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# Chapter 1 Introduction

Analyzing and visualizing fiber photometry data with fluoR is a continuously updated book of tutorials and background information for analyzing and visualizing time series data from behavioral experiments.

## 1.1 Why use fluoR?

The fluoR R package is the successor to the GCalcium package, which I initially wrote to help ensure that my fiber photometry data analyses were accurate, consistent, and transparent. Both R packages and this continuously-updated document were publicly released to save other researchers the time and uncertainty in working with their own data, along with helping keep my knowledge fresh. I will mostly avoid discussion on biological topics for now.

Calcium imaging technologies such as GCaMP produce massive datasets. With repeated trials for each subject, researchers can end up with tens of thousands of data points per subject. Complicating matters further, there seems to be no gold standard for working with and analyzing this type of data.

fluoR…

• is open-source and transparent
• has its own user manual
• is free to use

## 1.2 Who is fluoR for?

Some examples of researchers who may find fluoR useful are those who:

• have recorded multiple trials of time series waveform data
• want to look at their recorded data with minimal coding while still knowing how their code works
• want to test GCaMP data before using the hardware (see GCaMP sample dataset)

## 1.3 Background

### 1.3.1 pre-recording

I initially wrote the fluoR package (then named GCalcium) for a pilot study by Dr. Michael Baratta. After the main investigators set up the GCaMP6m fiber photometry technology, neural activity was continuously recorded in the infralimbic region (IL) of the ventromedial prefrontal cortex (mPFCv) during escapable tail shock - a “controllable” stressor. We wanted to examine if post-trial neural activity in the rat IL changes after repeated exposure to a controllable stressor.

There were two main issues that resulted in us using GCaMP for measuring neural activity:

1. electrophysiology is difficult to conduct when using tail shock as a stressor
2. fos examination is limited temporally

The included GCaMP dataset is a sample of 10 random trials from this pilot study.

### 1.3.2 recording

For recording, we used fiber photometry equipment from Tucker-Davis Technologies, which was set up by Dr. David Root.

### 1.3.3 post-recording

Dr. Root also provided us with a modified version of a Matlab script to load and pre-process the data (Root 2018). Ultimately, I decided to export the data for use in another program after the signal averaging step.

There were a couple of Python add-ons that looked promising. Unfortunately, none of them seemed to discuss how they worked or why the authors took the steps that they did. Using these would make me at odds with my philosophy of “don’t run analyses if you don’t know how they work”. I decided that R, which I had a much more solid background in, was the answer.

While R is generally slower than Matlab, the syntax is much simpler and it is easier to keep track of the steps you took along the way. Additionally, there are a handful of R packages (e.g. ggplot2, plotly) that allow for publication-ready graphs.

Did I mention R is free?

### References

Root, David H. 2018. “Fiber Photometry Epoch Averaging Example.” Fiber Photometry Epoch Averaging Example. https://www.tdt.com/support/matlab-sdk/offline-analysis-examples/fiber-photometry-epoch-averaging-example/.

format: plain


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Sunday, May 10, 2020 | History

2 edition of Capital deepening in an economy with heterogenous capital goods found in the catalog.

Capital deepening in an economy with heterogenous capital goods

Edwin Burmeister

# Capital deepening in an economy with heterogenous capital goods

## by Edwin Burmeister

• 240 Want to read
• 8 Currently reading

Published by Wharton School of Finance and Commerce, Dept. of Economics in Philadelphia .
Written in English

Edition Notes

 ID Numbers Statement by Edwin Burmeister and Stephen J. Turnovsky. Series Discussion paper / Wharton School of Finance and Commerce, Department of Economics -- No.209 Contributions Turnovsky, Stephen J. Open Library OL13835020M

Intertemporal Equity and Efficient Allocation of P.J. HammondMaximin paths of heterogeneous capital accumulation and the instability of paradoxical steady states. Econometrica, 45 (), pp. Google Scholar. 2. E. Burmeister, S.J. TurnovskyCapital deepening response in an economy with heterogeneous capital goods. Amer. Econ. Rev Cited by: Capital deepening refers to an increase in the amount of capital per worker, either human capital per worker, in the form of higher education or skills, or physical capital per worker. Technology, in its economic meaning, refers broadly to all new methods of production, which includes major scientific inventions but also small inventions and.

Human Capital Deepening in the U.S. Rising levels of education for persons 25 and older show the deepening of human capital in the U.S. economy. Even today, relatively few U.S. adults have completed a four-year college degree. There is clearly room for additional deepening of human capital . Downloadable! Author(s): Daron Acemoglu & Veronica Guerrieri. Abstract: This paper constructs a model of non-balanced economic growth. The main economic force is the combination of differences in factor proportions and capital deepening. Capital deepening tends to increase the relative output of the sector with a greater capital share (despite the equilibrium reallocation of capital and.

9 Some implications of capital heterogeneity Benjamin Powell* Introduction A tractor is not a hammer. Both are capital goods but they usually serve different purposes. Yet both can be used to accomplish more than one goal. A tractor can be used to plow a . response when we are confronted with a disaggregated economy witlh many heterogeneous capital goods. A slightly generalized definition has been made available by the Cambridge approach,3 in which a capital deepening response is defined in terms of the change in the value of per worker capital goods stock. This definition has an advantage.

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### Capital deepening in an economy with heterogenous capital goods by Edwin Burmeister Download PDF EPUB FB2

Capital Deepening Response in an Economy with Heterogeneous Capital Goods By EDWIN BURMEISTER AND STEPHEN J. IURNOVSKY* Capital deepening is an important con-cept in traditional capital theory. In a one-sector model it has an unambiguous definition, describing an increase in the physical capital-labor ratio.

Moreover, the. Capital deepening is an important con- cept in traditional capital theory. In a one-sector model it has an unambiguous definition, describing an increase in the physical capital-labor ratio Cited by: Capital deepening response in an economy with heterogeneous capital goods.

Capital deepening is an important con- cept in traditional capital theory. In a one-sector model it has an unambiguous definition, describing an increase in the physical capital-labor : Edwin Burmeister and S. J Turnovsky. Download PDF: Sorry, we are unable to provide the full text but you may find it at the following location(s): ?si (external link)Author: Edwin Burmeister and Stephen J Turnovsky.

Burmeister, E. and N.V. Long,On some unresolved questions in capital theory: An apphcation of Samuelson's correspondence principle, Quarterly Journal of Econom Burmeister, E. and S.J. Turnovsky,Capital deepening in an economy with heterogeneous capital goods, American Economic Rev Cited by: 6.

Part of the The New Palgrave book series (NPA) Abstract. In realistic Burmeister, E. Real Wicksell effects and regular economies.

In Essays in Modern Capital deepening response in an economy with heterogeneous capital goods. American Economic Rev December, – Google Scholar. Kuga, K. More about joint production. Definition capital widening. means that the capital stock will increase at the same rate as the labour force and lead to constant labour productivity (output per worker).

Capital widening involves greater investment to make use of existing technology and increase the amount of capital available. Capital deepening attempts to increase output through better technology and higher output per worker, for example, a new technology which makes capital.

As it becomes clear in this work, Menger would have opposed all attempts to define capital as a heterogeneous structure of higher-order goods - A definition that is associated with his name : Eduard Braun. In realistic economic models with n different types of capital goods, the value of the capital stock is $$V={\displaystyle \sum_{i=1}^n{P}_i{K}_i}$$ where P i is the price of the i th capital good in terms of some numéraire.

shares of capital) combined with capital deepening lead to nonbalanced growth because an increase in the capital-labor ratio raises output more in sectors with greater capital intensity.

We illustrate this economic mech-anism using an economy with a constant elasticity of substitution be. Capital deepening is a situation where the capital per worker is increasing in the economy. This is also referred to as increase in the capital intensity.

Capital deepening is often measured by the rate of change in capital stock per labour hour. Acemoglu and Guerrieri () show for a two-sector economy that capital deepening, i.e.

an increase in the economy-wide capital intensity tends to raise the output share of the capital-intensive. Capital Deepening and Non-Balanced Economic Growth Daron Acemoglu MIT Veronica Guerrieri University of Chicago First Version: May This Version: March Abstract We present a model of non-balanced growth based on di⁄erences in factor proportions and capital deepening.

Capital deepening increases the relative output of the more capital. Downloadable (with restrictions). We present a model of nonbalanced growth based on differences in factor proportions and capital deepening. Capital deepening increases the relative output of the more capital-intensive sector but simultaneously induces a reallocation of capital and labor away from that sector.

Using a two-sector general equilibrium model, we show that nonbalanced growth is. capital deepening. increases in an economy's stock of capital (buildings and equipment) relative to its workforce.

technological progress. economy operates more efficiently, producing more output, but without using any more inputs such as capital or labour. human capital. A situation when the capital stock grows at the same rate as the labour force, so that the capital–labour ratio remains constant, while the aggregate output continues to grow.

See also capital deepening. proportionsacrosssectors(i.e.,differentsharesofcapital)combinedwithcapitaldeepening 'All data are fromtheNational Income andProductAccounts(NIPA).For details and definitionsofservices, manufacturing,employment, real GDP and capitalshare,see Appendix B.

1With capital deepening an increase in the ratio of capital and labor used in production is meant here. 2E.g. Helpman, Melitz and Yeaple () or Grossmam, Helpman and Szeidl (). 3Horizontal FDI corresponds to the situation where a ﬁrm serves the foreign market by producing.

6 Figure 3: Reverse capital deepening According to the neoclassical doctrine1, the substitution should always ‘deepen’ the intensity of capital, whenever the wage rate w increases relatively to the rate of profit r. Reverse capital occurs, if the exact opposite takes place: A rise in the rate of profit r leads to the adoption of a more capital intensive technique.

The details of his argument, which extends over most of a dense pages, is beyond the scope of this article but has to do with the economic effect of capital deepening. He argues that in industrialized and post-industrial economies, the infusion of capital produces wealth at a growth rate that exceeds the growth rate of the broader economy.

Labor's share of the wealth : Mike Moffatt. Capital deepening is a situation where the capital per worker is increasing in the economy. This is also referred to as increase in the capital intensity.

Capital deepening is often measured by the rate of change in capital stock per labour hour. Overall, the economy .Figure Human Capital Deepening in the U.S. Rising levels of education for persons 25 and older show the deepening of human capital in the U.S.

economy. Even today, under one-third of U.S. adults have completed a four-year college degree. There is clearly room for additional deepening of human capital .Capital deepening refers to an increase in the proportion of the capital stock to the number of labor hours worked. Movements in this ratio are closely tied to movements in labor productivity, all other things held equal.

An increase in capital per hour (or capital deepening) leads to an increase in labor productivity.


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# How to design wheels for a soapbox-derby racer so that it rolls down a hill the fastest? [closed]

The following problem is from the book "University Physics", Chapter 10 entitled Dynamics of Rotational Motion.

10.2 Suppose you could use wheels of any type in the design of a soapbox-derby racer (an unpowered, four-wheel vehicle that coasts from rest down a hill). To conform to the rules on the total weight of the vehicle and rider, should you design with large massive wheels or small light wheels? Should you use solid wheels or wheels with most of the mass at the rim?

I am not sure what is meant by "conform to the rules" here, since no rules are specified.

It seems that by assumption these wheels are "round".

I started with the following conservation of mechanical energy calculation

$$mgh=\frac{mv^2}{2}+2\frac{I\omega^2}{2}=\frac{mv^2}{2}+\frac{Iv^2}{R^2}$$

$$v=\sqrt{\frac{2R^2mgh}{mR^2+2I}}\tag{1}$$

This calculation assumes that we have two identical wheels with moment of inertia $$I$$ and radius $$R$$.

We would like to maximize this speed.

Now, a previous similar calculation in the book assumed that these wheels were one of the following uniform shapes

• hollow cylinder
• solid cylinder
• thin-walled hollow cylinder
• solid sphere
• thin-walled hollow sphere

These are all shapes for which the moment of inertia about an axis passing through the center of mass has form $$CmR^2$$ where $$C$$ is a constant.

The constant is smallest for a solid sphere. Hence, if we were simply setting these shapes to roll down an incline, the solid sphere would reach the bottom first.

Now, if we substitute $$I=CmR^2$$ into (1) we obtain

$$v=\sqrt{\frac{2gh}{1+2C}}\tag{2}$$

It would seem at first sight that having solid spheres for wheels is the best option. Note that $$m$$ and $$R$$ disappear from the expression.

However, this seems fishy and weird.

At this point my idea was, for a given $$M$$ and $$R$$, to come up with some other round shape with a lower moment of inertia.

To do this, all you have to do is concentrate the mass within a small radius and have a bit of mass on the rim.

I tried out an example with some numbers I came up with to try to reach the configuration of what a normal bicycle wheel would look like (except that in my case since the mass is given, I concentrate most of the mass at the center of the wheel)

I did not draw it in the picture above, but the shape is cylindrical and has width of $$h$$.

Let $$r_2=10r_1$$ $$r_3=11r_1$$

Let the mass densities be

$$\rho_1=\frac{m_1}{\pi r_1^2 h}$$ $$\rho_2 = \frac{\rho_1}{10000}$$ $$\rho_3=\frac{\rho_1}{1000}$$

I imagine this as representing a dense core, some spokes, and a rim that is less dense than the core.

This results in

$$m_2=\frac{1}{100}m_1$$ $$m_3=\frac{121}{1000}m_1$$

and when we compute the moment of inertia of the entire thing, if my calculations are correct, we get

$$I=0.02426Mr_3^2$$

where $$M=m_1+m_2+m_3$$.

This is much lower than the initially considered shapes.

Now, this is still not a satisfactory result, because I assumed that $$M$$ and $$R=r_3$$ were given.

It is not clear to me how we can find the absolute best wheel design here. And this is my question.

Here is my attempt at answer

Starting from (1) and computing the partial derivatives with respect to $$R$$ and $$m$$ (and naively taking $$I_{cm}$$ as constant), it seems that both are positive. Hence it would seem the best thing is to choose these to be as small as possible.

However, then I realize that moment of inertia is dependent on $$m$$ and $$R$$ and if the relationship is $$I=CmR^2$$ then apparently $$m$$ and $$R$$ are irrelevant.

• I am not sure why I used two wheels instead of four or three, or one for that matter.

• I guess there would be a person on a platform above the wheels, and we would assume the wheels are turning about an axis that is somehow connected to the platform but without friction of any kind.

Equation 1 is reasonable for a lone rotating object of mass $$m$$. But the racer will have multiple components, not just wheels. The total mass of the racer will be larger than the total mass of the wheels.


text:
# When does “pairwise” strengthen and when does it weaken?

"Pairwise disjoint" is stronger than "disjoint"; it sometimes happens that $\displaystyle\bigcap\limits_{i\in I} A_i=\varnothing$ but for every $i,j$, or at least for some, one has $A_i \cap A_j\ne\varnothing$.

Likewise, "pairwise coprime" is stronger than "coprime".

"Pairwise independent" (in the probabilistic sense) is weaker than "independent". For example, suppose $X_1,\ldots,X_n$ are independent and uniformly distributed on the sphere $S^n$; then the great-circle distances $d(X_i,X_j)$ and $d(X_k,X_\ell)$ are independent if $\{i,j\}\ne\{k,\ell\}$ even if $i=k$, but $d(X_i,X_j), d(X_j,X_k), d(X_k,X_i)$ are not independent even though each of the three pairs of these three random variables is a pair of independent random variables.

Question: Is there a somewhat general rule that says for which sort of X the qualified "pairwise X" is stronger than "X" and for which sort it is weaker than "X"?

Here's a guess: Some sort of category-theoretic viewpoint can make some kind of sense of this. (?)

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Many people use "disjoint" and "pairwise disjoint" synonymously. I have seen "free" be used for families with nonempty intersection (as in "free ultrafilter"). The case of independence and pairwise independence is essentially about local and global properties. – Michael Greinecker Apr 16 '12 at 23:36
I am not entirely sure why this is tagged foundations. To me that tag suggests en.wikipedia.org/wiki/Foundations_of_mathematics This feels to me more a question about (notation) or (terminology). – Willie Wong Apr 17 '12 at 5:24
@WillieWong : Maybe it's because as soon as I suspect category theory of being involved, I think "foundations". Maybe that's obsolete by 75 years or so? – Michael Hardy Apr 17 '12 at 12:37
I agree with Willie that the [foundation] tag seems off, and personally I am not sure there is a real need for this tag too. – Asaf Karagila Apr 17 '12 at 21:51
I don't think I've ever seen "disjoint" used (for sets) in any other way than as a synonym for "pairwise disjoint". – Robert Israel Apr 27 '12 at 2:31

I used to ponder this question some time ago but didn't come up with a satisfactory answer. The problem seems to be that until someone gives a formal treatment of the adjective "pairwise" in mathematics, it must remain a linguistic problem.

For what it's worth, here's what I've got. It's just some examples and some loose thoughts. I'll be perhaps using some non-standard notation or terminology but I think it's all going to be clear from context. I may also be talking nonsense, and I would ask everyone to point that out. I'd like to know if what I've written is too vague, silly, or just false so I can try to correct this answer or delete it.

We have "pairwise disjoint" and "disjoint" (let's assume that people actually use "disjoint" without "pairwise" in the wanted sense). A non-empty family of sets $\mathcal A\subseteq 2^X$ for some set $X$ is pairwise disjoint iff $$(\forall A_1,A_2\in\mathcal A)\;\;A_1\cap A_2=\varnothing.$$

$\mathcal A$ is disjoint iff $$\bigcap \mathcal A=\varnothing.$$

So what we have here is the operation $\cap$ which we can feed as many sets as we like. We can feed it two, and we can feed it all.

We have "pairwise coprime" and "coprime". A non-empty set of natural numbers $S$ is pairwise coprime iff $$(\forall s_1,s_2\in\mathcal S)\;\;\gcd(s_1,s_2)=1.$$

$S$ is coprime iff $$\gcd(S)=1.$$

In both cases "pairwise" is stronger. $\cap$ and $\gcd$ are meet operations in complete lattices whose respective join operations are $\cup$ and $\operatorname{lcm},$ and $\varnothing$ and $1$ are the meets of those whole lattices. In such cases "pairwise" will always be stronger! Let $L$ be a complete lattice, $\varnothing\neq A\subseteq L$ and $a_1,a_2\in A.$ Then $$\bigwedge L\leq\bigwedge A\leq a_1\wedge a_2,$$

And so $\bigwedge L=a_1\wedge a_2$ implies $\bigwedge L=\bigwedge A.$ That is, even one pair, let alone all pairs, of elements of $A$ having $\bigwedge L$ as a meet implies that the meet $A$ is $\bigwedge L.$

What happens when we give dual definitions for the join operations?

Let's say $\varnothing\neq\mathcal A\subseteq 2^X$ is pairwise full (made-up term) iff $$(\forall A_1,A_2\in\mathcal A)\;\;A_1\cup A_2=X.$$

Let's say $\mathcal A$ is full iff $$\bigcup\mathcal A=X.$$

Again, "pairwise" is stronger, which is not surprising. For $\operatorname{lcm}$ the pairwise condition becomes too strong to be worth considering -- the join of the whole lattice is then $0$ and no two numbers have the least common multiple equal to $0$.

One more remark is that the non-emptiness I've kept assuming is necessary for the conclusions to be true. If we drop it, the "pairwise" conditions will stop being stronger! For example $$(\forall A_1,A_2\in\mathcal \varnothing)\;\;A_1\cap A_2=\varnothing$$ is true, but $\bigcap\varnothing$ is equal to $X.$

Now, an example of "pairwise" being weaker. These might be again made-up conditions, but I think they're justified enough linguistically. Let's again consider the family $\mathcal A$, and say that $\mathcal A$ is pairwise intersecting iff $$(\forall A_1,A_2\in\mathcal A)\;\;A_1\cap A_2\neq\varnothing.$$

Let's say that $\mathcal A$ is intersecting when $$\bigcap \mathcal A\neq\varnothing.$$

In fact, why not try making up some strange example and see what happens? All we need is a "formula" we can feed as many variables as we want (perhaps finitely many). Unfortunately, when I tried to define what I mean by "formula" here, it started becoming much more complicated than I wanted. But see if this example works. Let's say that a finite nonempty set $S$ of the set of positive integers "pairwise adds up to eight" iff $$(\forall s_1,s_2\in S)\;\;s_1+ s_2=8.$$ Let's say that $S$ "adds up to eight" iff $$\sum S=8.$$ Now $\{8\}$ adds up to eight, but not pairwise. Is the pairwise condition weaker then? No, the set $\{4\}$ adds up to eight pairwise, but doesn't add up to eight.

This seems very complicated. And I think I simplified some things above. I should have probably been talking about multisets instead of sets. (That is for example $\mathcal A$ should have been allowed to be a multiset.) Also, I used the operations $\cap$, $\cup$, $\gcd$ and $+$, which all yield results from the same set as the operands. This surely can't be necessary. I don't think the case of independence of random variables can be considered by using such operations.

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I understand why the intersection of no sets is the universe, but I don't understand why the intersection of any two members of the empty set is the empty set. – Michael Hardy May 2 '12 at 23:20
@MichaelHardy The formula can be rewritten as $(\forall A_1)(\forall A_2)((A_1\in\varnothing \wedge A_2\in\varnothing)\implies A_1\cap A_2=\varnothing)$ But there is no $A_1$ such that $A_1\in\varnothing.$ Therefore for every $A_1$ the antecedent is false. Therefore the whole quantified formula is true. – user23211 May 2 '12 at 23:52

It depends on which way the implication goes between the pairwise property and the property of the whole set.

More generally, sometimes if a property $P(S)$ holds for an entire set $S$, then we are assured that it also holds for all subsets of $T$ of $S$, such as pairs. In other words:

$$P(S) \implies \forall T:T \subset S \to P(T)$$

The implication sometimes goes the other way: if we know the property holds for subsets of $S$, then it holds for $S$:

$$\forall T:T \subset S \to P(T) \implies P(S)$$

Or it could be the case that the property of the whole is independent of the property of subsets.

It could also be the case that the relationship is actually $\Leftrightarrow$. For instance an equivalence relation is like this. If elements of a set are all equal pairwise, then necessarily, all elements are equal to each other, and vice versa.

Whether the subset-based proposition is weaker than the whole-set one depends on whether they are connected together logically, and, if so, how: which way does the implication point, or are they logically equivalent.

(Note that this is a very general idea; for instance I'm glossing over situations when, say, it is understood that the pairs in "pairwise" are formed by the cartesian product of the set with itself, and are tuples, rather than sets. The same principles apply, if not the exact formulas.)

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I've edited this answer without changing its content to remove my downvote, which I gave because I misunderstood the answer. (I thought it was completely trivial, which it's not.) I'm sorry. I'm changing it to an upvote. – user23211 May 1 '12 at 15:59


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# How to change the scene in Unity after all enemies have been killed?

I have a script that counts how many enemies are left and changes the scene when there are no more enemies. However, it doesn't work, and I can't find the error. I have a really similar script (it's almost the same to be honest) that works perfectly, but I can't figure out how to make this script work.

Here's the code:

public class enemyCountt : MonoBehaviour {

public static int enemiessCount = 5;

void Start() {}

void Update(){
print("Enemy count is " + enemiessCount );

if(enemiessCount <= 0)
{
}
}
}

and this is attached to the bullet script:

if (collision.gameObject.tag == "Enemy") {
enemyCountt.enemiessCount --;
}

• What do you mean by "it does not work"? What happens instead of what you expect? Is the same script attached to more than one scene? – Vaillancourt Nov 29 '17 at 13:49
• I want to change the scene when there are no more enemies (when enemiessCount <= 0) but it doesn't happen, it just keep going until the time ends and the game is over. And no, it's not the same script attached in more than one scene – tomy11010 Nov 29 '17 at 13:51
• Throw in a print("something"); line before SceneManager.LoadScene and tell us if it shows up. That will narrow down the problem – AzulShiva Nov 29 '17 at 13:51
• Maybe a dumb question, but are you sure enemyCountt script is attached to a gameobject in your scene? – Hellium Nov 29 '17 at 14:03
• You might find some use in this earlier question about reacting when all objects of a type have been destroyed – DMGregory Nov 29 '17 at 14:10

You are using 2 different scripts, so just enemyCountt.enemiessCount --; wont work. if both scripts are on the same gameobject, then you can use gameObject.enemyCountt.enemiessCount --;

if these arent in the same gameobject, then you can make a reference from the other gameobject with the other script

     public GameObject OtherObject;

void Update(){
if (collision.gameObject.tag == "Enemy") {
OtherObject.enemyCountt.enemiessCount --;
}

then you have in the object, where you added the script, a free field, where you can drag & drop your GameObject with the script "enemyCountt" and then it should work, but I'm not quite sure

• so just enemyCountt.enemiessCount --; wont work Yes it will, they've declared enemiessCount as being static. There are other small issues with your answer as well, the primary one being that it does nothing to address the asker's comments that their Update() method is not running. – Draco18s no longer trusts SE Nov 30 '17 at 19:24


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# Smooth Manifolds

 Title: Smooth Manifolds Authors: Fabian Immler and Bohua Zhan Submission date: 2018-10-22 Abstract: We formalize the definition and basic properties of smooth manifolds in Isabelle/HOL. Concepts covered include partition of unity, tangent and cotangent spaces, and the fundamental theorem of path integrals. We also examine some concrete manifolds such as spheres and projective spaces. The formalization makes extensive use of the analysis and linear algebra libraries in Isabelle/HOL, in particular its “types-to-sets” mechanism. BibTeX: @article{Smooth_Manifolds-AFP, author = {Fabian Immler and Bohua Zhan}, title = {Smooth Manifolds}, journal = {Archive of Formal Proofs}, month = oct, year = 2018, note = {\url{https://isa-afp.org/entries/Smooth_Manifolds.html}, Formal proof development}, ISSN = {2150-914x}, } License: BSD License


text:
Welcome to Doom9's Forum, THE in-place to be for everyone interested in DVD conversion. Before you start posting please read the forum rules. By posting to this forum you agree to abide by the rules.

 Doom9's Forum Guide to convert BD 3D to 3D Left+Right Stereoscopic and Anaglyph
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 21st June 2010, 17:50 #1  |  Link crl2007 Registered User   Join Date: Nov 2007 Posts: 650 Guide to convert BD 3D to 3D Left+Right Stereoscopic and Anaglyph This guide adresses to the new BD 3D format. Software and codecs needed: 1. ffdshow + haali 2. MVC Decoder - free 3. eac3to - free 4. x264 - free 5. Stereoscopic Player - not free 6. Preferred Filter Tweaker for Windows 7 - it's free and straight forward 7. multiAVCHD - free 8. ArcSoft TotalMedia Theatre 3 Platinum or PowerDVD 9 - not free Let's start. Pay attention and don't skip any steps. STEREOSCOPIC LEFT+RIGHT CONVERSION 1. Demux the mpls with eac3to. eac3to x:\path\movie.mpls -demux. You will get all streams demuxed, but you'll need only video and audio streams (left video + right video + audio stream). You'll see (left) and (right) as part of the file name of the video streams (h264). For convenience, rename the demuxed audio (dts/ac3/lpcm) to audio.dts (or audio.ac3 or audio.lpcm) or audio_01.dts/audio_02.ac3 if you have more than one audio track. 2. Create a 3D Workspace folder and copy in there the mvc decoder, the x264 codec, the avs script included and the left + right video + audio streams. 3. Rename the video streams (left.h264, right.h264). This is needed if you don't want to edit "decoder.cfg" all the time to insert the name of the streams in there. 4. Edit the avs script and put in there the duration, in frames, of the movie. You must include the ms. You can find out the frame number from eac3to. You can also do it manually. That's done like this: Example: For a 00:02:27.106 movie the ecuation is 147,106*(24000/1001) and you'll have 3527 frames. My script looks like this: LoadPlugin("H264StereoSource.dll") H264StereoSource("decoder.cfg",3527) Save it. 5. Open a command prompt for x264 and use the avs to encode the right eye stream (tutorials for x264 can be found on doom9 too). When x264 reaches the end, you will get an error. This has no impact on the movie. Keep in mind that this decoder is really, really slow. On a q9550 and 4 GB RAM it didn't go higher than 3 fps. 6. Open mkvmerge and add left.h264 + audio.dts (or audio.ac3, audio.lpcm). Select the video stream and from the "Format specific option" tab and set the fps to 24000/1001 (mkvmerge will set it to 25 fps by default). Mux them together. 7. After the remux is done, remove all from mkvmerge and insert the encoded right eye stream. Set the FPS to 24000/1001 as for the left one above and hit mux. 8. Now they are ready to be played in Stereoscopic Player. Open Stereoscopic Player - File - Open Left and Right file, select the 2 streams and check "Use audio track from left file". ANAGLYPH ONLY CONVERSION 1. Open multiAVCHD and drag and drop the movie playlist. 2. Do the following settings: 3. Press transcode, choose your settings and check "Create 3D Anaglyph". Click "Apply". 4. You can add as many subtitle streams you want and as many audio streams you want from the "Audio" and "External Subtitles" stream. 5. Click "OK". 6. Click start and let multiAVCHD work. Important Update: You can now select from multiavchd more 3D modes ( green/magenta, top/bottom, left/right etc ). All you have to do is to set your mode before adding a playlist. The same steps as for anaglyph are used here too. SUBTITLE FOR STEREOSCOPIC 3D MOVIES Software Needed: 1. 3D Subtitler The software is pretty straightforward. If you have something to add, please feel free. Last edited by crl2007; 10th December 2010 at 00:02.
 29th June 2010, 02:51 #2  |  Link chocolate elvis Registered User   Join Date: Jun 2010 Posts: 4 Hi, Thanks for the post. Have trouble getting it to work though. Do you mind expanding #5 "Open a command prompt for x264 and use the avs to encode the right eye stream (tutorials for x264 can be found on doom9 too)." Thanks!
 29th June 2010, 03:05 #3  |  Link Guest Guest   Join Date: Jan 2002 Posts: 21,922 What do you not understand about it? Looks perfectly clear to me.
 29th June 2010, 09:58 #4  |  Link crl2007 Registered User   Join Date: Nov 2007 Posts: 650 You open a command prompt and you write there: x264 --x264 parameters --output.264 *.avs l.e. I've updated the guide with the new MVC Decoder ( now it supports 720p sources too ) and with an alternate option for stereoscopic + new modes conversion ( for people that don't know how to use x264 ). Last edited by crl2007; 29th June 2010 at 10:14.
 29th June 2010, 09:58 #5  |  Link deank Programmer (or just 教务长)     Join Date: Oct 2008 Location: Valencia, Spain Posts: 4,248 Btw the latest version of the H264StereoSource.dll supports 1280x720. __________________ multiAVCHD - donate | popBD | uncropMKV | mkv2avi | easySUP
 30th June 2010, 01:50 #6  |  Link chocolate elvis Registered User   Join Date: Jun 2010 Posts: 4 Can someone cut and paste a sample command for a moron? Can get left to decode but not right. Thanks
 30th June 2010, 13:37 #7  |  Link crl2007 Registered User   Join Date: Nov 2007 Posts: 650 I wrote in the guide that now you can achieve the same with multiavchd only. You don't need x264 if you don't know how to use it.
 30th June 2010, 18:22 #8  |  Link chocolate elvis Registered User   Join Date: Jun 2010 Posts: 4 Thanks, but I'm trying to reconstruct the right eye as a mp4. So the result is a full 1920x1080 left eye, and 1920x1080 right eye, Can't seem to decode the right eye w/o errors.
 30th June 2010, 20:37 #9  |  Link crl2007 Registered User   Join Date: Nov 2007 Posts: 650 x264.exe --crf 17 --tune film -I 24 --weightp 0 --b-pyramid none --sar 1:1 --aud --rc-lookahead 6 --output right_final.264 sample.avs This is a useful commandline.
 9th August 2010, 21:20 #10  |  Link rik1138 Registered User   Join Date: Mar 2008 Location: LA Posts: 607 Is the Right eye stream sort of a 'difference' stream based on the Left eye? Can the right eye MVC be re-built from the PlayList without actually re-encoding the video? (I'm gathering the x264 command above is actually re-encoding the right eye stream to create the .264 file...) I need to take 3D video from multiple Blu-ray discs and combine it all on one disc, preferably without re-encoding any of it... I can't seem to find an easy way to pull it off. (I'll re-encode if I have to, just trying to avoid it...)
 9th August 2010, 21:44 #11  |  Link deank Programmer (or just 教务长)     Join Date: Oct 2008 Location: Valencia, Spain Posts: 4,248 Alex's mod for Version JM 17.1 allows YUV decoding of right eye stream. Source files for regular H.264 decoding are available, but he didn't respond after requests to share the mod source for right eye decoding. Either way we/you need a way to recreate the 'delta' ssif files (which are same content wise) as r-eye m2ts files. I'll try again to poke him __________________ multiAVCHD - donate | popBD | uncropMKV | mkv2avi | easySUP
 9th August 2010, 23:21 #12  |  Link rik1138 Registered User   Join Date: Mar 2008 Location: LA Posts: 607 Are there any tools available yet that can take a couple of lt + right-dependent MVC streams and build a functioning disc (creating the ssif, etc)? If that's not available yet, I might have to go with re-encoding anyway... The authoring software I'm using won't seem to take MVC streams ripped off of a Blu-ray disc, unless they are MVC streams it created in the first place... Not sure why. But, if I have to, I can re-encode the two streams, it's just a matter of getting that right-eye stream as a valid AVC file by itself. I tried the .x264 method above, but it gives me an error about loading the h264StereoSource.dll and doesn't work... My first time trying it, so I'm probably doing something wrong, just haven't figured it out yet...
 10th August 2010, 07:22 #13  |  Link crl2007 Registered User   Join Date: Nov 2007 Posts: 650 There is no such software yet. And as far as that error, you most probably wrote the wrong path for the dll in the avs script.
 10th August 2010, 08:17 #14  |  Link rik1138 Registered User   Join Date: Mar 2008 Location: LA Posts: 607 That's what I figured... I have the .dll in the same directory as the .avs script, so I just had the file name itself. I then tried using the complete path, and I still got the error... Is it just that one .dll that's needed, or should there be other files with it? (Or maybe point it to the one in the MultiAVCHD directory?) I'll play with it more tomorrow... I'm sure I've just done something wrong.
 10th August 2010, 14:59 #15  |  Link crl2007 Registered User   Join Date: Nov 2007 Posts: 650 It's just that dll and that cfg file.
 10th August 2010, 18:54 #16  |  Link rik1138 Registered User   Join Date: Mar 2008 Location: LA Posts: 607 Not sure what I'm doing wrong here... I have these files in the directory: H264StereoSource.cfg H264StereoSource.dll l.h264 r.h264 sample.avs x264.exe Config file: Code: InputFile = "l.h264" InputFile2 = "r.h264" FileFormat = 0 POCScale = 1 # decoder control parameters DisplayDecParams = 1 ConcealMode = 0 RefPOCGap = 2 POCGap = 2 IntraProfileDeblocking = 1 DecFrmNum = 0 sample.avs: Code: LoadPlugin("H264StereoSource.dll") H264StereoSource("H264StereoSource.cfg",3788) I use your x264 command line posted above exactly, and get this: avc [error]: LoadPlugin: unable to load "H264StereoSource.dll" (sample.avs, line 1) x264 [error]: could not open input file 'sample.avs' Any thoughts? Does anything look wrong? I can play the l.h264 file in Media Player just fine... But could it be related to other installed AVC codecs?
 10th August 2010, 20:00 #17  |  Link deank Programmer (or just 教务长)     Join Date: Oct 2008 Location: Valencia, Spain Posts: 4,248 I got the same error yesterday on my office computer (with multiAVCHD, trying to load the plugin). I believe it is compiled for certain CPU (OS?!) Works fine on my laptop Vista 32bit Intel PC, but fails with my desktop office XP SP2 Intel PC. Both with Core2Duo CPUs. // Thinking about it, I'll try to install .NET on my office PC and will test again tomorrow. It may be .NET compiled (the .dll). __________________ multiAVCHD - donate | popBD | uncropMKV | mkv2avi | easySUP Last edited by deank; 10th August 2010 at 20:16.
 11th August 2010, 03:02 #18  |  Link rik1138 Registered User   Join Date: Mar 2008 Location: LA Posts: 607 Hmm, maybe it's a Visual C++ thing? I had to install the Microsoft Visual C++ libraries for another app (didn't have it installed apparently), and now the x264 gets further (seems to load the .dll okay, recognizes the video file, but then crashes with an exception error...). The crash could be due to the video files I'm using, I'll try it on others tomorrow... I would have though x264 wouldn't work at all if it needed the VisC stuff, but it did seem to get further... Vis C here: http://www.microsoft.com/downloads/e...displayLang=en
 23rd October 2010, 19:18 #19  |  Link Limobar aka Rabomil   Join Date: Sep 2005 Posts: 82 My way of creating a single file 3d encode, is the following: 1. I encode the right eye lossless (x264 -q0 -m1 -A i4x4 --no-cabac), using the MVC sample script, to create a right eye that has the same quality as the left eye. MVC sample script: Code: LoadPlugin("H264StereoSource.dll") H264StereoSource("decoder.cfg",135266) 2. After that I create a half side-by-side encode using the following Avisynth script: Code: VideoLeft = directshowsource("C:\x264\left.mkv", audio=false) VideoRight = directshowsource("C:\x264\right.mkv", audio=false) VideoStacked = StackHorizontal(VideoRight,VideoLeft) lanczosresize(1920,1080) ConvertToYV12(VideoStacked) and high quality x264 settings, depending on the source. My question is: Is it possible to leave out step one and do the final encode directly? I think it is possible, otherwise it wouldn't be possible to do step 1, but how?
 24th October 2010, 00:49 #20  |  Link crl2007 Registered User   Join Date: Nov 2007 Posts: 650 You have to decode the MVC stream, there's no faster method yet.


text:
• question_answer 76) What will be the compound interest accrued on an amount of Rs. 15,000 at the rate of 8% per annum in 2 years? A) Rs. 2376B)               Rs. 2, 596C) Rs. 2, 476                     D) Rs. 2, 496

Compound interest $=15000\,\,\left[ {{\left( 1+\frac{8}{100} \right)}^{2}}-1 \right]$ $=15000\,\,\left[ {{\left( \frac{27}{25} \right)}^{2}}-1 \right]$ $=15000\,\,\left[ \frac{104}{625} \right]$ $=Rs.\,\,2496$


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Tag Info

5

Here is a working paper that you may be interested in.

2

Do you refer with 'negative tail dependence' to the case that one variable has a extremely low value and the other random variable has an extremely large value, i.e., $$\tau=\lim_{p \rightarrow 0} \frac{Pr[x>Q_x(1-p),y<Q_y(p)]}{p},$$ where $Q_x(1-p)$ and $Q_y(p)$ refer to the $(1-p)$-th quantile of the random variable $x$ and the $p$-th quantile of ...

2

The answer of user27915816 led me into the right direction, yet I think I found an even better generalization: Distance Correlation (dCor) There are several reasons for that: It generalizes classical (i.e. linear) correlation in the sense that linearity is a special case. It gives identical readings for linear dependence. There are analogs for variance, ...

2

Mutual information measures how much knowing one variable reduces uncertainty about another variable. It considers any type of dependency (linear or non-linear), it's measured in bits, and it is widely used in machine learning, computer vision NLP and other fields.

Only top voted, non community-wiki answers of a minimum length are eligible


text:
Facility Location¶

class apricot.functions.facilityLocation.FacilityLocationSelection(n_samples, metric='euclidean', initial_subset=None, optimizer='lazy', optimizer_kwds={}, n_neighbors=None, reservoir=None, max_reservoir_size=1000, n_jobs=1, random_state=None, verbose=False)[source]

A selector based off a facility location submodular function.

Facility location functions are general purpose submodular functions that, when maximized, choose examples that represent the space of the data well. The facility location function is based on maximizing the pairwise similarities between the points in the data set and their nearest chosen point. The similarity function can be species by the user but must be non-negative where a higher value indicates more similar.

Note

All ~pairwise~ values in your data must be non-negative for this selection to work.

In many ways, optimizing a facility location function is simply a greedy version of k-medoids, where after the first few examples are selected, the subsequent ones are at the center of clusters. The function, like most graph-based functions, operates on a pairwise similarity matrix, and successively chooses examples that are similar to examples whose current most-similar example is still very dissimilar. Phrased another way, successively chosen examples are representative of underrepresented examples.

The general form of a facility location function is

$f(X, Y) = \sum\limits_{y in Y} \max_{x in X} \phi(x, y)$

where $$f$$ indicates the function, $$X$$ is a subset, $$Y$$ is the ground set, and $$\phi$$ is the similarity measure between two examples. Like most graph-based functons, the facility location function requires access to the full ground set.

This implementation allows users to pass in either their own symmetric square matrix of similarity values, or a data matrix as normal and a function that calculates these pairwise values.

For more details, see https://las.inf.ethz.ch/files/krause12survey.pdf page 4.

Parameters: n_samples (int) – The number of samples to return. metric (str, optional) – The method for converting a data matrix into a square symmetric matrix of pairwise similarities. If a string, can be any of the metrics implemented in sklearn (see https://scikit-learn.org/stable/modules/ generated/sklearn.metrics.pairwise_distances.html), including “precomputed” if one has already generated a similarity matrix. Note that sklearn calculates distance matrices whereas apricot operates on similarity matrices, and so a distances.max() - distances transformation is performed on the resulting distances. For backcompatibility, ‘corr’ will be read as ‘correlation’. Default is ‘euclidean’.
initial_subset : list, numpy.ndarray or None, optional
If provided, this should be a list of indices into the data matrix to use as the initial subset, or a group of examples that may not be in the provided data should beused as the initial subset. If indices, the provided array should be one-dimensional. If a group of examples, the data should be 2 dimensional. Default is None.
optimizer : string or optimizers.BaseOptimizer, optional

The optimization approach to use for the selection. Default is ‘two-stage’, which makes selections using the naive greedy algorithm initially and then switches to the lazy greedy algorithm. Must be one of

‘random’ : randomly select elements (dummy optimizer) ‘modular’ : approximate the function using its modular upper bound ‘naive’ : the naive greedy algorithm ‘lazy’ : the lazy (or accelerated) greedy algorithm ‘approximate-lazy’ : the approximate lazy greedy algorithm ‘two-stage’ : starts with naive and switches to lazy ‘stochastic’ : the stochastic greedy algorithm ‘sample’ : randomly take a subset and perform selection on that ‘greedi’ : the GreeDi distributed algorithm ‘bidirectional’ : the bidirectional greedy algorithm

Default is ‘two-stage’.

optimizer_kwds : dict or None
A dictionary of arguments to pass into the optimizer object. The keys of this dictionary should be the names of the parameters in the optimizer and the values in the dictionary should be the values that these parameters take. Default is None.
n_neighbors : int or None
When constructing a similarity matrix, the number of nearest neighbors whose similarity values will be kept. The result is a sparse similarity matrix which can significantly speed up computation at the cost of accuracy. Default is None.
reservoir : numpy.ndarray or None
The reservoir to use when calculating gains in the sieve greedy streaming optimization algorithm in the partial_fit method. Currently only used for graph-based functions. If a numpy array is passed in, it will be used as the reservoir. If None is passed in, will use reservoir sampling to collect a reservoir. Default is None.
max_reservoir_size : int
The maximum size that the reservoir can take. If a reservoir is passed in, this value is set to the size of that array. Default is 1000.
n_jobs : int
The number of threads to use when performing computation in parallel. Currently, this parameter is exposed but does not actually do anything. This will be fixed soon.
random_state : int or RandomState or None, optional
The random seed to use for the random selection process. Only used for stochastic greedy.
verbose : bool
Whether to print output during the selection process.
n_samples

The number of samples to select.

Type: int
ranking

The selected samples in the order of their gain.

Type: numpy.array int
gains

The gain of each sample in the returned set when it was added to the growing subset. The first number corresponds to the gain of the first added sample, the second corresponds to the gain of the second added sample, and so forth.

Type: numpy.array float
fit(X, y=None, sample_weight=None, sample_cost=None)[source]

Run submodular optimization to select the examples.

This method is a wrapper for the full submodular optimization process. It takes in some data set (and optionally labels that are ignored during this process) and selects n_samples from it in the greedy manner specified by the optimizer.

This method will return the selector object itself, not the transformed data set. The transform method will then transform a data set to the selected points, or alternatively one can use the ranking stored in the self.ranking attribute. The fit_transform method will perform both optimization and selection and return the selected items.

Parameters: X (list or numpy.ndarray, shape=(n, d)) – The data set to transform. Must be numeric. y (list or numpy.ndarray or None, shape=(n,), optional) – The labels to transform. If passed in this function will return both the data and th corresponding labels for the rows that have been selected. sample_weight (list or numpy.ndarray or None, shape=(n,), optional) – The weight of each example. Currently ignored in apricot but included to maintain compatibility with sklearn pipelines. sample_cost (list or numpy.ndarray or None, shape=(n,), optional) – The cost of each item. If set, indicates that optimization should be performed with respect to a knapsack constraint. self – The fit step returns this selector object. FacilityLocationSelection
fit_transform(X, y=None, sample_weight=None, sample_cost=None)

Run optimization and select a subset of examples.

This method will first perform the fit step and then perform the transform step, returning a transformed data set.

Parameters: X (list or numpy.ndarray, shape=(n, d)) – The data set to transform. Must be numeric. y (list or numpy.ndarray or None, shape=(n,), optional) – The labels to transform. If passed in this function will return both the data and the corresponding labels for the rows that have been selected. Default is None. sample_weight (list or numpy.ndarray or None, shape=(n,), optional) – The sample weights to transform. If passed in this function will return the selected labels (y) and the selected samples, even if no labels were passed in. Default is None. sample_cost (list or numpy.ndarray or None, shape=(n,), optional) – The cost of each item. If set, indicates that optimization should be performed with respect to a knapsack constraint. X_subset (numpy.ndarray, shape=(n_samples, d)) – A subset of the data such that n_samples < n and n_samples is the integer provided at initialization. y_subset (numpy.ndarray, shape=(n_samples,), optional) – The labels that match with the indices of the samples if y is passed in. Only returned if passed in. sample_weight_subset (numpy.ndarray, shape=(n_samples,), optional) – The weight of each example.
transform(X, y=None, sample_weight=None)

Transform a data set to include only the selected examples.

This method will return a selection of X and optionally selections of y and sample_weight. The default setting is to select items based on the ranking determined in the fit step with examples in the same order as that ranking. Optionally, the whole data set can be returned, with the weights corresponding to samples that were not selected set to 0. This setting can be controlled by setting pipeline=True.

Parameters: X (list or numpy.ndarray, shape=(n, d)) – The data set to transform. Must be numeric. y (list or numpy.ndarray or None, shape=(n,), optional) – The labels to transform. If passed in this function will return both the data and the corresponding labels for the rows that have been selected. Default is None. sample_weight (list or numpy.ndarray or None, shape=(n,), optional) – The sample weights to transform. If passed in this function will return the selected labels (y) and the selected samples, even if no labels were passed in. Default is None. X_subset (numpy.ndarray, shape=(n_samples, d)) – A subset of the data such that n_samples < n and n_samples is the integer provided at initialization. y_subset (numpy.ndarray, shape=(n_samples,), optional) – The labels that match with the indices of the samples if y is passed in. Only returned if passed in. sample_weight_subset (numpy.ndarray, shape=(n_samples,), optional) – The weight of each example.


text:
# [pdftex] pdftex Digest, Vol 131, Issue 5

Cirilo Alvarez cirilo_alvarez at hotmail.com
Thu Jul 16 06:45:55 CEST 2015

> From: pdftex-request at tug.org
> Subject: pdftex Digest, Vol 131, Issue 5
> To: pdftex at tug.org
> Date: Tue, 14 Jul 2015 00:23:53 +0200
>
> Send pdftex mailing list submissions to
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> or, via email, send a message with subject or body 'help' to
> 	pdftex-request at tug.org
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> 	pdftex-owner at tug.org
>
> than "Re: Contents of pdftex digest..."
>
>
> Today's Topics:
>
>    1.  Please make the CreationDate, ModDate and ID field
>       deterministic (Nicolas Boulenguez)
>    2. Embedding a font to use it in a form (Gregory Heytings)
>    3. Re: Embedding a font to use it in a form (Karl Berry)
>    4. Re: Embedding a font to use it in a form (Gregory Heytings)
>
>
> ----------------------------------------------------------------------
>
> Message: 1
> Date: Mon, 13 Jul 2015 16:08:51 +0200
> From: Nicolas Boulenguez <nicolas at debian.org>
> To: <pdftex at tug.org>
> Subject: [pdftex]  Please make the CreationDate, ModDate and ID field
> 	deterministic
> Message-ID: <20150713140851.GA19905 at pegase>
> Content-Type: text/plain; charset="us-ascii"
>
> Hello all.
>
> As the original submitter, I would have liked an opportunity to
> discuss the choices, or else a word of explanation about them, or at
> least an alert about the commit, as I did mention that I was not
>
> I understand that upstream authors of a widely used software need to
> discuss privately before announcing changes, but now that you are at
> selected design.
>
> The CreationDate and ModDate are optional.  Why set them, unless
>
> If you set them by default, and we do not find a work-around like [2],
> everyone concerned with reproducible builds will need to insert
>   \pdfinfo{/CreationDate(D:19900101000000Z00'00')/ModDate(D:19900101000000Z00'00')}
> or
>   \pdfinfo{/CreationDate(D:\$DATEZ00'00')/ModDate(D:\$DATEZ00'00')}
> into every TeX source during each build, or patch pdftex for its own
> use.  What concrete need does \pdfinfoomitdate answer?
>
> The ID field is optional. Why set it, unless \pdftrailerid or similar
>
> If you set it by default, the following suggestion may help doing so
> without a new \pdftrailerid macro.
>
> As I understand section 10.3 of the PDF specification [3], a md5 sum
> of the time, directory and base name is only a very vague
> implementation suggestion. Any randomly generated string, or
> non-cryptographic hash sum of the PDF file would satisfy the purpose
> better, with the latter being reproducible.
>
> For example, would you consider defining the ID as an 8 characters
> hexadecimal represention of a 32 bits XOR sum of all contents written
> to the output file so far? The performance impact and collision risk
> would both be very small.
>
> Is there any benefit in keeping the current implementation by default?
>
> In the current implementation, what is the benefit of taking gmtime()
> into acount for the md5 sum, instead of CreationDate?
>
> [1] http://tug.org/mailman/htdig/pdftex/2015-May/008940.html
> [2] http://tug.org/pipermail/pdftex/2015-July/008954.html
>
>
> ------------------------------
>
> Message: 2
> Date: Mon, 13 Jul 2015 15:31:51 +0200
> From: Gregory Heytings <ghe at sdf.org>
> To: <pdftex at tug.org>
> Subject: [pdftex] Embedding a font to use it in a form
> Message-ID: <alpine.DEB.2.11.1507131521440.7198 at svobanppv.bet>
> Content-Type: text/plain; format=flowed; charset="US-ASCII"
>
>
> Hi,
>
> I try to use pdfTeX to create (text field) forms, and I would like to use
> an embedded font for the text fields, instead of the standard system
> fonts.  This is feasible (Acrobat can do it), be it that the font needs to
> be embedded in full (i.e. not a subset), and apparently in a special way
> (they do not appear in the list of embedded fonts in Acrobat).
>
> This question is more or less similar to: http://tex.stackexchange.com/questions/36630/hyperref-how-to-format-text-in-a-forms-text-field , but it got no answer.
>
> Does anyone know how to do this?
>
> Thanks,
>
> Gregory
>
>
> ------------------------------
>
> Message: 3
> Date: Mon, 13 Jul 2015 21:57:04 +0000
> From: Karl Berry <karl at freefriends.org>
> To: <ghe at sdf.org>
> Cc: <pdftex at tug.org>
> Subject: Re: [pdftex] Embedding a font to use it in a form
> Message-ID: <201507132157.t6DLv4Jg012826 at freefriends.org>
> Content-Type: text/plain
>
> It should work to fully embed a font (no subsetting) by using <<foo.pfb
> in the map file entry instead of <foo.pfb.  This is tersely discussed in
> the pdftex manual under "fontfile", page 11 in the pdftex-a.pdf that is
> in TeX Live 2015.
>
> However, I have no knowledge of how to specify a font for use in text
> field forms.  Maybe someone else here (Heiko, Martin ... ?) can help.
>
> Best,
> Karl
>
>
> ------------------------------
>
> Message: 4
> Date: Tue, 14 Jul 2015 00:23:45 +0200
> From: Gregory Heytings <ghe at sdf.org>
> To: Karl Berry <karl at freefriends.org>
> Cc: <pdftex at tug.org>
> Subject: Re: [pdftex] Embedding a font to use it in a form
> Message-ID: <alpine.DEB.2.11.1507140004210.26890 at svobanppv.bet>
> Content-Type: text/plain; format=flowed; charset="US-ASCII"
>
>
> Hi Karl,
>
>
> >
> > It should work to fully embed a font (no subsetting) by using <<foo.pfb
> > in the map file entry instead of <foo.pfb.  This is tersely discussed in
> > the pdftex manual under "fontfile", page 11 in the pdftex-a.pdf that is
> > in TeX Live 2015.
> >
>
> After some more research, it seems indeed that one aspect of the problem
> is to fully embed the font.  Apparently it does not work with pfa/pfb
> fonts, however (but I am not sure that it cannot be done); it does work,
> for sure, with an otf font file.
>
> >
> > However, I have no knowledge of how to specify a font for use in text
> > field forms.  Maybe someone else here (Heiko, Martin ... ?) can help.
> >
>
> So far my best answer to my own question goes as follows: one has to
> insert the otf file as a pdf object, with something like "\pdfobj stream
> attr { /Subtype /OpenType } file {Font.otf}", and then create two other
> pdf objects manually, namely a /FontDescriptor and a /Font, the latter
> containing /FirstChar 0 /LastChar 255, and 256 values in the /Width array.
> Then that font can be used in a form, by adding a reference to it in the
> resource dictionary of the form.
>
> (Once I got the above scheme working, I tried to remplace the "\pdfobj
> stream attr { /Subtype /OpenType } file {Font.otf}" with a "\pdfobj stream
> attr { /Subtype /Type1 } file {Font.pfa}", but it did not work anymore.)
>
> The problem is that doing this involves a lot of manual work.  A more
> direct way to do this (with pdfTeX) would be much appreciated.
>
> Gregory
>
>
> ------------------------------
>
> Subject: Digest Footer
>
> _______________________________________________
> pdftex mailing list
> pdftex at tug.org
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>
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>
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Letter | Published:

# Visualizing vibrational normal modes of a single molecule with atomically confined light

## Abstract

The internal vibrations of molecules drive the structural transformations that underpin chemistry and cellular function. While vibrational frequencies are measured by spectroscopy, the normal modes of motion are inferred through theory because their visualization would require microscopy with ångström-scale spatial resolution—nearly three orders of magnitude smaller than the diffraction limit in optics1. Using a metallic tip to focus light and taking advantage of the surface-enhanced Raman effect2 to amplify the signal from individual molecules, tip-enhanced Raman spectromicroscopy (TER-SM)3,4 reaches the requisite sub-molecular spatial resolution5, confirming that light can be confined in picocavities6,7,8,9,10 and anticipating the direct visualization of molecular vibrations11,12,13. Here, by using TER-SM at the precisely controllable junction of a cryogenic ultrahigh-vacuum scanning tunnelling microscope14,15,16, we show that ångström-scale resolution is attained at subatomic separation between the tip atom and a molecule in the quantum tunnelling regime of plasmons6,8,9,17. We record vibrational spectra within a single molecule, obtain images of normal modes and atomically parse the intramolecular charges and currents driven by vibrations. Our analysis provides a paradigm for optics in the atomistic near-field.

## Access optionsAccess options

from\$8.99

All prices are NET prices.

## Data availability

The data supporting the findings of this study are available within the paper. Experimental source data for Figs. 14 are provided with the paper.

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## References

1. 1.

Betzig, E. Nobel lecture: single molecules, cells, and super-resolution optics. Rev. Mod. Phys. 87, 1153–1168 (2015).

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Jeanmaire, D. L. & Van Duyne, R. P. Surface Raman spectroelectrochemistry: part I. Heterocyclic, aromatic, and aliphatic amines adsorbed on the anodized silver electrode. J. Electroanal. Chem. 84, 1–20 (1977).

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Jiang, N. et al. Tip-enhanced Raman spectroscopy: from concepts to practical applications. Chem. Phys. Lett. 659, 16–24 (2016).

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Stöckle, R. M., Suh, Y. D., Deckert, V. & Zenobi, R. Nanoscale chemical analysis by tip-enhanced Raman spectroscopy. Chem. Phys. Lett. 318, 131–136 (2000).

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Zhang, R. et al. Chemical mapping of a single molecule by plasmon-enhanced Raman scattering. Nature 498, 82–86 (2013).

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Zhang, P., Feist, J., Rubio, A., García-González, P. & García-Vidal, F. J. Ab initio nanoplasmonics: the impact of atomic structure. Phys. Rev. B 90, 161407 (2014).

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Trautmann, S. et al. A classical description of subnanometer resolution by atomic features in metallic structures. Nanoscale 9, 391–401 (2017).

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Urbieta, M. et al. Atomic-scale lightning rod effect in plasmonic picocavities: a classical view to a quantum effect. ACS Nano 12, 585–595 (2018).

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Chen, X. & Jensen, L. Morphology dependent near-field response in atomistic plasmonic nanocavities. Nanoscale 10, 11410–11417 (2018).

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Benz, F. et al. Single-molecule optomechanics in ‘picocavities’. Science 354, 726–729 (2016).

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Duan, S. et al. Theoretical modeling of plasmon-enhanced Raman images of a single molecule with subnanometer resolution. J. Am. Chem. Soc. 137, 9515–9518 (2015).

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Duan, S., Tian, G. & Luo, Y. Visualization of vibrational modes in real space by tip-enhanced non-resonant Raman spectroscopy. Angew. Chem. Int. Ed. 55, 1041–1045 (2016).

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Liu, P., Chulhai, D. V. & Jensen, L. Single-molecule imaging using atomistic near-field tip-enhanced Raman spectroscopy. ACS Nano 11, 5094–5102 (2017).

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Pozzi, E. A. et al. Ultrahigh-vacuum tip-enhanced Raman spectroscopy. Chem. Rev. 117, 4961–4982 (2017).

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Steidtner, J. & Pettinger, B. Tip-enhanced Raman spectroscopy and microscopy on single dye molecules with 15 nm resolution. Phys. Rev. Lett. 100, 236101 (2008).

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Chiang, N. et al. Molecular-resolution interrogation of a porphyrin monolayer by ultrahigh vacuum tip-enhanced Raman and fluorescence spectroscopy. Nano Lett. 15, 4114–4120 (2015).

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Savage, K. J. et al. Revealing the quantum regime in tunnelling plasmonics. Nature 491, 574–577 (2012).

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Moskovits, M. Criterion for determining resolving power in the optical near field. J. Nanophotonics 11, 046018 (2017).

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Lee, J. et al. Tip-enhanced Raman spectromicroscopy of Co(ii)-tetraphenylporphyrin on Au(111): toward the chemists’ microscope. ACS Nano 11, 11466–11474 (2017).

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Tallarida, N., Rios, L., Apkarian, V. A. & Lee, J. Isomerization of one molecule observed through tip-enhanced Raman spectroscopy. Nano Lett. 15, 6386–6394 (2015).

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Tallarida, N., Lee, J. & Apkarian, V. A. Tip-enhanced Raman spectromicroscopy on the angstrom scale: bare and CO-terminated Ag tips. ACS Nano 11, 11393–11401 (2017).

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Hugall, J. T. & Baumberg, J. J. Demonstrating photoluminescence from au is electronic inelastic light scattering of a plasmonic metal: the origin of SERS backgrounds. Nano Lett. 15, 2600–2604 (2015).

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Dey, S. et al. Observation and analysis of Fano-like lineshapes in the Raman spectra of molecules adsorbed at metal interfaces. Phys. Rev. B 93, 035411 (2016).

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Lee, J., Tallarida, N., Chen, X., Jensen, L. & Apkarian, V. A. Microscopy with a single-molecule scanning electrometer. Sci. Adv. 4, eaat5472 (2018).

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Le Ru, E. C. & Etchegoin, P. G. Rigorous justification of the |E|4 enhancement factor in surface enhanced Raman spectroscopy. Chem. Phys. Lett. 423, 63–66 (2006).

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Banik, M. et al. Surface-enhanced Raman trajectories on a nano-dumbbell: transition from field to charge transfer plasmons as the spheres fuse. ACS Nano 6, 10343–10354 (2012).

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Di Santo, G. et al. Conformational adaptation and electronic structure of 2H-tetraphenylporphyrin on Ag(111) during Fe metalation. J. Phys. Chem. C 115, 4155–4162 (2011).

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## Acknowledgements

This research was supported by the NSF Center for Chemical Innovation dedicated to Chemistry at the Space-Time Limit (CHE-1414466). Theoretical calculations were performed on the UCI Greenplanet cluster system (CHE-0840513). We thank P. El-Khoury for advice on DFT calculations. We have benefited from discussions with L. Jensen, X. Chen and P. Liu.

### Reviewer information

Nature thanks Eric Le Ru and the other anonymous reviewer(s) for their contribution to the peer review of this work.

## Author information

### Author notes

• Kevin T. Crampton

Present address: Physical Sciences Division, Pacific Northwest National Laboratory, Richland, WA, USA

• Nicholas Tallarida

Present address: Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, USA

### Affiliations

1. #### Department of Chemistry, University of California, Irvine, CA, USA

• Joonhee Lee
• , Kevin T. Crampton
• , Nicholas Tallarida
•  & V. Ara Apkarian

### Contributions

J.L. and K.T.C. carried out experimental work and data analysis. J.L. performed theoretical simulations. N.T. produced nanoscopically smooth silver tips and performed preliminary principal component analysis. J.L. and V.A.A. conceived and coordinated the project and authored the paper with input from all co-authors.

### Competing interests

The authors declare no competing interests.

### Corresponding authors

Correspondence to Joonhee Lee or V. Ara Apkarian.

## Extended data figures and tables

1. ### Extended Data Fig. 1 Conformational transformation of CoTPP on Cu(100).

a, An imaging sequence starting at −0.5 V is followed by repeated scans at –12 mV. The size of the images is 35 × 35 Å2. The pressing scanning condition at −12 mV leads to planarity of the phenyl groups. b, Optimized geometry of a free CoTPP molecule and flat geometry of an adsorbed CoTPP molecule with artificially flattened phenyl rings. c, Lattice registry of the flat CoTPP and the marker CO molecule, which adsorbs on the copper on-top site.

2. ### Extended Data Fig. 2 Disappearance of the Kondo resonance.

The Kondo resonance observed on the saddled CoTPP adsorbed on the Au(111) surface disappears on the flat CoTPP adsorbed on the Cu(100) surface. The gap distances are set at 1 nA, +0.2 V and 1 nA, −0.2 V for Au and Cu, respectively.

3. ### Extended Data Fig. 3 Gap dependence of Raman intensity and vibrational frequency.

a, b, Measurements on cobalt (a) and pyrrole (b). Colour-coded vertical grid lines in the leftmost graph indicate vibrational modes analysed in terms of intensity and frequency shift in the middle and right panels, respectively. The extracted powers n from the curve fit (I = azn) are indicated in the corresponding colours.

4. ### Extended Data Fig. 4 Maps of omitted normal modes.

The modes presented here are extensively delocalized and do not yield unique assignments.

5. ### Extended Data Fig. 5 Dominance of Δαzz in the observed TERS.

Raman images of the 388-cm−1 mode, simulated using out-of-plane (zz) and in-plane (xx) polarizability differences, and the map of the xx component of the polarizability at equilibrium (α0,xx). The Δαzz component reproduces the experiment, whereas the Δαxx fails despite its large magnitude. The charge accumulation at the edges upon polarization is demonstrated in both Δαxx and α0,xx. This trend applies to all of the observed normal modes.

6. ### Extended Data Fig. 6 Vibrational Stark effect of the C–H stretch.

Evolution of the C–H stretch upon tuning of the integration window. The image size and resolution are 28 × 28 Å2 and 80 × 80 pixels, respectively. Images are low-pass-filtered for clarity.

7. ### Extended Data Fig. 7 Schematic diagram for the resolution of near-field optical microscopy.

a, Local electric field along the z axis, Ez, arising from a charge. Only the z component is considered because in-plane dipoles induced by tangential components are cancelled by their images in the metallic substrate. b, Comparison between the fourth power of the Coulomb field distribution (q = 1) and equivalent Gaussian with the associated FWHM value.

8. ### Extended Data Fig. 8 Selection rules of atomistic TERS.

Top right, orientationally averaged Raman spectrum of the free molecule. The intensities of the selected vibrational modes shown in Fig. 3 are indicated by red dots and dashed lines. Bottom right, atomic polarizability differences and their colour-coded amplitudes in atomic units. The colour represents the phase of the out-of-plane atomic dynamic dipole associated with $${\alpha }_{zz}^{i}$$. Left, while a nonlocal excitation leads to the cancellation of induced dipoles (top), the atomistic near field samples each radiating vertical dipole that is reinforced by its image (bottom). h0 and σ0 are Rayleigh length and waist, respectively, as defined in ‘Gaussian optics’ in Methods.

## Source data

### DOI

https://doi.org/10.1038/s41586-019-1059-9


text:
The Poincare upper half-plane

The upper half-plane, $\mathbb{H}$, with coordinates $(x,y)$ ($x\in \mathbb{R}$ and $y>0$) with the Poincar\'e metric

(1)
\begin{align} ds^2 =\frac{dx^2+dy^2}{y^2}\ , \end{align}

is called the Poincar\'e half-plane.It is also known as the Lobachevsky plane in the Russian literature. It is known that all Riemann surfaces with genus $>1$ can be obtained as quotients of this space by a discrete subgroup of $PSL(2,\mathbb{R})$ — this is a consequence of the uniformization theorem.

The Christoffel connection for the


text:
# For an non-constant and non-vanishing entire function $f$ , the set $U = { z in C : | f(z) | <1 }$ has unbounded connected component.

Suppose $$f$$ is an non constant entire function with $$f(z) neq 0$$ for all $$z in C$$. Then the set $$U = { z in C : | f(z) | <1 }$$ has unbounded connected component.

My attempt

I have concluded some facts:

• $$U$$ is an open set;

• $$f(z) neq 0$$ for all $$z in C$$, then there exists $$epsilon >0$$ such that $$| f(z) | > epsilon$$;

• Since $$f$$ is non-vanishing, we can define another entire function g such that $$g(z) = frac{1}{ f(z) }$$.

But I was not able to conclude the result.

Mathematics Asked by Learner_Shas on January 1, 2021

note that assuming $$f$$ non-constant ($$f=2$$ has $$U$$ empty), $$g=1/f$$ is non-constant and entire hence $$g$$ is unbounded, so $$U$$ being given by $$|g(z)|>1$$ must be unbounded (hence it has at least one unbounded connected component) as $$V$$ given by $$|g(z)| le 1$$ cannot contain the exterior of a disc radius $$R$$ for all $$R$$ large enough as that would imply $$g$$ bounded (as $$g$$ is bounded inside the closed disc of radius $$R$$, if it were bounded by $$1$$ outside, it would be bounded on the plane), while the union of $$U$$ and $$V$$ is the plane! Done!

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