don't reduce if desired
* value is already zero. */
if (i.r2 !== i.r && matrix[i.r2][p.lp] !== 0) {
/* Scale row (i.r) using pivot position
* from row (i.r2) as the multiplier. */
for (i.c = 0; i.c < len.c; i.c += 1) {
tmp.v[i.c] = matrix[i.r][i.c];
tmp.v[i.c] *= matrix[i.r2][p.lp];
}
// Row reduction.
for (i.c = 0; i.c < len.c; i.c += 1) {
matrix[i.r2][i.c] -= tmp.v[i.c];
}
}
}
}
}
// Finally, we sort our rows, keeping zeros at the bottom and return.
return sort_reduced_matrix(matrix);
}

// Compere this to wolframalpha.com answers.

var matrix = [
[5, -7, -8, -4],
[2, 8, -22, -55],
[-3, 0, -36, 12]
];

matrix = reduced_row_echolon_form(matrix);

console.log(matrix);

matrix = [
[5, -23, 2, 4, 5, 11],
[4, -3, 6, 4, 5, 2],
[3, 7, -18, 7, 9, -6],
[4, 87, -12, 7, 12, 6],
[5, 4, 7, 11, 7, -7]
];

matrix = reduced_row_echolon_form(matrix);
console.log(matrix[0]);
console.log(matrix[1]);
console.log(matrix[2]);
console.log(matrix[3]);
console.log(matrix[4]);

matrix = [
[1, 2, 2, 2],
[1, 3, 3, 3],
[1, 4, 16, 5]
];

matrix = reduced_row_echolon_form(matrix);
console.log(matrix);

matrix = [
[0, 2, -1, -6],
[0, 3, -2, -16],
[0, 0, -3, 11]
];

matrix = reduced_row_echolon_form(matrix);
console.log(matrix);

Is there something...

1. That I am doing in these two functions that you would consider as a bad practice and why?
2. That would explain why the code is slower than it needs to be?
3. That is just bad in some other way?

I am not working as a programmer and I don't know anyone who makes a living as a programmer, so any hint or tips would be welcome.

Partial answer. Wait around and I'm sure someone will do the actual reduction function justice. It's a bit much for me to digest right now.

From a cursory glance, though, I'd suggest breaking things out into functions where possible. But again, I haven't delved too deep.

Overall stuff:

• You misspelled echelon in the function name ("echolon")
• Conventionally, names in JavaScript are camelCased, not under_scored
• You have a lot of really short variable names. Yes, there are comments explaining them where they're declared, but that doesn't help much, when you're in the middle of a dense line later, having to refer back to the comments again and again. Yes, lines will get longer with longer variable names, but they'll also become a lot more readable!
• There's no need to first assign an empty object to a variable, and then add properties to that object. It'd be clearer to define the object's initial state in one go:

len = {
i: matrix.length,    // matrix length (rows)
j: matrix[0].length  // vector length (columns)
};

Looking at the above code, the object should perhaps be called simply size, and i and j could well be called rows and columns - it's what the comments say, so you might as well just call them that.

The above things are fixable without changed to the actual logic. What's more troublesome to me is that your reduced_row_echelon_form function produces side effects: It alters the matrix you pass it, rather than returning a new one. After calling it, you have the answer, but you've lost the question.

I'd suggest making a lot more use of map(). Again, I haven't had the courage to dive into the reduced_row_echelon_form function, but - for instance - the sorting function can be cleaned up rather nicely using it:

function sortRows(matrix) {
// map rows to arrays with the structure
// [<column index>, <pivot coefficient>, <row index>]
// which makes them easily sortable
var pivots = matrix.map(function (row, r) {
for(var c = 0, l = row.length ; c < l ; c++) {
if(row[c]) {
return [c, row[c], r]; // found a non-zero coefficient at matrix[r][c]
}
}
return [Infinity, null, r]; // row is all-zero
});

// sort the pivots array, and use it to (re)build
// the matrix with the rows in the correct order
return pivots.sort().map(function (pivot) {
return matrix[pivot[2]];
});
}

Which will do something like (in some sort of ascii-notation)

[ 0, 0, 0 ]                   [ 1, 2, 3 ]
[ 0, 0, 0 ]                   [ 0, 1, 3 ]
[ 0, 2, 1 ]         =>        [ 0, 2, 1 ]
[ 0, 1, 3 ]                   [ 0, 0, 3 ]
[ 1, 2, 3 ]                   [ 0, 0, 0 ]
[ 0, 0, 3 ]                   [ 0, 0, 0 ]

• @user1235831 No problem. I may still take a crack at reviewing the main function, but I haven't found the time. Generally, though, using Array's map, reduce and their friends should help (also things like findIndex - see link in answer - which aren't available everywhere, but easy to write yourself). Factoring out some commonly used functions like scaling a vector/row, transposing a matrix, etc., would also help clean things up, I'd bet. Lastly, if you've got a normal for loop, consider using continue to skip an iteration instead of wrapping everything in an if block – Flambino Jun 18 '14 at 21:25
• Don't worry about the main function; there is usable information in the fact that you read it, but found it too time consuming to digest it. You literally told me the simple and valid reason: too short variable names. (They are also just bad) I was mostly asking about general review about my style, and you delivered nicely. The code itself is too terse and that is a big problem. I will add the revision in another answer later, it might be the next weekend when I have more time. I will let you know here in the comment section when it is ready. Again, thanks. – user1235831 Jun 18 '14 at 22:42
• @user1235831 Awesome, glad you found it useful! And yes, do feel free to add your own answer, or (better yet, if you feel like it) to post a new question with the revised code. Let more people look it over. I should add that I also got bogged down simply because linear algebra's never been my strong suit and it's been a long time since I last dealt with it :) – Flambino Jun 18 '14 at 23:14
• I have made the revision. Here is the link: codereview.stackexchange.com/questions/54667/… I made this into a single function and added your method within it as a choice. I am new to this so let me know if I am giving credits incorrectly. – user1235831 Jun 18 '14 at 23:23
• Linear algebra is also my weakness... That is why I am challenging it ;) – user1235831 Jun 18 '14 at 23:30


text:
##### Child pages
• Formula
Go to start of banner

# Formula

### Formula

Stress Pattern

Number of Syllables

Primary Stress

FOR mu la

3

first

The formula for vitamin B12 is C63H90CoN14O14P.

Statement

Instructor's Question

Student's Question

Non-Chemistry Usage

The formula for the gas law is PV = nRT.

Do you remember the right formula to use in the calculation of energy?

I assumed that I should use the formula E = (1/2)mv 2 for kinetic energy.

Baby formula is designed to be easily digested. In auto racing, "Formula 1" is the same as "Grand Prix."

• No labels


text:
# Linguistics

2 thoughts
last posted May 8, 2017, 6:11 p.m.
0

I like really impressed by how useful a well designed Markdown editor can be in previewing the final result.

Why can't we have the same thing for linguistics.

Imagine what a basic CFG syntax markdown could look like. I could write simple rules:

S --> NP VP NP --> Det N VP --> V NP

And they'd just be converted into a simple tree in the preview just like that (without lexical items in notes).

And we could have:

[.S [.NP Something ] [.VP [.V like ] [.NP this ] ] ]

There's no reason why not.

1 later thought


text:
$$\renewcommand{\AA}{\text{Å}}$$

Syntax¶

compute ID group-ID smd/tlsph/defgrad

• ID, group-ID are documented in compute command

• smd/tlsph/defgrad = style name of this compute command

Examples¶

compute 1 all smd/tlsph/defgrad

Description¶

Define a computation that calculates the deformation gradient. It is only meaningful for particles which interact according to the Total-Lagrangian SPH pair style.

See this PDF guide to use Smooth Mach Dynamics in LAMMPS.

Output info¶

This compute outputs a per-particle vector of vectors (tensors), which can be accessed by any command that uses per-particle values from a compute as input. See the Howto output doc page for an overview of LAMMPS output options.

The per-particle vector values will be given dimensionless. See units. The per-particle vector has 10 entries. The first nine entries correspond to the xx, xy, xz, yx, yy, yz, zx, zy, zz components of the asymmetric deformation gradient tensor. The tenth entry is the determinant of the deformation gradient.

Restrictions¶

This compute is part of the MACHDYN package. It is only enabled if LAMMPS was built with that package. See the Build package page for more info. TThis compute can only be used for particles which interact via the total Lagrangian SPH pair style.

none


text:
Finding the coordinates of a point

I have the $x$ and $y$ values to $2$ points $A(x_a,y_a)$ and $B(x_b,y_b)$. I need to determine the coordinates of a third point $S(x_s,y_s)$ that is at $r$ distance away from both A and B points and lies on a line that is perpendicular to the line $AB$ in the midpoint of $AB$. Also picture because it explains it better than words:

Thank you for the help.

-
What have you done so far? – mixedmath Mar 1 '12 at 1:14

Note that you already know the co-ordinates of the mid-point of the line $AB$ joining $(x_a,y_a)$ and $(x_b,y_b)$. Call this point $D$. So, the co-ordinates of $D$ are $\left(\dfrac{x_a+x_b}{2},\dfrac{y_a+y_b}{2}\right)$.

Also note that $SD \perp AB$. Therefore, the product of the slope of $SD$ and AB is $-1$.

Slope of $AB$=$\dfrac{y_b-y_a}{x_b-x_a}$

So, this gives us the slope of $SD$ and we know a point that lies on it. So, we get the equation of the line $SD$.

The equation of the line $SD$ is $y-\dfrac{y_a+y_b}{2}=\dfrac{x_a-x_b}{y_b-y_a}\cdot\left(x-\dfrac{x_a+x_b}{2}\right)$

Now write the parametric equation of the line $SD$ with respect to the parameter $d$, distance of the point from $D$ and get hold of the co-ordinate $(x_s,y_s)$, by setting $d=\dfrac{\sqrt{r^2-l^2}}{2}$.

Alternatively, note that $SA=SB$ as $S$ is on the perpendicular bisector of $AB$. This coupled with the equation of the line will give you the co-ordinates of $S$.

I'll work the explicit details if you still have problem.

-


text:
# How to use pattern matching within curried function

I'm learning F# and I'm trying the following exercise (exercise 4.10 of Functional Programming Using F#).

Declare an F# function prefix: 'a list -> 'a list -> bool when a:equality. The value of the expression prefix[x_0;x_1;...;x_m] [y_0;y_1;...;y_n] is true if m<=n and x_i=y_i for 0<=i<=m, and false otherwise.

I wanted to use pattern matching on the two inputs, but wasn't sure how to do this with a curried function (as opposed to a function taking a 2-tuple). So I wrote:

let rec prefix a b = (function
| ([], _) -> true
| (_, []) -> false
| (x0::xst,y0::yst) -> x0 = y0 && prefix xst yst) (a,b);;

I wasn't very happy with this, because I thought it would be better (clearer and more efficient) if the inner function called itself, so I tried declaring the inner function locally.

let prefix a b =
let rec prefixt = function
| ([], _) -> true
| (_, []) -> false
| (x0::xst,y0::yst) -> x0 = y0 && prefixt (xst,yst)
prefixt (a,b);;

Is this the right way to approach such a problem in F#?

You can use the match … with … syntax:
let rec prefix a b =


text:
# How do I go ahead in this?

Got this from daily challenge of sudoku app.

• Your sudoku image is a bit misleading because in the lower right quadrant, you don't have any 3's marked there for some reason. So I'm not sure that your marks can be trusted at all. – JS1 Feb 9 at 17:54

It's certainly not an easy one to tackle here to find a number. There are probably easier ways to chip away at the pencil marks (after filling in the missing $$3$$s as per JMP's comment), but...

Labeling:
* the cells as $$(column, row)$$ with $$(1,1)$$ in the top-left; and
* sets as $$\{\cdots\}$$

If $$(7,1)$$ were a $$3$$
then $$(7,8)$$ is a $$9$$
and so $$(6,8)$$ would be a $$7$$
leaving $$(6,1)$$ as an $$8$$ and $$(6,2)$$ as a $$3$$
as such $$(5,3)$$ would be a $$1$$
so one of $$\{(7,3), (8,3), (9,3)\}$$ would be a $$3$$
but If $$(7,1)$$ were a $$3$$ none of $$\{(7,3), (8,3), (9,3)\}$$ could be a $$3$$
Therefore $$(7,1)$$ cannot be a $$3$$ and must be a $$9$$

• Idk how you guys have so good eyes to spot such tricks. I try to use pencil markings and eventually I get lost, similar to what happened in this puzzle – Kashish Maheshwari Feb 9 at 18:47
• This was a "guess and check" rather than spotting a pattern. – Jonathan Allan Feb 9 at 18:50

r5c7 can't be a $$3$$, because then r1c7 and r3c7 are $$6$$ and $$9$$, which forces the remaining 2 cells in the column to be $$5,7$$, which forces a $$6,8$$ in the right column of the lower-right block, which means both r7c8 and r9c8 are $$2$$. Also the is only one option for the $$3$$ in r9.