dna - Is telomere shortening consistant over consecutive cell divisions from zygote to a differentiated cell?

Considering the complexity of embryogenesis, a temporal referance would be helpful to coordinate the developmental sequences during embryogenesis and fetal development which is to be completed within the gestation period. Can telomere shortening if consistant be used as a reference by every cell to do what it is destined to do at particular time frame? This is without considering the influence of telomerase etc.

This is also without prejudice to the role of DNA directed molecular signalling.

To repeat the question is telomere shortening consistant over consecutive cell divisions from zygote to a differentiated cell? If so can it function as temporal control of embryogenesis?

microscopy - What to look for when buying a light microscope?

I am a science lover and want to buy a microscope to explore things around me. Like studying cell structures, microorganisms, blood and plants. It would be great if there is way to photograph slides. Just curious to know and explore things around me.

I want to know which features I should consider while buying it?

nt.number theory - The difficulties in proving modularity lifting theorems over non-totally real fields

Note: This is a fairly precise and detailed question about an important but technical aspect of algebraic number theory. My answer is written at a level that I think is appropriate for the question; it assumes some familiarity with the topic at hand.

---

The most basic difficulty is that there is non a map $R rightarrow {mathbb T}$ in general
(i.e. one typically doesn't know how to create Galois representations attached to automorphic forms).

The second difficulty is that in the TWK method, one must argue with auxiliary primes (the primes typically labelled $Q$), and show that as you add these primes, ${mathbb T}$ grows in a reasonable way (basically, is free over $mathcal O[Delta_Q],$ where $Delta_Q$ is something like the $p$-Sylow subgroup of $({mathbb Z}/Q{mathbb Z})^{times}.)$

One shows this (or some variant of it) by considering the analogous queston about cohomology of the arithmetic quotients. Suppose for a moment we are in the Shimura variety context, or perhaps the compact at infinity context. Then it will be the middle dimensional cohomology that is of interest, and if we localize at a non-Eisenstein maximal ideal we might hope to kill all other cohomology. Then we can replace a comuptation of middle dimensional cohomology by an Euler characteristic computation, and its easy to see that the Euler char. will multiply by $|Delta_Q|$ when we add the auxiliary primes $Q$.

But in more general contexts, there won't be a single middle dimension in which the maximal ideal of interest is supported (even if it is non-Eisenstein), and computing Euler characteristics will just give $0$, which is not much use. It's not clear that it's even true that adding the auxiliary primes forces the approriate growth of cohomology, and possible torsion in the cohomology just adds to the complication.

There is much current work, by various groups of researchers, with various different approaches, aimed at breaking this barrier.

---

I should add that one can now handle certain questions about non-totally real field,
say question related to conjugate self-dual Galois reps. over CM fields, because
these are still related to a Shimura variety context. This plays a role in the recent
progress on Sato--Tate for higher weight forms by Barnet-Lamb--Geraghty--Harris--Taylor
and Barnet-Lamb--Gee--Geraghty, and is also the basis for a recent striking theorem
of Calegari showing that if $rho:G_{mathbb Q} to GL_2({mathbb Q}_p)$ is ordinary
at $p$ and de Rham with distinct Hodge--Tate weights (and probably $overline{rho}$ should satisfy some technical conditions), then $rho$ is necessarily odd!

---

big picture - Why is 2 so odd?

My take on this issue is that p=2 isn't really strange---all small primes are strange, it's just that the smaller you are, the earlier you become troublesome. Look at recent R=T results in the theory of automorphic representations. Nowadays people can prove these sorts of things for $n$-dimensional representations, but they need to assume $p>n+1$ or some such thing. The thing about $p=2$ is that it's so small that it's already causing problems when one is considering $GL(1)$, which is an abelian situation. Now abelian situations are so much easier to understand than the general situation that they are more prevalent in the literature. For example things like quadratic reciprocity can be viewed of as some consequence of class field theory, which is really 1-dimensional representations of Galois groups, and already $p=2$ is causing a problem. Similarly Fontaine's results on commutative group schemes of $p$-power order runs into some trouble when $p=2$ (his basic linear algebra data doesn't give you an equivalence between finite flat group schemes over ${mathbf Z}_p$ and "easy semilinear algebra" when $p=2$) and again it's because 2 is just too small. But as people formulate higher-dimensional analogues of these things, they will no doubt have to rule out more primes. So it's not that 2 is behaving badly, it's just that from 2's point of view the theory is more advanced, so you have to deal with more special cases.

ag.algebraic geometry - morphism closed + fibres proper => proper?

The answer is no. Consider an integral nodal curve $Y$ over an algebraically closed field, normalize the node and remove one of the two points lying over the node. Then you get a morphisme $f : Xto Y$ which is bijective (hence homeomorphic), separated and of finite type, and the fibers are just (even reduced) points. But $f$ is not proper (otherwise it would be finite and birational hence coincides with the normalization map).

In the positive direction, you can look at EGA, IV.15.7.10.

[Add] There is an elementary way to see that $f$ is not proper just using the definition. Let $Y'to Y$ be the normalization of $Y$. So $X$ is $Y'$ minus one closed point $y_0$. It is enough to show that the base change of $f$ to $Xtimes Y' to Y times Y'$ is not closed. Consider the closed subset
$$Delta=leftlbrace (x, x) mid xin X rightrbrace subset Xtimes Y'.$$
Its image by $f_{Y'} : Xtimes Y' to Ytimes Y'$ is $leftlbrace (f(x), x) mid xin Xrightrbrace$ which is the graph of $Y'to Y$ minus one point $(f(y_0), y_0)$. So $f$ is not universally closed, thus not proper.

gn.general topology - Unusual Space-Filling Curve

Around 1998, I encountered a (forgotten) reference to a particularly strange space-filling curve.

Consider a foliation as a collection of continuous nonintersecting curves that start at (0,0) and end at (1,1) and collectively fill the unit square, such as the graphs of functions f_t(x) = x^t where t >=0. Supposedly there exists a continuous curve G that starts at (1,0), ends at (0,1), fills the unit square, and crosses each f_t curve only once.

This initially sounds even more impossible than the Cantor curve. But intuitively a space-filling curve could trace back and forth over the f_t curves and only cross at the corners (0,0) and (1,1). Can someone please explain a construction of such a space-filling curve?

entomology - How do small animals make loud sounds?

The Cicada

A careful study of the noise-making apparatus of the cicada can be found in a 1994 paper by Young and Bennet-Clark.$^1$ The authors generated sounds at about 0-16 kHz at peaks on the order of 100 dB using cicadas in various stages of deconstruction. The cicada uses a resonant organ-system called the tymbal which buckles and unbuckles rapidly to produce sound. The buckling-in is caused by muscle contraction and is louder than the buckling-out (relaxation) phase. Air sacs (a feature of many other small noisemakers) serve to amplify the sound. The tymbal itself, for the species in this paper, has a resonant frequency of about 4kHz (Young, page 1017). The song of the cicada as modified/amplified by air sacs and other structures, is often around 10kHz.$^{2}$

Pure Tone vs. Diffuse Tone?

The vocalizations of large vertebrates are a complex superposition of waves that in the frequency spectrum are somewhat spread out. To the extent that a frog or a bird emits a pure tone, the energy will be confined to a narrow frequency range and this may be a strategy for achieving greater amplitude. Given comparable audio sensitivity, however, the intensity of pure tones will depend on amplitude (intensity), regardless of frequency.$^{3,4}$

Other Small Loud Animals

While the songs of cicadas are intense, especially in concert, on an individual level there is competition from other species. According to a Gizmodo article quoting assorted scientists, the snapping shrimp produces a transient snap that is around 200 decibels, a level that one site describes as "deafening." For perspective, dolphins can emit short chirps of 220 dB but these are outside the range of human hearing. The lion emits a roar of 115 dB which is sustained and audible 5 miles away, according to the article. Elephants also are capable of 117 dB cries, as are howler monkeys.

Both the shrimp and the cicada use non-vocal vibration to create their sounds. The shrimp uses a "spring-loaded claw" (the spring is muscle). The localized force of one part of the claw hitting the other generates a bubble (this is known as inertial cavitation). When the bubble collapses it generates a shock wave (noise) that stuns fish (prey).$^5$ The noise of frogs is produced as air passes from the lungs through the larynx, amplified by distended air sacs which resonate. Birds can produce up to 135dB (the Mollucan Cockatoo). They generally force air past (membranes and) a specialized organ called the syrinx located at the bottom of the trachea (see the Wikipedia note on bird vocalization).

Micronecta scholtzi, a 2mm-long aquatic insect, is for its size the loudest known animal. It creates a sound of 99.2 dB intensity which (despite being largely lost in transition from water to air) is audible to humans ashore. According to the Wikipedia note it creates this sound by "stridulating a ridge on its penis across corrugations on its abdomen." The area involved is about 50$\mu m$ across. Details of the mechanism are poorly understood. The article's comparison of the sperm whale's 236 (underwater) dB song gives perspective, as a sperm whale can weigh 14 metric tons.

A Common Aspect of Sound Intensity: Cavity Resonance

Descriptive studies of sound-creation by small animals (with the possible exception of the snapping shrimp) do not fully explain why a one-gram bug can make a bigger noise than a lion. Purely vocal methods of larger vertebrates produce sustained noise on the order of 100 dB but the non-vocal instruments of smaller creatures are capable of short bursts of amazing intensity.

It is difficult to generalize but because air sacs are part of many sound-making schemes, cavity resonance probably plays an important role. Like spring-mass systems or RLC circuits, cavities have resonant frequencies at which amplitude of a signal may be increased (the policeman's whistle is a familiar example). Another paper by Bennet-Clark and Young gives a sketch of a theory along these lines. At resonant frequencies the impedance of the instrument falls sharply and instead of being dissipated (generally as heat) the energy emerges as sound.$^6$

---

$^1$ Bennet-Clark and Young, The Role of the Tymbal in Cicada Sound Production, J. of Experimental Biol. (1995) 198, 1001-1019.

$^{2}$ The frequency of cicadas is variable, mostly on the order of 10kHz but occasionally very low (< 1kHz), mostly due to body size. See this article.

$^3$ Sound--essentially a compression wave--diminishes with distance. So when the Wiki article on noise levels compares noise levels it includes the distance from the object. For example, 100 db (comparable to the cicada) is the level of noise associated with a jack-hammer at 1 meter away.

$^4$ Audible range for humans is roughly 15 Hz-16000 Hz. As mentioned below, the dolphin can emit very intense high-pitched sounds that we don't hear at all, so the analogy to EM waves (higher frequency = higher energy) doesn't help predict perception. See Pfaff and Stecker, Loudness and Frequency Content of Noise in the Animal House, Lab. Animals (1976) 10, 111-117.

$^5$ M. Versluis, B. Schmitz, A von der Heydt & D. Lohse (2000). "How snapping shrimp snap: through cavitating bubbles". Science 289 (5487): 2114–2117.

$^6$ Bennet-Clark and Young, Short Communication, The Scaling of Song Frequency in Cicadas, J. Exp. Biol. 191, 291-294 (1994).

ct.category theory - Is a functor which has a left adjoint which is also its right adjoint an equivalence ?

There are lots of examples. Here's what I think is in some sense the minimal one.

Let $C$ be the terminal category $mathbf{1}$ (one object, and only the identity arrow). Then for any category $D$, a left adjoint to the unique functor $G: D to mathbf{1}$ is an initial object of $D$, and a right adjoint is a terminal object. So, we're looking for a category $D$ that has a zero object (one that is both initial and terminal), but is not equivalent to the terminal category.

There are plenty of such categories $D$, e.g. $mathbf{Vect}$. But I guess the minimal one is the category $D$ generated by a split epimorphism. In other words, it consists of two objects, $0$ and $d$, and non-identity arrows
$$
p: d to 0, i: 0 to d, ip: d to d,
$$
satisfying $pi = 1_0$. Then $0$ is a zero object but $D$ is not equivalent to the terminal category.

Describe the second cohomology group $H^2(Z_n times Z_n. k^*)$.

I would take the standard cyclic resolution of $G = Z/nZ$:
$$
dots stackrel{1-t}to Z[G] stackrel{sum t^i}to Z[G] stackrel{1-t}to Z[G] to Z to 0,
$$
where $t$ is the generator of $G$, and then take the tensor square of two such --- this would give a resolution
$$
dots to Z[G_1times G_2]^3 stackrel{d_2}to Z[G_1times G_2]^2 stackrel{d_1}to Z[G_1times G_2] to Z to 0,
$$
where $G_1 = G_2 = Z/nZ$ and the maps are given by
$$
d_1 = (1-t_1,1-t_2),
qquad
d_2 = left(begin{array}{ccc}
sum t_1^i & 1-t_2 & 0 cr
0 & 1-t_1 & sum t_2^i
end{array}right)
$$
($t_1$ and $t_2$ are the generators of $G_1$ and $G_2$ respectively).
I think you can use this for the calculations.

imaging - Can this image be the result of a Western Blot?

I do not think that a publication quality blot should have such an artifact, but I was able to find something similar by purposely over blotting (not the same as over exposing) a gel. If you use too much primary, secondary, or developing reagent, you can get your HRP signal to "burn in" a membrane where you get a distinct "negative band."

By negative band I mean a region that is more clear/white than background. This happens mostly when you have way too much secondary antibody. Normally when this happens, the CENTER of the band burns in first so you would see a white center with dark edges. And that's only when you are imaging the membrane as it is burning in. Often the whole band is white.

After going through the westerns of grad-student who is working with me, I found this image:

It came with the clear notation that it was burned in and disregarded (said student was learning how to do Westerns at the time). It's a GAPDH blot for those that care. When this does happen, it's obvious because you can then see the band with your naked eye on the membrane. Again this would be a reason to not publish the blot.

The image could have non-maliciously been edit via compression, screens, filters, etc as mentioned by others in the comments. This is the only way I can think of to experimentally have a similar image. Ether way I don't think the image should be reported as is.

math communication - Is a free alternative to MathSciNet possible?

This was discussed a little on the algebraic topology list last autumn, you can look up the archives to see what was said.

Technologically, this is easy. The problems come in when you think beyond that.

1. How would such a site start? Initially, there would be very few reviews so no one would have a reason to visit the site (the probability of the paper wanted being reviewed being almost nil). For obvious reasons, importing an initial dataset from MathSciNet or Zentralblatt is extremely unlikely. If no-one visits, no-one's going to contribute.




2. How would such a site maintain itself? The big problem with reviews is that the person writing the review gets almost no gain from it but (to do it properly) has to put in a fair amount of effort (which is why so many reviews on MathSciNet and Zentralblatt are so appalling, just copying out the summary of the paper, and why the few gems are so greatly appreciated). That's a huge imbalance. MathSciNet sorts this out by awarding "points" to reviewers ("And points mean prizes!"). What would a free alternative offer?




3. How would such a site maintain its standards? Here, one gets into extremely murky waters. One idea suggested on the alg-top list was to use something like the stackoverflow model, but as this is going to involve opinions it could be extremely dangerous. Often, the most useful information in a review is a reason not to read a given paper - if you're looking at the review, you are probably already inclined to read it - and some of the classic reviews are those that rip apart a paper. Who's going to write those on an open system?

There are other ways of essentially filling the same role as reviews. You read a review to find out whether or not it's worth reading a paper. But the main problem comes before that, which papers should I read? Once I've found that, then I use the review more to figure out whether or not I should bother finding the paper in my library or not. If the paper is freely available, it's almost as quick to read the paper itself as to read the review (but I often read the review first because I find the paper via MathSciNet so the review is there anyway). So I would much prefer something to speed up finding papers. A better system of linking papers together: "If you enjoyed this paper, you might also enjoy ..." sort of thing.

So a really useful thing to do would be to have a "related papers" section linked to a given paper. This could be started by the author - who would have every incentive to do so (since it increases the likelihood that their paper is understood) and who would find it very easy to do (since they would have such a list of papers lying on their desk - it's all the articles, books, and so forth that they read when writing the paper in the first place). Basically, it's an expanded and commented reference list, and one which can be added to by others (so that if reading a paper, you find some other paper very useful which the original author didn't know about, or knew so well they didn't think to mention it, then you can add it).

---

Added later in response to some of the comments and the changes in the question.

First, a minor point. MathSciNet and the arXiv already have the capability to link articles together. If you look at a typical MathSciNet review then you'll see at the top right corner a box linking to where the article was cited, either in articles or reviews. I've found this an invaluable tool and I hope that the AMS will extend it historically (the links are only to recent articles where this data could be found fairly automatically). The arXiv has experimental support for full text search, so you can search for the arXiv identifier of one of your articles and find all those that cite it, for example.

Now on to my major point. "Someone should set up a site that ...". Who's to say that this has to be centralised? After the discussions on the alg-top list and the subsequent discussions on the rForum, I've come to the conclusion that having a central system isn't the best idea. All that is really needed is a central place from which all other places can be reached. And that already exists. It's called the arXiv. The arXiv accepts trackbacks (subject to some approval) so when you blog about a paper, send a trackback to the arXiv and then you should get linked to from the page on the paper.

Of course, this only works for articles that are on the arXiv. So then lobby the AMS to accept trackbacks as well (they can bung their standard "the AMS has no responsibility for non-AMS sites" disclaimer on). The basic information in MathSciNet is freely available, these trackbacks can easily be added to those.

In the meantime, instead of waiting for someone to come along with some central setup (which probably won't be quite what you personally were thinking of) simply put your notes online. Here's the message from the front page of the nLab:

We all make notes as we read papers, read books and doodle on pads of paper. The nLab is somewhere to put all those notes, and, incidentally, to make them available to others. Others might read them and add or polish them. But even if they don’t, it is still easier to link from them to other notes that you’ve made.

On the nLab you will find information about papers that people have found useful. You can search for a particular paper to see if anyone's commented on it, use it, or cited it. Some papers/books have their own pages. Here's one example http://ncatlab.org/nlab/show/Topological+Quantum+Field+Theories+from+Compact+Lie+Groups and here's another http://ncatlab.org/nlab/show/Elephant.

The basic point is that you can do this yourselves, now, without needing someone else to say "Here's the way to do it". You benefit right now without doing loads of extra work, and everyone else benefits incidentally as a result. Everyone wins. It doesn't have to be the nLab, you can use whatever software you like. Just put it online. Somewhere. Anywhere. Stick the arXiv/MR identifier somewhere prominent and the search engines will pick it up.

Then the rest of us will get into the habit of searching on the internet for articles of articles and find your comments.

(Incidentally, along with this, make sure that you put your own articles on your webpages. Every journal that I've ever encountered allows you to do this and this is really a Must-Do for academics. Even if you just put a scan of older papers, it's invaluable for those whose libraries don't carry subscriptions to every single journal under the sun (and those that have no library at all). There is No Excuse for not doing this, especially given that photocopiers now can easily scan straight to PDF.)

metabolism - Food Intake versus ability to flee among birds, particularly the hummingbird?

Logically speaking, if a hummingbird drinks too much nectar, it will be temporarily overweight and less able or unable to fly to escape danger. However if the same hummingbird doesn't drink enough nectar, it will suffer the same problem of not being able to flee danger, but for the different reason of it wouldn't have enough energy to do so. Hummingbirds are incredibly small, so I would assume they would have the most problem with this issue due to the fact it would have very little margin for error. I am not sure how much that margin is though or the marginal percent of body weight, so I'll ask that question too.

What mechanisms do (humming)birds have to regulate and control their body weight and their energy needs and scouting and timing the acquisition of their next potential food source? What is their margin for error and how do they meet it and how did they meet it in the past?

EDIT: I want a more concise question, so hopefully this is answerable:

Alternatively and optionally, Can you describe to me a general day in the life of a Hummingbird? I want to know what good decisions it makes over the course of its "perfectly average" day to survive. Such things as what it does to avoid dangers, and how it finds its time to eat and how much it eats and at what intervals, and what it does with the rest of its time?

nt.number theory - A product of gamma values over the numbers coprime to n.

Denote $$f(n)=prod_{k=1}^{n-1}Gamma left(frac{k}{n}right)$$ and $$ F(n)=prod_{1le kle n-1, kperp n}Gamma left(frac{k}{n}right)$$
We have $f(n)=prod_{d|n}F(n)$ and therefore by Mobius inversion $F(n)=prod_{d|n}f(d)^{mu(n/d)}$

By the multiplication theorem we have $f(n)=frac{1}{sqrt{n}}(2pi)^{frac{n-1}{2}}$, so if $n$ is not a prime power $$F(n)=prod_{d|n}left(frac{1}{sqrt{d}}(2pi)^{frac{d-1}{2}}right)^{mu(n/d)}=(2pi)^{frac{1}{2}varphi (n)}$$
The formula $F(n)=sqrt{varphi(n)+1}f(varphi(n)+1)$ follows.

nt.number theory - Linear equation with primes

Assuming the Hardy-Littlewood prime tuples conjecture, any n which is coprime to k will have infinitely many representations of the form q-kp.

Assuming the Elliot-Halberstam conjecture, the work of Goldston-Pintz-Yildirim on prime gaps (which, among other things, shows infinitely many solutions to 0 < q-p <= 16) should also imply the existence of some n with infinitely many representations of the form q-kp for each k (and with a reasonable upper bound on n). [UPDATE, much later: Now that I understand the Goldston-Pintz-Yildirim argument much better, I retract this claim; the GPY argument (combined with the more recent methods of Zhang) would be able to produce infinitely many $m$ such that at least two of $m + h_i$ and $km + h'_i$ are prime for some suitably admissible $h_i$ and $h'_i$, but this does not quite show that $q-kp$ is bounded for infinitely many $p,q$, because the two primes produced by GPY could both be of the form $m+h_i$ or both of the form $km+h'_i$. So it is actually quite an interesting open question as to whether some modification of the GPY+Zhang methods could give a result of this form.]

Unconditionally, I doubt one can say very much with current technology. For any N, one can use the circle method to show that almost all numbers of size o(N) coprime to k have roughly the expected number of representations of the form q-kp with q,p = O(N). However we cannot yet rule out the (very unlikely) possibility that as N increases, the small set of exceptional integers with no representations covers all the small numbers, and eventually grows to encompass all numbers as N goes to infinity.

oc.optimization control - Approximating a probability distribution by a mixture

Let us consider a probability distribution $(g_n)_{n in mathbb{N}}$ which we want to approximate by a mixture of $(f_n(lambda))_{n in mathbb{N}}$ where $lambda in mathbb{R}$ is a parameter.

Are there known techniques that allow one to find the mixture minimizing the $L^1$ norm:
begin{equation}
min_{p} sum_{n=0}^{infty} left|g_n - int rm{d} lambda ; p(lambda) f_n(lambda) right|
end{equation}
where $p(lambda)$ is a normalized probability distribution?

The motivation of this problem is linked to experimental physics: ideally one would like to generate an experimental process characterized by the probability distribution $g$ but this is really not practical. What is really easy, however, is to generate an experimental process with the distribution $f(lambda)$ where $lambda$ is a tunable parameter.
Therefore, the goal is to approximate $g$ as closely as possible with such a mixture of $f(lambda)$, where the distance between the two distribution is computed with the $L^1$ norm, that is, I want to minimize the variation distance between the two distributions.

In the specific problem I consider, $f(lambda)$ is a Poisson distribution with parameter $lambda geq 0$, but I really am interested in a general method to approach this problem-

Any pointer to the relevant literature would be greatly appreciated.
Thanks a lot!

gt.geometric topology - Database of polyhedra

As part of many hobbies (origami, sculpting, construction toys) I often find myself building polyhedra from regular polygons. I am intimately familiar with all of the Archimedean and Platonic solids, and can construct most of the other isohedra, deltahedra, and Johnson solids from memory. The smaller prisms, antiprisms, and trapezohedra are of course trivial. However, I often forget the precise arrangement of faces and vertices for some of the Johnson solids and most of the Catalan solids. Thus, the question that I pose is this:

Where can I find the most complete, robustly indexed, and searchable database of polyhedra?

I would like to use such a database to answer, in short order, questions of the following nature:

Which solid is comprised of exactly eight hexagons and six squares? Which solids are comprised of less than 10 triangles, eight squares, and six hexagons? How many solids can be constructed with exactly 24 edges?
What solid with 12 vertices has the most edges (or faces)? etc...

I imagine that such a database does not exist and I am going to be forced to create one, so answers suggesting features for such a database (likely to be web-based) are welcome as well.

co.combinatorics - Expected number of steps for a discrete random walk to visit every point on an N-dimensional rectangular lattice

Please imagine a discrete random walk on an N-dimensional rectangular lattice with dimensional lengths $(l_1, ..., l_N) in L$ and total lattice points $P = prod{l_i}$, for $i = 1, ..., N$. At each time step, the walker will move to one of it's adjacent lattice points with equal probability. The N-dimensional random walk is non-self-avoiding, the walker must move with each time step, and the boundaries of the lattice are reflecting. However, jump probabilities must be adjusted at edges and corners due to a reduction in the number of adjacent nodes - i.e. jump probabilities will vary from $frac{1}{2N}$ internal to the lattice to $frac{1}{N}$ at the edges of the lattice.

Provided the random walk specifications above, what might be the expected step-time distribution for the walker visiting every position in the N-dimensional rectangular lattice with dimensional lengths $L$?

lab techniques - Is DNA green viewer carcinogenic?

SYBR green is designed to be much less carcinogenic than ethidium bromide (EtBr).

All these gel dyes work by intercalating themselves into the DNA stack between the bases specifically which has a great potential for causing mutations and messing with the workings of the nucleus. My remembrance is that the SYBR and GelGreen/Red etc dyes are large and relatively hydrophilic and can't find their way into the nucleus, greatly reducing their toxicity. They also do not transfer energy to the DNA itself due to their structure and so also cause less DNA damage when being viewed on a transilluminator.

genetics - What is an epistasis group?

I have been trying to wrap my head around the concept of epistasis for a couple of days now, and I think I understand it, at least at a basic level, but I still don't understand some of the ways that the term is used.

What does it mean if gene A is epistatic to gene B? Does this simply mean that gene A masks the phenotype of gene B when expressed? or is there more to it?

Also, what does it mean when genes are in the same epistasis group? I am currently studying the transcriptional up-regulation of PSY3 in yeast as a result of UV treatment. PSY3 codes for a protein that forms the Shu complex along with 3 other proteins. One paper I am reading states that PSY3, is in the same epistasis group as the three other genes that code for these other proteins. What does this mean?

genetics - Suggestions for an experiment?

This is a bit hard - most possible answers you still aren't going to like, but I'll give you three suggestions.

It sounds like you want to take something with a mathematical model and try to modulate it with molecular biology.

It seems unlikely that I can really give you a specific project, but there are four sources I will recommend you look at.

I think I'd suggest the further limiting assumptions:

1. you want to work with E coli - its the easiest and most readily available organism to work with.


2. you want to work with a system that is self contained within a single plasmid - so it relies only upon 2 genes to act, 3 at the outside or you will have issues getting it all to work.


3. you want a mathematical system that already has a well fit model that you will peturb. building a new model might be a bit of a big first off project. (but who am I to tell you what to do - these are just suggestions).

The First suggestion I have is Jeff Hasty at UCSD. He has focused a lot on oscillating gene circuits. He has simple systems that might be reproducible with a small lab, most recent work that combines a GFP oscillator with LUX is pretty cool. Both oscillators and LUX are independently good systems to work with. . I've been a science fair judge and I can tell you, just reproducing one of his systems would be an impressive lot of work

Another body of work to look at is Adam Arkin. He has looked at lots of circuitry component candidates. Articles such as "The hunt for the biological transistor" might get you thinking. This is a broader body of work, and so it might take a while to get an idea from it.

Third, if this is boring to you and you want to look more broadly, you can look through the iGEM competitions. These are projects with oscillators and bio synthesis systems which sometimes have mathematical models associated with them. The big advantage here is that you might be able to start or join an iGEM team and then some or all the plasmids will be made already - mol bio gets very expensive if someone doesn't gift you some materials.

neuroscience - Cat purring: What are some possible underlying mechanisms behind purring and bone remodeling and formation?

The author is likely referring to the mechanosensory behavior of bone (reviewed in Huang and Ogawa, 2010; lots of Google Scholar citations). Bone loading produces very tiny mechanical deflections (strain) which are translated into biochemical signals that promote bone growth through the action of osteoblasts. Burger and Klein-Nuland (1999) review possible mechanisms.

The low frequency soundwaves produced during purring overlap the frequencies that have been shown experimentally to induce bone formation (1-50Hz; e.g., Castillo et al., 2006; Xie at al. 2006). Although an interesting hypothesis, I don't think that osteogenesis in response to purring has ever been experimentally shown in cats.

Huang C, Ogawa R. 2010 FASEB J. 2010 Mechanotransduction in bone repair and regeneration. 24(10):3625-3632.

Burger EH, Klein-Nulend. 1999. Mechanotransduction in bone--role of the lacuno-canalicular network. FASEB J 13(Suppl):S101-S112.

Castillo AB, et al. 2006 Low-amplitude, broad-frequency vibration effects on cortical bone formation in mice. Bone 39:1087-1096.

Xie L, et al. 2006. Low-level mechanical vibrations can influence bone resorption and bone formation in the growing skeleton. Bone 39:1059-1066.

immunology - Autophagy in eukaryotic cells

Autophagy is a cellular process that is occurring all the time, but it can be elevated during times of need (see below).

In autophagy, cargo (can be anything - mostly macromolecules but also bacteria/viruses etc) is taken up by a lipid membrane which folds on itself to form an autophagosome, which is like a vesicle but have markers on it that makes it specialized in carrying out autophagy. These autophagosomes are then transported to, and merge with, lysosomes, releasing the cargo into the lysosome to be degraded. The broken down materials are then released back into the cytosol, where other processes can make use of them. That is the "some kind of recycling" you are referring to.

There are two types of autophagy - selective and general. In selective autophagy, receptors on the membrane of the autophagosome specifically selects for ligands (e.g. p62, ndp52 selects for ubiquinylated substrates, which usually marks molecules for degradation). In general autophagy, the uptake into the autophagosome is random.

So, you can think of general autophagy as maintaining a basic level of turnover - to ensure everything in the cell is not worn out; and selective autophagy as a response to specific ligands that needs to be degraded.

By this logic, autophagy activity increases during infection because those infectious agents, once gaining entry into the cell (either through phagocytosis or by forced entry), will need the autophagy machinery to transport it to the lysosome to be degraded. Interestingly, some bacteria actualy hi-jacks this process to ensure its survival in the cell. Here's a good review to get you started if you are interested.

Note that the proteasome also recycles macromolecules, although the things it can recycle is limited by size.

allele - Can sexual reproduction create new genetic information?

Biological information has several hierarchies is ambiguous between syntactic information in a hierarchical modular system, and functional information, without a particular context[1].

Out of necessity the DNA is sequence is generally highly conserved, but small changes can easily lead to gross changes in folding, function and the minimum energy states of the protein. (Proteins are ultimately dynamic systems, with many constantly sampling their minimum energy conformation structures - the static pictures on magazine and book covers are misleading)

Additionally an allele, by definition, is a gene variant that occurs in at least 1% of the population - by consensus (and and sufficient statistical power). As such the term is part of population genetics. For instance, for a 400AA long protein, that would mean that a particular homologous recombination event has to occur very frequently and be favored by at least one of many (known) mechanisms.

Is new genetic information ever created during sexual reproduction, or only through mutations during an organisms life time?

Yes. Recombination has several mechanisms, is not a perfect event, and shows different efficiencies depending on the type of mechanism and "helpers"/helper-types as well as helper concentrations involved, - notwithstanding cofactor-concentrations.

[1]John Collier, Hierarchical Dynamical Information Systems With a Focus on
Biology, Entropy 2003, 5, pg. 100-124

gn.general topology - Topologizing free abelian groups

I don't know if such a topology is unique, but it exists if and only if $S$ is completely regular. This includes locally compact hausdorff spaces and CW complexes.

With Freyd's Adjoint Functor Theorem, it can be shown that the forgetful functor from abelian top. groups to top. spaces has a left adjoint. This is essentially the same proof as in the discrete case. Explicitely, $mathbb{Z}[S]$, the free abelian top. group over the top. space $S$, is the usual free abelian group endowed with the weak topology for all homomorphisms $mathbb{Z}[S] to A$, such that $S to mathbb{Z}[S] to A$ is continuous. Here, $A$ is an arbitrary abelian top. group. In order to show that this topology exists, we may assume that $A$ is, as a group, a quotient of $mathbb{Z}[S]$, so that these $A$ form a set. But the description of the topology does not change and even without Freyd's Theorem it is easy to see that $mathbb{Z}[S]$ thus becomes an abelian top. group satisfying the desired universal property.

Now I claim that the three assertions

1. $S to mathbb{Z}[S]$ is a homeomorphism onto its image.




2. $S$ is a subspace of an abelian top. group.




3. $S$ is completely regular.

are actually equivalent!

1) implies 2), that's clear. Now assume 2), thus $S subseteq A$ for some top. abelian group. Extend the inclusion $S to A$ to a continuous homomorphism $mathbb{Z}[S] to A$. Every open subset of $S$ can be extended to an open subset of $A$. Pull it back to $mathbb{Z}[S]$. This is an open subset of $mathbb{Z}[S]$ which restricts to the given oben subset of $S$. This proves 1).

2) implies 3), this follows from the fact that every topological group is completely regular and subspaces of completely regular spaces are obviously completely regular.

Finally assume 3), i.e. $S$ carries the initial topology with respect to all continuous functions $S to mathbb{R}$. Endow $mathbb{R}^{(S)}$ with the initial topology with respect to all homomorphisms $mathbb{R}^{(S)} to mathbb{R}$, such that the restriction $S to mathbb{R}$ is continuous. Then $mathbb{R}^{(S)}$ is an abelian topological group and $S to mathbb{R}^{(S)}$ is an embedding, thus 2).

I also believe that (but cannot prove)

• If $S$ is hausdorff and completely regular, $mathbb{Z}[S]$ is hausdorff.

In another comment, it was suggested to endow $mathbb{Z}[S]$ with the final topology with respect to $S to mathbb{Z}[S]$. But this does not even yield a translation invariant topology: If $S={a,b}$ with the only nontrivial open subset ${a}$, then ${a}$ is open in $mathbb{Z}[S]$, but ${b}$ is not.

But maybe, if $S$ is a completely regular space, the topology of $mathbb{Z}[S]$ used above is the final topology?

diy biology - How can I create a microcapillary for manipulation of single cells?

Here is a reference for pulling quartz glass pipettes using a custom oxy hydrogen burner. Here is a video of a commercial burner based pipette puller. Not sure what the specs are. I guess if you can melt your glass using a filament it could be easier than using a torch (a lightbulb circuit is easier to control than flame). People move to flame when dealing with high melting point quartz.

You can get a micropipette puller from Sutter for $1500 off of Ebay. I'm not completely sure how they work mechanically, but I have used many models. Someday I'd like to look inside them (the true mechanism is underneath, inside the box). They use a metal "boxcar shaped" filament that fits around the cappilary, and this heats up when a current is passed through. Two pulleys pull at the pipette, attached to something below doing the actual pulling.

I think there might be a spring-loaded mechanism for achieving the pull, rather than a motorized linear stage moving so fast. Maybe a stage or other actuator below pre-stretches a spring so that it is pulled to different degrees during melt cycle?

co.combinatorics - Combinatorics of lattice walks with forbidden points

First, let me confirm your formula for walks $(0,0) xrightarrow{m}(x,y)$ with $x+yequiv m ~mod 2$, $p_m(x,y)$, which you stated for $m=2n$.

Choose $(m+x+y)/2$ out of $m$ steps $s_i$ to be $(+1/2,+1/2)$ versus $(-1/2,-1/2)$.

Choose $(m+x-y)/2$ out of $m$ steps $t_i$ to be $(+1/2,-1/2)$ versus $(-1/2,+1/2)$.

Then letting $w_i = s_i + t_i$, $(w_i)$ are the steps of a walk $(0,0) xrightarrow{m}(x,y)$ with steps of $(pm 1,0)$ or $(0,pm 1)$.

---

Second, let me fill in some details for the generating function approach.

Any walk $(0,0) xrightarrow m (x,y)$ either avoids $(x_f,y_f)$, or it can be broken into $3$ pieces:

$(0,0) xrightarrow t (x_f,y_f)$ which first visits $(x_f,y_f)$ at the end,

$(x_f,y_f) xrightarrow {2u} (x_f,y_f)$ of size ${2u choose u}^2$.

$(x_f,y_f) xrightarrow {m-t-2u} (x,y)$ which last visits $(x_f,y_f)$ at the start.

The first and third pieces have the same form reversed in time. Let $q_n(a,b)$ be the number of paths $(0,0)xrightarrow n (a,b)$ which only visit (a,b) at the end.

$$sum_n p_n(a,b)x^n = bigg(sum_n q_n(a,b)x^nbigg)bigg(sum_n sideset{}{^{^{^2}}}{2n choose n} x^{2n}bigg)$$

$$sum_n q_n(a,b)x^n = sum_{n} p_n(a,b)x^n bigg/sum_n sideset{}{^{^{^2}}}{2n choose n} x^{2n}$$

So, a generating function for walks $(0,0) to (x,y)$ which visit $(x_f,y_f)$ is

$$bigg(sum_n q_n(x_f,y_f)x^nbigg)bigg( sum_nq_n(x-x_f,y-y_f)x^nbigg)bigg(sum_n sideset{}{^{^{^2}}}{2n choose n} x^{2n}bigg)$$

$$=bigg(sum_n p_n(x_f,y_f)x^nbigg)bigg( sum_nq_n(x-x_f,y-y_f)x^nbigg)$$

$$=bigg(sum_n p_n(x_f,y_f)x^nbigg)bigg( sum_np_n(x-x_f,y-y_f)x^nbigg)bigg/sum_n sideset{}{^{^{^2}}}{2n choose n} x^{2n}$$

You want to subtract this from $sum_n p_n(x,y)x^n$.

I don't see a closed form expression for the coefficients.

soil - How Do Acid and Base Loving Plants Get Enough PO4?

Fixation of phosphorous occurs when the chemical equations tip in favour of less soluble compounds. Plants are able to absorb Orthophosphate ions, such as H₂PO₄^- and HPO₄^2-.

Orthophosphate is most available to plants at pH values near neutrality. It is believed that in relatively acidic soils, orthophosphate ions are precipitated or sorbed by species of Al(III) and Fe(III). In alkaline soils, orthophosphate may react with calcium carbonate to form relatively insoluble hydroxyapatite:

3HPO₄^2- + 5CaCo₃(s) + 2H₂O -> Ca₅(PO₄)₃(OH)(s) +5HCO₃^- + OH^-

Environmental Chemistry, Seventh Edition -Stanley E. Manahan

This does tend to make it more difficult for plants to obtain their phosphorous when it is stuck to something that they cannot absorb, but it is not hopeless. These equations are equilibria, so they can be made to go both directions by adding or removing reagents from each side.

• The plants will pull from the left side of the equations by removing the orthophosphate ions. More will be released to maintain the equilibrium.


• In acidic or basic environments, rainwater will serve as a base or acid to push the equations from the right.


• Decaying organic matter releases orthophosphates that the plant can absorb.

In this way, plants living in acidic or basic environments would still obtain enough phosphorous.

evolution - Were there lifeforms before LUCA?

Well, what you seem to be suggesting is "Did life evolve twice on Earth?"

Your original question has an answer: Probably yes. It's not unlikely to think that the original cell evolved into two different paths and then one went extinct. However, that doesn't address LUCA. If we found fossil evidence of what we thought was LUCA, and then fossil evidence that LUCA had a genetic cousin - all that would do is push the application of the term "LUCA" on more evolutionary step backwards until both shared a common ancestor which would then be called LUCA. You can do this indefinitely until all life originates from a single cell, with countless offshoots which have gone extinct.

If you mean was there a whole other type of life - one that did not originate from LUCA and existed - then the best answer we have right now is "No." All life we know of, no matter how different and old, is still based on RNA/DNA and proteins. Fossil evidence supports this premise until about 3.5 BYA.

If there was an 'alternate' construction of life, we have not found the fossil evidence for it, and might not know what it was if we did. If the alternate form didn't utilize cells, we might not be aware we had it. If it did, but utilized different metabolisms or structures for proteins and storage - that evidence would be long gone by now.

Our best bet for answering if life can evolve differently than what we have today is out among the stars.

botany - Filamentous algae - what exactly am I looking at?

It looks indeed like a Spirogyra, or at least a member of the Zygnematales.
And yes, the green things are the chloroplasts (or one long chloroplast?), and they are arranged in spiral.

The "empty" space in the middle is likely the nucleus, and the darker circles within the chloroplast(s) could be the starch accumulated at the periphery of pyrenoids.

bioinformatics - Any tool to align whole genome sequence data to another genome and give exon regions a higher mark?

If you are not trying to assemble but just to align each read to the genome, you can use exonerate. On a Unix/Linux platform, once you have installed it run something like:

exonerate -m genome2genome WGS.fasta genome.fasta > out.txt 

From the exonerate manual:

          genome2genome
                 This  model  is  similar  to  the  cod‐
                 ing2coding  model,  except  introns are
                 modelled on both sequences.  (not work‐
                 ing well yet)

What I would recommend though, is to align against a reference cDNA dataset, not the whole genome. In that case, you should use this instead:

exonerate -m cdna2genome genome_cdna.fasta WGS.fasta > out.txt 

From the exonerate manual:

          cdna2genome
                 This   combines   properties   of   the
                 est2genome and coding2genome models, to
                 allow modeling of an whole cDNA where a
                 central coding region can be flanked by
                 non-coding UTRs.  When  the  CDS  start
                 and  end  is  known it may be specified
                 using  the  --annotation  option   (see
                 below)  to permit only the correct cod‐
                 ing region to appear in the alignemnt.

immunology - Multi-nucleated cells: advantages and examples?

Muscle cells are the only cells I know of that are polynuclear. With respect to monocytes, a concise review of their nomenclature can be found in this paper by L Ziegler-Heitbrock, P Ancuta, S Crowe, et al. (Blood, 2010). Apparently it has had quite a complex and confused biochemical characterization, but the article states the name indeed derived from its single lobed, mononuclear morphology. This is in distinction to other phagocytes which have multi-lobular nuclei (polymorphonuclear cells).

With respect to advantages, a multinucleated cell makes sense when the speed of intracellular signalling is important (e.g., calcium diffusion). It may also be useful in the case of cells when the cell needs to coordinate the synthesis of large amounts of protein.

I think evolution has goal

Yes you are wrong I am afraid. Evolution is the process of change through time of species by inherited changes. Heritable differences mainly come about from random mutation in the genome. These genetic differences between individuals lead to fitness differences between individuals, ie one individual is better able to produce offspring, thus spreading more of its genes in to the following generation, than another individual. For example, environmental change causes selection for a dark body morph in moths, stabding genetic variation and new mutations affecting body colour is then more favored by selection, and those with the dark body genes survive and reproduce better.

There is no end or goal to evolution. It is often mistakenly said that humans have stopped evolving. This is wrong and to suggest we have is to suggest that evolution is directed and has an ultimate goal. As long as genetic fitness variation exists there will always be some level of evolution because there is a difference between individuals in selection coefficient. Selection is also very unstable, it can change drastically an rapidly, evolution could only then stop if selection was constant and favored one "ultimate genotype" over all others in which case all genetic variation would cease to exist.

If we found another planet which had the exact same conditions and time as earth we may find the same species, but it is not likely. It requires the same mutations and selection processes occurring. Analogous to this is the observation of "many solutions to one problem" where different species use different adaptations to deal with a common problem. For example, geting oxygen is difficult for water deelling species. Sea mammals like whales gather oxygen by going to the surface and breathing and then holding their breath. Fish have evolved gills, a different solution to the same problem, to harvest oxygen from the water. These solutions evolve from random changes with selection acting only on the results (those that could filter oxygen from the water or hold their breath the best survived and reproduce best).

cell biology - Intracellular lipid transport

I know that lipids are carried around the body in the blood either as micelles or by lipid-binding proteins which allow them to be solved.

Lipids can't always be integrated in a membrane though, the phospholipids used in membranes have to be synthesised somewhere from a precursor which will also by hydrophobic.

Consequently, at some point there will have to be transport of lipids within the cell where the lipids will need to be in solution. How is this facilitated?

proteins - Why glycoproteins are better than non-glycoproteins in fulfilling biological tasks?

I have just an intuition that the carbohydrate part of glycoproteins help them to fulfil those tasks like in plasma membranes.
You can also get many more receptors if you can use carbohydrates too.

For instance, glycoproteins are necessary in recognising white blood cells. Antibodies are examples of glycoproteins. So they play a crucial role in our innate and adaptive immunity: MHC interaction with T cells in adaptive immunity.
Other examples: necessary in platelet aggregation and adherence, components of zona pellucida and connective tissue. Some hormones are also glycoproteins so necessary in humoral adaptive immunity: FSH, LH, TSH and EPO.

But why glycoproteins are "better" than proteins without carbohydrates moiety in fulfilling biological tasks?

I still see that both are important, but why the one is better than the other one.

In other words: Are there any biological tasks that only non-glycoproteins can fulfil, not glycoproteins? Are non-glycoproteins necessary in some essential biological tasks?

I think the answer to the last two questions is "yes", so why would one say that glycoproteins are better in fulfilling biological tasks than non-glycoproteins.

molecular biology - Will eukaryotic RNA fold in the same way in prokaryotes?

As you have mentioned ions and temperature affect RNA structure. There are also different types of RNA structures and their dependence on ions are different. Mg²⁺, as Mad Scientist mentioned, stabilizes duplexes; so do monovalent cations like K⁺ and Na⁺. However, Mg²⁺ favors duplex over quadruplex if the same RNA can adopt both these conformations.
Dependence on temperature is a trivial case.

Ions and temperature should be more or less same for prokaryotes and eukaryotes unless we are talking about extremophiles.

Apart from these factors I can think of two other factors that can cause difference in RNA structure between prokaryotes and eukaryotes:

• Osmolytes


• RNA binding proteins/chaperones (Already mentioned in comments by Mad Scientist)

Osmolytes

It has been shown that TMAO (Trimethylamine N-oxide) stabilizes RNA secondary structures. The metabolism of TMAO is different in prokaryotes and eukaryotes.

From this paper:

Although eukaryototes can endogenously produce L-carnitine, only
prokaryotic organisms can catabolize L-carnitine¹¹. A role for
intestinal microbiota in TMAO production from dietary carnitine was
first suggested by studies in rats; moreover, while TMAO production
from alternative dietary trimethylamines has been suggested in humans,
a role for microbiota in production of TMAO from dietary L-carnitine
in humans had not yet been demonstrated^30-32. The present studies
reveal an obligatory role of gut microbiota in the production of TMAO
from ingested L-carnitine in humans (Fig. 6c)

I cannot ascertain that this will affect RNA folding but is possible.

RBP

This is something that you can be certain about. Some RNAs require protein counterparts to adopt a functionally capable structure. In the absence of the protein they may not form the relevant structure. So if an RNA needs Hfq then you have to express it in the eukaryotic system where you want to use the RNA (and converse).

human biology - Whence fecal E. coli (et al.) if swallowing it is dangerous?

E. coli is mostly harmless; only a few strains are harmful.

I don't believe the route by which gut biota is established has been entirely established for any species but, for example, koala feed their faeces to their offspring to help them establish biota capable of digesting eucalyptus. It seems that a small proportion of ingested bacteria somehow survive passage through the stomach to the gut and then begin multiplying and colonising the intestines.

It's also important to realise that just because an organism is sometimes harmful doesn't mean it always is. There are many microorganisms that are pretty much ubiquitously found on or in your body which are capable of causing disease but only do so very rarely; usually when the body's defences have already been compromised (e.g. Pseudomonas aeruginosa, Candida albicans aka thrush, and so on).