text:
# Math Help - Fibonacci members and powers of the golden ratio

1. ## Fibonacci members and powers of the golden ratio

Hello. I searched for a topic for the same question, but my queries were fruitless, although they returned some similar questions. If i have missed it, please lock this one, and redirect me to the proper thread.
It's not a homework assignment, but a personal inquiry due to some home studies I'm performing. I have a little background in maths, but haven't done anything of the sorts in quite a while ( > 4 years), and was looking for some confirmation on my work. Anyhow, here's the problem.
Prove that $i$th Fibonacci number satisfies the equality
$
F_n = \frac{{\phi}^n - {\hat{\phi}}^n}{\sqrt{5}}
$

Where $\phi$ is the golden ratio and $\hat{\phi}$ is its conjugate.

What I've done:
Proof by induction.
Base cases:
$
F_0 = {\phi}^0 - {\hat{\phi}}^0
$

$
\\F_0 = 0
$

$
F_1 = {\phi}^1 - {\hat{\phi}}^1
$

$
\\F_1 = 1
$

Inductive hypothesis:
Suppose that it holds for [LaTeX ERROR: Convert failed]
The same for $\hat{\phi}$.

From that we trivially arrive at
$
\frac{{\phi}^{n+1} - {\hat{\phi}}^{n+1}}{\sqrt5} = \frac{{\phi}^n + {\phi}^{n-1}}{\sqrt5} - \frac{{\hat{\phi}}^{n} + {\hat{\phi}}^{n-1}}{\sqrt5}
$

Which is what we were trying to prove. Can you please confirm my reasoning? I'm not sure if I'm allowed such an assumption in my inductive hypothesis, and also my reasoning looks a little circular. If there's a gap, can you please point it out to me, as well as any hints at getting the proper solution?

2. Originally Posted by ossinator
Hello. I searched for a topic for the same question, but my queries were fruitless, although they returned some similar questions. If i have missed it, please lock this one, and redirect me to the proper thread.
It's not a homework assignment, but a personal inquiry due to some home studies I'm performing. I have a little background in maths, but haven't done anything of the sorts in quite a while ( > 4 years), and was looking for some confirmation on my work. Anyhow, here's the problem.
Prove that $i$th Fibonacci number satisfies the equality
$
F_n = \frac{{\phi}^n - {\hat{\phi}}^n}{\sqrt{5}}
$

Where $\phi$ is the golden ratio and $\hat{\phi}$ is its conjugate.

What I've done:
Proof by induction.
Base cases:
$
F_0 = {\phi}^0 - {\hat{\phi}}^0
$

$
\\F_0 = 0
$

$
F_1 = {\phi}^1 - {\hat{\phi}}^1
$

$
\\F_1 = 1
$

Inductive hypothesis:
Suppose that it holds for $F_n$ and $F_{n-1}$
We also know, that $\phi$ and $\hat{\phi}$ are the roots of the equation $x^2 = x + 1$
Therfore, if we multiply both sides of the equation by ${\phi} ^ {n-1}$, we get ${\phi}^{n+1} = {\phi}^{n} + {\phi}^{n-1}$
The same for $\hat{\phi}$.

From that we trivially arrive at
$
\frac{{\phi}^{n+1} - {\hat{\phi}}^{n+1}}{\sqrt5} = \frac{{\phi}^n + {\phi}^{n-1}}{\sqrt5} - \frac{{\hat{\phi}}^{n} + {\hat{\phi}}^{n-1}}{\sqrt5}
$

Which is what we were trying to prove. Can you please confirm my reasoning? I'm not sure if I'm allowed such an assumption in my inductive hypothesis, and also my reasoning looks a little circular. If there's a gap, can you please point it out to me, as well as any hints at getting the proper solution?
That is a very nice proof.

3. Does that mean that it works?
Also, there's a mistake in my base cases, a $\sqrt{5}$ is missing.

4. Originally Posted by ossinator
Does that mean that it works?
Also, there's a mistake in my base cases, a $\sqrt{5}$ is missing.
Yes, you should have $F_0 = ({\phi}^0 - {\hat{\phi}}^0)/\sqrt5$ and $F_1 = ({\phi}^1 - {\hat{\phi}}^1)/\sqrt5$. But apart from that the proof is completely correct.


text:
# How to put 2 buttons in the same line

Sorry to bother for something so simple (or so I believe). I was trying to put two buttons side by side, and normally it’s intuitive to do so, but on this occasion I just can’t get it. Basically I had a similar need to the one I found here https://groups.google.com/g/tiddlywiki/c/qo0kmYAhyMg, where asked for a way to tag multiple tiddlers. The proposed solution (which I later adopted) was to use a button that added the tag in question to all currently open tiddlers. I was going to insert this button next to “close all” in $:/core/ui/SideBar/Open like so: Unhighlighted code is the same as $:/core/ui/SideBar/Open and buttons right now are just an example with “123” so as not to complicate unnecessarily things. The button I added is highlighted in blue, and I assigned the macrocall “droppable item” (highlighted in green) to it instead of the close all button (highlighted in yellow).

I dont know if its the $macrocall$name="droppable-item" button that doesn’t make things work for how I’m using it, or if I’m missing something else. Maybe I should wrap both buttons in the same macrocall? (Btw, when I tried moving the "/> that closes the macrocall after the close all button the $macrocall$name="droppable-item" button broke)

• How can I put the two buttons in the same line?

Full code: (It is mostly the same as$:/core/ui/SideBar/Open, I put it whole for convenience; it is long but the affected parts, as can be seen in the figure, are very few) \whitespace trim \define lingo-base()$:/language/CloseAll/

\define drop-actions()
<$action-listops$tiddler=<<tv-story-list>> $subfilter="+[insertbefore<actionTiddler>,<currentTiddler>]"/> \end \define placeholder()
 \end \define droppable-item(button) \whitespace trim <$droppable actions=<<drop-actions>> enable=<<tv-allow-drag-and-drop>> tag="div">
<<placeholder>>

$button$

</$droppable> \end
 <$list filter="[list<tv-story-list>]" history=<<tv-history-list>> storyview="pop">

<$macrocall$name="droppable-item" button="<$button message='tm-close-tiddler' tooltip={{$:/language/Buttons/Close/Hint}} aria-label={{$:/language/Buttons/Close/Caption}} class='tc-btn-invisible tc-btn-mini tc-small-gap-right'>{{$:/core/images/close-button}}</$button><$link to={{!!title}}><$view field='title'/></$link>"/>

</$list> <$tiddler tiddler="">

<$macrocall$name="droppable-item" button="<$button class='tc-btn-mini'>Tag with 123 <$list filter='[list[$:/StoryList]]'> <$fieldmangler tiddler=<<currentTiddler>>>
<$action-sendmessage$message='tm-add-tag' $param=123/> </$fieldmangler>
</$list> </$button>"/><$button message='tm-close-all-tiddlers' class='tc-btn-mini'><<lingo Button>></$button>

</$tiddler>
  You could wrap your buttons in your stuff. The droppable-item macro explicitly wraps its output within
...
, which is forcing your button to appear on a line by itself. However… the droppable-item macro is only intended for use within the list of currently open titles (the code starting with <$list filter="[list<tv-story-list>]" history=<<tv-history-list>> storyview="pop"> and ending with </$list>). It makes the individual titles within that list droppable, so that you can change the display order of the tiddlers shown in the StoryRiver. For your purposes, the added “Tag with 123” button doesn’t need to be a “droppable-item”, so you should remove the <$macrocall $name="droppable-item" button=" and matching "/> Also, you can simplify your button’s actions by eliminating the use of the $fieldmangler widget. Instead of using a tm-add-tag message (which needs the surrounding $fieldmangler widget), you can use $action-listops to easily add the desired tag, like this:

<$button class='tc-btn-mini'>Tag with 123 <$list filter='[list[$:/StoryList]]'><$action-listops $tags="[[123]]"/></$list>
</$button>  1 Like Almost solved. Thank you Eric. Really interesting insight that the droppable-item macro wraps in
...
. Thank you, it explained a lot. There is only one problem that remains at the moment. Unfortunately, apparently, the droppable-item macro was not without purpose (indeed I didn’t add it but it was already there in $:/core/ui/SideBar/Open and now I find out why).
Basically if I wanted to move a currently opened tiddler at the bottom of the StoryRiver I can’t unless there is a droppable-item macro that can accommodate it at the bottom. (And so the droppable-item that was on the close all button in the original $:/core/ui/SideBar/Open was there for just that.) • Is there a way to wrap two buttons in the same droppable-item? Maybe I need to change how it’s defined at the top to do that (?) Try this: 1. Add a macro definitions, like this: \define addTagToAll() <$button class='tc-btn-mini'>Tag with 123
<$list filter='[list[$:/StoryList]]'><$action-listops$tags="[[123]]"/></$list> </$button>
\end

\define closeAll()
<$button message='tm-close-all-tiddlers' class='tc-btn-mini'> <<lingo Button>> </$button>
\end

1. Then, replace the last droppable-item macrocall with:
<$macrocall$name="droppable-item" button="<<addTagToAll>> <<closeAll>>"/>

Note:

• The new button code COULD have been added “inline” in the button="..." parameter of the last droppable-item macrocall, but moving both button definitions into small macros makes the droppable-item macrocall MUCH more readable.
• Using macros for the individual button definitions also eliminates the parsing problem of not being able to use double-quotes within the button="..." parameter value.
• The HTML   character entity forces a small separation between the two buttons

enjoy,
-e

1 Like

Works like a charm, brilliant. Thanks for the help and also for the explanations, I really did appreciate them
Thank you Eric!

format: plain


text:
22-27 March 2015
Hotel do Bosque
Brazil/East timezone

## CP Violation in three-body $B^\pm$ decay with final state interaction and CPT invariance

Not scheduled
3h 30m
Hotel do Bosque

#### Hotel do Bosque

Rodovia Mário Covas (Rio-Santos) BR - 101 Sul, Km 533, Angra dos Reis, RJ, Brazil
Poster Hadronic and quark matter - applications in astrophysics

### Speaker

Mr Jorge Nogueira (ITA)

### Description

In three-body charmless $B^{\pm}$ meson decay CPT symmetry is an important constraint that must be obeyed by the decay amplitude. Consistent with this requirement the final state interaction (FSI) in the decay amplitude has a important relationship with the CP asymmetry pattern in the decay of charge conjugates mesons $B^\pm$ as shown in [1]. Recent experiments of LHCb [2] bring results for the charged channels $K^{\pm}K^{+}K^{-}$, $K^\pm \pi^+\pi^-$, $\pi^\pm K^+ K^-$ and $\pi^\pm \pi^+\pi^-$ . In this work we propose an extension of the formalism of reference [1], which was the final state interaction introduced in the decay of $B^{\pm}$ in the coupled channels $K^\pm \pi^+\pi^-$ and $K^\pm K^+ K^-$. In this previous work it was considered only two interacting mesons and the other meson $K^\pm$ was acting only as a spectator. In the present contribution we symmetrize the decay amplitude in the $K^\pm K^+ K^-$ channel based on the two-body formalism presented in [1] but including interference effects due to the dynamical role of the third meson. The new experimental data of reference [2] suggests the presence of such interference in different regions of the Dalitz plot. [1] I. Bediaga, O. Lourenço, T. Frederico. Phys. Rev. D89, 094013 (2014). [2] R. Aaij et al. The LHCb Collaboration. arXiv: 1408.5373 [hep-ex]. To appear in Phys. Rev. D (2014).

### Presentation Materials

There are no materials yet.


text:
14 Divisors

What is the smallest number with exactly 14 divisors?

Summing Consecutive Numbers

Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?

Dozens

Do you know a quick way to check if a number is a multiple of two? How about three, four or six?

Think of Two Numbers

Stage: 3 Challenge Level:

Here is an alternative and more unusual version of the "Think of a Number" game which you may have heard of before.

Think of two whole numbers under $10$.
Take one of them and add $1$.
Multiply by $5$.
Add $1$ again.
Subtract $1$.
Add $2$.
Subtract $8$.


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# Hard disks and the liquid-solid transition in two dimensions_Questions

To edit the page, you have to become a member of the wiki by clicking on the Join link (top-right of the page), or by sending an email to one of us.
You can insert math formulæ using LaTeX code: e.g. typing
[[math]]
\pi_C(t+1)=\sum_{C'} \pi_{C'}(t) p_{C' \to C}
[[math]]
yields:
$\pi_C(t+1)=\sum_{C'} \pi_{C'}(t) p_{C' \to C}$

## Questions and Remarks:

• Q: in the first variant we should replace a=choice(L) - actually there are two line which read "a = choice(L)": one two choose a random disc to propose a move, and one to calculate the pair correlation. Which lines should be replaced? the first, the second or both?
• A: you have to replace both instances.

• Q: in the question about the two variants of the MC algorithm, the second variant includes both the replacements or only the second one?
• A: the second variant include only the replacement for b.

• Q: In the question 2 of the very first section ("why can we forget about the velocities?"), I'm not sure what the question is about: should we disscuss the fact that we are sampling equilibrium, distribution or compare the algorithms to molecular dynamics?
• A: The dynamics of hard spheres is described by their individual uniform motion punctuated by collisions. It occurs in phase space, whose coordinates consists of the set of their positions and velocities. As discussed in the lectures and in the class sessions, according to the ergodic hypothesis, their stationnary distribution is uniform in phase space (which includes positions and velocities). However, in the proposed programs, the sampling is performed uniquely on positions. We ask to justify why we can forget about the velocities.

• Q: In the questions about the algorithm A, what is exactly the property ? I read it as "the probability to find a disk at position (x,y) is uniform in space" but this is clearly false (as the histogram of the x-coordinate of the disks shows), so I do not understand the following questions.
• A: The hard spheres are distributed with the microcanonical distribution: their probability density in phase space is uniform. The property that we ask you to decide whether it is true of false indeed reads: "the probability to find the center of a disk at spatial position (x,y) is uniform". In question 2, you have to justify theoretically why you think this property is true or false. In the following questions (3 and 4), you have to test your choice numerically.
Besides, we cannot comment on the rest of your remark « but this is clearly false (as the histogram of the x-coordinate of the disks shows) », as it would partially answer to the question. However, we advice you to clearly identify and rethink of the premises and implications of your reasoning.

• Q: I think %1 is missing in the last question (second variant).
• A: Yes. The question is now reformulated in a clearer way.

• Q: It seems that the definition of N is missing for a = L[iter%N] (for the last part of the homework).
Should it be a = L[iter%len(L)]?
• A: Yes, here N is the number of disks in the specific problem (the way you propose should work).

• Q: in the part about Version A, are we expected to compare our results with the results from Version B, or not?
• A: Your question is not very precise. If you refer to this question: "Explain why (and in which limit) direct_disks.py and markov_disks_box_B.py give the same results." the answer is yes. If you refer to the following questions, the answer is no.

• Q: The last part of the question is not clear to me. Is the detailed balance referred to the detailed balance of a markov chain as discussed in lecture 1?
• A: yes
• It is not obvious to me how the pair-correlation function can give information on the balance properties (e.g. what are the transition probabilities in this case)? [[user:yiteng]* A: This is not the question. You have two things to do: 1) Answer the question about the detailed balance being respected or not. 2) Calculate the pair-correlation function and check that the results make sense. We do not ask you to find the link between 1) and 2).

• Q: In the question of drawing the histogram of x-coordinates, is it about running the program many times and getting a large number of realizations of L, and drawing the histograms of x-coordinates in all these realizations?
• Q: About the super bonus: do we have to explain simply by reasoning or by explicit calculation?


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# How is the Weighted Gini Criterion defined?

I am interested in trying out and/or implementing the Weighted Random Forest (WRF) algorithm described in Chen, Liaw, Breiman. How is the Weighted Gini impurity actually defined? What implementations of the algorithm exist?

My best guess would be that the weighted Gini impurity is defined by

$$\sum_i w_i * f_i * (1-f_i)$$

where $i$ is the class index, $w_i$ is the class weight, and $f_i$ is the fraction of elements in the group of class $i$. And that splits at each node are chosen by minimizing the weighted average sum of these impurities.

The implementation available at Breiman's website uses the weighted random forest method described in the paper. It's in Fortran 77 though, which may be off-putting to you. I also found the method that they use to calculate the impurity to be more unclear and complicated than needs be, but that's just my opinion (and probably an artifact of the method that they use to grow their trees).

For any potential split, the weight of all the observations in a potential child node, $c$, is

$$t_c = \sum_i w_i * n_i$$

where $n_i$ is the number of observations of class $i$ in $c$, and $w_i$ is the weight assigned to class $i$. The impurity of child node $c$ is then

$$i_c = 1 - \sum_i (w_i * n_i / t_c)^2$$

where $n_i$ is again the number of observations of class $i$ in the node, $w_i$ is the weight assigned to the class and $t_c$ is as calculated previously.

The impurity of the entire potential split is then

$$\sum_c(t_c / t_p) * i_c$$

where $t_c$ and $i_c$ are as calculated previously, and $t_p$ is the total weight of all observations in the parent node that is being split. Basically the fraction of the parent node's total weight that is in each child node $c$ multiplied by $c$'s impurity. You then choose the potential split that has the lowest impurity over all potential splits.

• Shouldn't $i_c$ be $1 - \sum_i (w_i n_i / t_c)^2$? if you increase the weights too much the impurity goes to 1. – Simone Sep 5 '13 at 4:55
• You're right. I seem to always make typos when converting code into mathematical expressions. I've fixed it now. – user28504 Sep 5 '13 at 10:46

Just a follow-up on Simon's answer.

The Gini index (impurity index) for a node $$c$$ can be defined as: $$i_c = \sum_i f_i \cdot ( 1- f_i) = 1 - \sum_i f_i^2$$ where $$f_i$$ is the fraction of records which belong to class $$i$$.

If we have a two class problem we can plot the Gini index varying the relative number of records of the first class $$f$$. That is $$f_1 = f$$ and $$f_2 = f - f_1$$.

We have very high impurity when the class distribution is uniform.

If we assign a weight to each class we are actually rebalancing the impurity index - a high weight for one class (say $$\bar{i}$$) leads to a stronger decrease of impurity when the number of records for that class increases. We will not have the maximum impurity when the class distribution is uniform anymore. Just a small amount of records in $$\bar{i}$$ will be enough to decrease the node impurity.

We can still sketch a two class problem example. In Simon's formulas our $$f_i$$s are $$f_i = \frac{w_i \cdot n_i}{\sum_i w_i \cdot n_i}$$ We can see that the formula does not change if $$\sum_i n_i = 1$$ and $$\sum_i w_i = 1$$ (it is enough to multiply numerator and denominator by the total number of records and total weight). Let $$f$$ be $$f = \frac{w \cdot n}{w \cdot n + (1-w)(1-n)}$$ where $$n$$ is the relative number of records for the first class and $$w$$ their weight. Now we could compute the Gini when we vary the relative number of records for the first class $$n$$.

For example if we choose a weight of $$0.9$$ we have maximum impurity when $$n \approx 0.1$$. If $$n$$ increases the impurity steeply decreases as well.

If we define the weigthed Gini index as the OP did we would for example have a strange behaviour in a two class problem: $$\sum_i w_i \cdot f_i \cdot (1 - f_i) = w \cdot f \cdot (1 - f) + (1 - w) \cdot (1-f) \cdot f = f \cdot ( 1- f)$$ However, I found a paper that uses that index here but I didn't read it, so I might be wrong.

Breiman's weighted index makes actually sense - we are trying to reweight the classes in a cost-sensitive way. The same approach is used in the MetaCost classifier implemented in WEKA.

In case anyone is interested, this is the R code I used to plot the figures:

require(ggplot2)

# two class probability distribution
f <- seq(0,1,0.01)

# Standard Gini impurity
# f1 = f and f2 = 1 - f
Gini <- f*(1-f) + (1-f)*f
qplot(f,Gini, geom = "path")

# Weighted Gini impurity
w <- seq(0,1,0.1)
w_ <- as.vector( sapply(w, function(x) rep(x,length(f))))
n <- rep(f,length(w))

f <- w_*n / ( w_*n + (1-w_)*(1-n) )
WeightedGini <- f*(1-f) + (1-f)*f

Weight <- as.factor(w_)
qplot(n, WeightedGini, colour = Weight, geom = "path")


text:
Volume 364 - European Physical Society Conference on High Energy Physics (EPS-HEP2019) - Heavy Ion Physics
On the pair correlations of neutral $K, D, B$ and $B_s$ mesons with close momenta produced in inclusive multiparticle processes
V.V. Lyuboshitz,* V.L. Lyuboshitz
*corresponding author
Full text: Not available
Abstract
The phenomenological structure of inclusive cross-sections of the production of two neutral $K$ mesons in hadron--hadron, hadron--nucleus and nucleus--nucleus collisions is theoretically investigated taking into account the strangeness conservation in strong and electromagnetic interactions. Relations describing the dependence of the correlations of two short-lived and two long-lived neutral kaons $K^0_S K^0_S$, $K^0_L K^0_L$ and the correlations of "mixed" pairs $K^0_S K^0_L$ at small relative momenta upon the space-time parameters of the generation region of $K^0$ and $\bar{K}^0$ mesons have been obtained. These relations involve the contributions of Bose-statistics and $S$-wave strong final-state interaction of two $K^0$ ($\bar{K}^0$) mesons as well as of the $K^0$ and
$\bar{K}^0$ mesons, and also the additional contribution of
transitions $K^+ K^- \rightarrow K^0 \bar{K}^0$, and they depend upon the relative fractions of generated pairs $K^0 K^0$,
$\bar{K}^0 \bar{K}^0$ and $K^0 \bar{K}^0$. It is shown that under the strangeness conservation the correlation functions of
the pairs $K^0_S K^0_S$ and $K^0_L K^0_L$, produced in the same
inclusive process, coincide, and the difference between the
correlation functions of the pairs $K^0_S K^0_S$ and $K^0_S K^0_L$ is conditioned exclusively by the production of the pairs of non-identical neutral kaons $K^0 \bar{K}^0$.

For comparison, analogous correlations for the pairs of neutral heavy mesons $D^0$, $B^0$ and $B_s^0$, generated in multiple inclusive processes with charm ( beauty ) conservation, are also theoretically analyzed -- neglecting, just as for the case of $K^0$ mesons, the weak effects of $CP$ violation. These correlations have a quite similar character and they are described by quite similar expressions: in particular, just as for $K^0$ mesons, the correlation functions for the pairs of states with the same $CP$ parity ($R_{SS}=R_{LL}$) and with different $CP$ parity ($R_{SL}$) do not coincide, and the difference between them is conditioned exclusively by the production of pairs $D^{0}\bar{D}^{0}$, $B^{0}\bar{B}^{0}$ and $B_s^{0}\bar{B}_s^{0}$ . However, contrary to the case of $K^0$ mesons, here the distinction of $CP$-even and $CP$-odd states ( and, hence, the experimental observation of respective pair correlations ) encounters difficulties -- due to the insignificant differences of their lifetimes and the relatively small probability of purely $CP$-even and $CP$-odd decay channels. Nevertheless, one may expect that this will become possible at future colliders.

How to cite

Metadata are provided both in "article" format (very similar to INSPIRE) as this helps creating very compact bibliographies which can be beneficial to authors and readers, and in "proceeding" format which is more detailed and complete.

Open Access
Copyright owned by the author(s) under the term of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.


text:
# Set of orthonormal vectors can be identified with set of matrices

Let $V_k(\mathbb{R}^n)$ be the set of all orthonormal $k$-tuples of vectors $v_1,\ldots,v_k\in\mathbb{R}^n$. Let $M_{k,n}$ be the set of all $k\times n$ matrices. Let $W=\{A\in M_{k,n}\mid AA^t=I_k\}$, where $I_k$ is the identity $k\times k$ matrix. Prove that $V_k(\mathbb{R^n})$ can be identified with $W$.

(I'm not sure what "can be identified with" means. Maybe it just means showing there is a bijection.)

We just put in the vectors $v_1,\ldots,v_k$ as rows of $A$. Then these vectors are columns of $A_t$, so that $AA^t=I_k$ by definition of orthonormality. Conversely, given any $A$, we can let $v_1,\ldots,v_k$ be its rows.

It is exactly as you say. One says "identified" because you are not defining a bijection at random (after all, both sets have the same cardinality as $\mathbb R$), but rather you are creating your bijection in terms of the properties of the objects you are using.
• Thank you, Martin. May I know why both sets have the same cardinality as $\mathbb{R}$? It does not seem obvious to me. – Mika H. Nov 9 '13 at 3:44
• You are welcome. The cardinality of $\mathbb R^n$ is the same as that of $\mathbb R$, so that's the upper limit. So all we need to show is that there are uncountably many orthogonal tuples. And that already happens for the $2$-tuples: $(\cos t,\sin t)$, $(-\sin t, \cos t)$ for $t\in[0,2\pi)$. – Martin Argerami Nov 9 '13 at 3:55


text:
• ### Crossover from itinerant to localized magnetic excitations through the metal-insulator transition in NaOsO$_{\text{3}}$(1707.05551)

Feb. 4, 2019 cond-mat.str-el
NaOsO$_{\text{3}}$ undergoes a metal-insulator transition (MIT) at 410 K, concomitant with the onset of antiferromagnetic order. The excitation spectra have been investigated through the MIT by resonant inelastic x-ray scattering (RIXS) at the Os L$_{\text{3}}$ edge. Low resolution ($\Delta E \sim$ 300 meV) measurements over a wide range of energies reveal that local electronic excitations do not change appreciably through the MIT. This is consistent with a picture in which structural distortions do not drive the MIT. In contrast, high resolution ($\Delta E \sim$ 56 meV) measurements show that the well-defined, low energy magnons in the insulating state weaken and dampen upon approaching the metallic state. Concomitantly, a broad continuum of excitations develops which is well described by the magnetic fluctuations of a nearly antiferromagnetic Fermi liquid. By revealing the continuous evolution of the magnetic quasiparticle spectrum as it changes its character from itinerant to localized, our results provide unprecedented insight into the nature of the MIT in \naoso. In particular, the presence of weak correlations in the paramagnetic phase implies a degree of departure from the ideal Slater limit.
• ### High-pressure insulator-to-metal transition in Sr$_3$Ir$_2$O$_7$ studied by x-ray absorption spectroscopy(1801.02234)

Jan. 7, 2018 cond-mat.str-el
High-pressure x-ray absorption spectroscopy was performed at the Ir $L_3$ and $L_2$ absorption edges of Sr$_3$Ir$_2$O$_7$. The branching ratio of white line intensities continuously decreases with pressure, reflecting a reduction in the angular part of the expectation value of the spin-orbit coupling operator, $\left\langle {\bf L} \cdot {\bf S} \right\rangle$. Up to the high-pressure structural transition at 53 GPa, this behavior can be explained within a single-ion model, where pressure increases the strength of the cubic crystal field, which suppresses the spin-orbit induced hybridization of $J_{\text{eff}} = 3/2$ and $e_g$ levels. We observe a further reduction of the branching ratio above the structural transition, which cannot be explained within a single-ion model of spin-orbit coupling and cubic crystal fields. This change in $\left\langle {\bf L} \cdot {\bf S} \right\rangle$ in the high-pressure, metallic phase of Sr$_3$Ir$_2$O$_7$ could arise from non-cubic crystal fields or a bandwidth-driven hybridization of $J_{\text{eff}}=1/2,\,3/2$ states, and suggests that the electronic ground state significantly deviates from the $J_{\text{eff}}=1/2$ limit.
• ### Strongly Gapped Spin-Wave Excitation in the Insulating Phase of NaOsO3(1608.08477)

NaOsO3 hosts a rare manifestation of a metal-insulator transition driven by magnetic correlations, placing the magnetic exchange interactions in a central role. We use resonant inelastic x-ray scattering to directly probe these magnetic exchange interactions. A dispersive and strongly gapped (58 meV) excitation is observed indicating appreciable spin-orbit coupling in this 5d3 system. The excitation is well described within a minimal model Hamiltonian with strong anisotropy and Heisenberg exchange (J1=J2=13.9 meV). The observed behavior places NaOsO3 on the boundary between localized and itinerant magnetism.
• ### Bound states and field-polarized Haldane modes in a quantum spin ladder(1609.00198)

Sept. 1, 2016 cond-mat.str-el
The challenge of one-dimensional systems is to understand their physics beyond the level of known elementary excitations. By high-resolution neutron spectroscopy in a quantum spin ladder material, we probe the leading multiparticle excitation by characterizing the two-magnon bound state at zero field. By applying high magnetic fields, we create and select the singlet (longitudinal) and triplet (transverse) excitations of the fully spin-polarized ladder, which have not been observed previously and are close analogs of the modes anticipated in a polarized Haldane chain. Theoretical modelling of the dynamical response demonstrates our complete quantitative understanding of these states.
• ### Pressure dependence of the structure and electronic properties of Sr3Ir2O7(1508.04320)

We study the structural evolution of Sr$_3$Ir$_2$O$_7$ as a function of pressure using x-ray diffraction. At a pressure of 54 GPa at room temperature, we observe a first-order structural phase transition, associated with a change from tetragonal to monoclinic symmetry, and accompanied by a 4% volume collapse. Rietveld refinement of the high-pressure phase reveals a novel modification of the Ruddlesden-Popper structure, which adopts an altered stacking sequence of the perovskite bilayers. As the positions of the oxygen atoms could not be reliably refined from the data, we use density functional theory (local-density approximation+$U$+spin orbit) to optimize the crystal structure, and to elucidate the electronic and magnetic properties of Sr$_3$Ir$_2$O$_7$ at high pressure. In the low-pressure tetragonal phase, we find that the in-plane rotation of the IrO$_6$ octahedra increases with pressure. The calculations further indicate that a bandwidth-driven insulator-metal transition occurs at $\sim$20 GPa, along with a quenching of the magnetic moment. In the high-pressure monoclinic phase, structural optimization resulted in complex tilting and rotation of the oxygen octahedra, and strongly overlapping $t_{2g}$ and $e_g$ bands. The $t_{2g}$ bandwidth renders both the spin-orbit coupling and electronic correlations ineffectual in opening an electronic gap, resulting in a robust metallic state for the high-pressure phase of Sr$_3$Ir$_2$O$_7$.
• ### All-in all-out magnetic order and propagating spin-waves in Sm2Ir2O7(1604.06401)

April 21, 2016 cond-mat.str-el
Using resonant magnetic x-ray scattering we address the unresolved nature of the magnetic groundstate and the low-energy effective Hamiltonian of Sm$_2$Ir$_2$O$_7$, a prototypical pyrochlore iridate with a finite temperature metal-insulator transition. Through a combination of elastic and inelastic measurements, we show that the magnetic ground state is an all-in all-out (AIAO) antiferromagnet. The magnon dispersion indicates significant electronic correlations and can be well-described by a minimal Hamiltonian that includes Heisenberg exchange ($J=27.3(6)$ meV) and Dzyaloshinskii-Moriya interaction ($D=4.9(3)$ meV), which provides a consistent description of the magnetic order and excitations. In establishing that Sm$_2$Ir$_2$O$_7$ has the requisite inversion symmetry preserving AIAO magnetic groundstate, our results support the notion that pyrochlore iridates may host correlated Weyl semimetals.
• ### Ultrafast energy and momentum resolved dynamics of magnetic correlations in photo-doped Mott insulator Sr$_2$IrO$_4$(1604.02439)

Measuring how the magnetic correlations throughout the Brillouin zone evolve in a Mott insulator as charges are introduced dramatically improved our understanding of the pseudogap, non-Fermi liquids and high $T_C$ superconductivity. Recently, photoexcitation has been used to induce similarly exotic states transiently. However, understanding how these states emerge has been limited because of a lack of available probes of magnetic correlations in the time domain, which hinders further investigation of how light can be used to control the properties of solids. Here we implement magnetic resonant inelastic X-ray scattering at a free electron laser, and directly determine the magnetization dynamics after photo-doping the Mott insulator Sr$_2$IrO$_4$. We find that the non-equilibrium state 2~ps after the excitation has strongly suppressed long-range magnetic order, but hosts photo-carriers that induce strong, non-thermal magnetic correlations. The magnetism recovers its two-dimensional (2D) in-plane N\'eel correlations on a timescale of a few ps, while the three-dimensional (3D) long-range magnetic order restores over a far longer, fluence-dependent timescale of a few hundred ps. The dramatic difference in these two timescales, implies that characterizing the dimensionality of magnetic correlations will be vital in our efforts to understand ultrafast magnetic dynamics.
• ### Emergent excitation at the magnetic metal-insulator transition in the pyrochlore osmate Cd2Os2O7(1508.01848)

The rich physics manifested by 5d oxides falls outside the Mott-Hubbard paradigm used to successfully explain the electronic and magnetic properties of 3d oxides. Much consideration has been given to the extent to which strong spin-orbit coupling (SOC), in the limit of increased bandwidth and reduced electron correlation, drives the formation of novel electronic states, as manifested through the existence of metal-insulator transitions (MITs). SOC is believed to play a dominant role in 5d5 systems such as iridates (Ir4+), undergoing MITs which may or may not be intimately connected to magnetic order, with pyrochlore and perovksite systems being examples of the former and latter, respectively. However, the role of SOC for other 5d configurations is less clear. For example, 5d3 (e.g Os5+) systems are expected to have an orbital singlet and consequently a reduced effect of SOC in the groundstate. The pyrochlore osmate Cd2Os2O7 nonetheless exhibits a MIT intimately entwined with magnetic order with phenomena similar to pyrochlore iridates. Here we report the first resonant inelastic X-ray scattering (RIXS) measurements on an osmium compound, allowing us to determine the salient electronic and magnetic energy scales controlling the MIT in Cd2Os2O7, which we benchmark against detailed quantum chemistry calculations. In particular, we reveal the emergence at the MIT of a magnetic excitation corresponding to a superposition of multiple spin-flip processes from an Ising-like all-in/all-out magnetic groundstate. We discuss our results with respect to the role of SOC in magnetically mediated MITs in 5d systems
• ### The importance of XY anisotropy in Sr2IrO4 revealed by magnetic critical scattering experiments(1506.07720)

June 25, 2015 cond-mat.str-el
The magnetic critical scattering in Sr$_2$IrO$_4$ has been characterized using X-ray resonant magnetic scattering (XRMS) both below and above the 3D antiferromagnetic ordering temperature, T$_{\text{N}}$. The order parameter critical exponent below T$_{\text{N}}$ is found to be \beta=0.195(4), in the range of the 2D XYh$_4$ universality class. Over an extended temperature range above T$_{\text{N}}$, the amplitude and correlation length of the intrinsic critical fluctuations are well described by the 2D Heisenberg model with XY anisotropy. This contrasts with an earlier study of the critical scattering over a more limited range of temperature which found agreement with the theory of the isotropic 2D Heisenberg quantum antiferromagnet, developed to describe the critical fluctuations of the conventional Mott insulator La$_2$CuO$_4$ and related systems. Our study therefore establishes the importance of XY anisotropy in the low-energy effective Hamiltonian of Sr$_2$IrO$_4$, the prototypical spin-orbit Mott insulator.
• ### Fractional excitations in the square-lattice quantum antiferromagnet(1501.01767)

Jan. 8, 2015 cond-mat.str-el
The square-lattice quantum Heisenberg antiferromagnet displays a pronounced anomaly of unknown origin in its magnetic excitation spectrum. The anomaly manifests itself only for short wavelength excitations propagating along the direction connecting nearest neighbors. Using polarized neutron spectroscopy, we have fully characterized the magnetic fluctuations in the model metal-organic compound CFTD, revealing an isotropic continuum at the anomaly indicative of fractional excitations. A theoretical framework based on the Gutzwiller projection method is developed to explain the origin of the continuum at the anomaly. This indicates that the anomaly arises from deconfined fractional spin-1/2 quasiparticle pairs, the 2D analog of 1D spinons. Away from the anomaly the conventional spin-wave spectrum is recovered as pairs of fractional quasiparticles bind to form spin-1 magnons. Our results therefore establish the existence of fractional quasiparticles in the simplest model two dimensional antiferromagnet even in the absence of frustration.
• ### Magnetic excitation spectrum of LuFe2O4 measured with inelastic neutron scattering(1406.7418)

June 28, 2014 cond-mat.str-el
We report neutron inelastic scattering measurements and analysis of the spectrum of magnons propagating within the Fe2O4 bilayers of LuFe2O4. The observed spectrum is consistent with six magnetic modes and a single prominent gap, which is compatible with a single bilayer magnetic unit cell containing six spins. We model the magnon dispersion by linear spin-wave theory and find very good agreement with the domain-averaged spectrum of a spin-charge bilayer superstructure comprising one Fe3+ -rich monolayer and one Fe2+ -rich monolayer. These findings indicate the existence of polar bilayers in LuFe2O4, contrary to recent studies that advocate a charge-segregated non-polar bilayer model. Weak scattering observed below the magnon gap suggests that a fraction of the bilayers contain other combinations of charged monolayers not included in the model. Refined values for the dominant exchange interactions are reported.
• ### Crystal field splitting in Sr$_{n+1}$Ir$_n$O$_{3n+1}$ ($n$ = 1, 2) iridates probed by x-ray Raman spectroscopy(1405.6522)

May 26, 2014 cond-mat.str-el
Non-resonant Raman spectroscopy in the hard X-ray regime has been used to explore the electronic structure of the first two members of the Ruddlesden-Popper series Sr$_{n+1}$Ir$_n$O$_{3n+1}$ of iridates. By tuning the photon energy transfer around 530 eV we have been able to explore the oxygen K near edge structure with bulk sensitivity. The angular dependence of the spectra has been exploited to assign features in the 528-535 eV energy range to specific transitions involving the Ir 5d orbitals. This has allowed us to extract reliable values for both the t2g-eg splitting arising from the cubic component of the crystal field (10Dq), in addition to the splitting of the eg orbitals due to tetragonal distortions. The values we obtain are (3.8, 1.6) eV and (3.55, 1.9) eV for Sr$_2$IrO$_4$ and Sr$_3$Ir$_2$O$_7$, respectively.
• ### Quantum and classical criticality in a dimerized quantum antiferromagnet(1405.2391)

May 10, 2014 cond-mat.str-el
A quantum critical point (QCP) is a singularity in the phase diagram arising due to quantum mechanical fluctuations. The exotic properties of some of the most enigmatic physical systems, including unconventional metals and superconductors, quantum magnets, and ultracold atomic condensates, have been related to the importance of the critical quantum and thermal fluctuations near such a point. However, direct and continuous control of these fluctuations has been difficult to realize, and complete thermodynamic and spectroscopic information is required to disentangle the effects of quantum and classical physics around a QCP. Here we achieve this control in a high-pressure, high-resolution neutron scattering experiment on the quantum dimer material TlCuCl3. By measuring the magnetic excitation spectrum across the entire quantum critical phase diagram, we illustrate the similarities between quantum and thermal melting of magnetic order. We prove the critical nature of the unconventional longitudinal ("Higgs") mode of the ordered phase by damping it thermally. We demonstrate the development of two types of criticality, quantum and classical, and use their static and dynamic scaling properties to conclude that quantum and thermal fluctuations can behave largely independently near a QCP.
• ### Spin wave spectrum of the quantum ferromagnet on the pyrochlore lattice Lu2V2O7(1405.2284)

May 9, 2014 cond-mat.str-el
Neutron inelastic scattering has been used to probe the spin dynamics of the quantum (S=1/2) ferromagnet on the pyrochlore lattice Lu2V2O7. Well-defined spin waves are observed at all energies and wavevectors, allowing us to determine the parameters of the Hamiltonian of the system. The data are found to be in excellent overall agreement with a minimal model that includes a nearest- neighbour Heisenberg exchange J = 8:22(2) meV and a Dzyaloshinskii-Moriya interaction (DMI) D =1:5(1) meV. The large DMI term revealed by our study is broadly consistent with the model developed by Onose et al. to explain the magnon Hall effect they observed in Lu2V2O7 [1], although our ratio of D=J = 0:18(1) is roughly half of their value and three times larger than calculated by ab initio methods [2].
• ### Circularly Polarised X-ray Scattering Investigation of Spin-Lattice Coupling in TbMnO$_3$ in Crossed Electric and Magnetic Fields(1311.6617)

Jan. 10, 2014 cond-mat.str-el
We present a study of the magnetic and crystallographic structure of TbMnO$_3$ in the presence of crossed electric and magnetic fields using circularly polarised X-ray non-resonant scattering. A comprehensive account is presented of the scattering theory and data analysis methods used in our earlier studies, and in addition we present new high magnetic field data and its analysis. We discuss in detail how polarisation analysis was used to reveal structural information, including the arrangement of Tb moments which we proposed for $H = 0$ T, and how the diffraction data for $H<H_C$ can be used to determine specific magnetostrictively induced atomic displacements with femto-metre accuracy. The connection between the electric polarisation and magnetostrictive mechanisms is discussed. Similar magnetostrictive displacements have been observed for $H > H_C$ as for $H < H_C$. Finally some observations regarding the kinetics and the conservation of domain population at the transition are described.
• ### Orbital occupancies and the putative jeff = 1/2 groundstate in Ba2IrO4: a combined oxygen K edge XAS and RIXS study(1312.0857)

Dec. 3, 2013 cond-mat.str-el
The nature of the electronic groundstate of Ba2IrO4 has been addressed using soft X-ray absorption and inelastic scattering techniques in the vicinity of the oxygen K edge. From the polarization and angular dependence of XAS we deduce an approximately equal superposition of xy, yz and zx Ir4+ 5d orbitals. By combining the measured orbital occupancies, with the value of the spin-orbit coupling provided by RIXS, we estimate the crystal field splitting associated with the tetragonal distortion of the IrO6 octahedra to be small, \Delta=50(50) meV. We thus conclude definitively that Ba2IrO4 is a close realization of a spin-orbit Mott insulator with a jeff = 1/2 groundstate, thereby overcoming ambiguities in this assignment associated with the interpretation of X-ray resonant scattering experiments.
• ### Resonant X-ray scattering and the $j_{\mathrm{eff}}=1/2$ electronic ground state in iridate perovskites(1308.0128)

Aug. 1, 2013 cond-mat.str-el
The resonant X-ray scattering (magnetic elastic, RXMS, and inelastic, RIXS) of Ir$^{4+}$ at the L$_{2,3}$ edges relevant to spin-orbit Mott insulators A$_{n+1}$Ir$_{n}$O$_{3n+1}$ (A=Sr, Ba, etc.) are calculated using a single-ion model which treats the spin-orbit and tetragonal crystal-field terms on an equal footing. Both RXMS and RIXS in the spin-flip channel are found to display a non-trivial dependence on the direction of the magnetic moment, $\boldsymbol\mu$. Crucially, we show that for $\boldsymbol\mu$ in the \emph{ab}-plane, RXMS at the L$_2$ edge is zero \emph{irrespective} of the tetragonal crystal-field; spin-flip RIXS, relevant to measurements of magnons, behaves reciprocally being zero at L$_2$ when $\boldsymbol\mu$ is perpendicular to the \emph{ab}-plane. Our results provide important insights into the interpretation of X-ray data from the iridates, including that a $j_{\mathrm{eff}}=1/2$ ground state cannot be assigned on the basis of L$_2$/L$_3$ intensity ratio alone.
• ### Robustness of basal-plane antiferromagnetic order and the $J_{eff}=1/2$ state in single-layer iridate spin-orbit Mott insulators(1212.5912)

Dec. 24, 2012 cond-mat.str-el
The magnetic structure and electronic groundstate of the layered perovskite Ba2IrO4 have been investigated using x-ray resonant magnetic scattering (XRMS). Our results are compared with those for Sr2IrO4, for which we provide supplementary data on its magnetic structure. We find that the dominant, long-range antiferromagnetic order is remarkably similar in the two compounds, and that the electronic groundstate in Ba2IrO4, deduced from an investigation of the XRMS $L_3/L_2$ intensity ratio, is consistent with a $J_{eff}=1/2$ description. The robustness of these two key electronic properties to the considerable structural differences between the Ba and Sr analogues is discussed in terms of the enhanced role of the spin-orbit interaction in 5d transition metal oxides.
• ### The J_{eff}=1/2 insulator Sr3Ir2O7 studied by means of angle-resolved photoemission spectroscopy(1207.1556)

Sept. 26, 2012 cond-mat.str-el
The low-energy electronic structure of the J_{eff}=1/2 spin-orbit insulator Sr3Ir2O7 has been studied by means of angle-resolved photoemission spectroscopy. A comparison of the results for bilayer Sr3Ir2O7 with available literature data for the related single-layer compound Sr2IrO4 reveals qualitative similarities and similar J_{eff}=1/2 bandwidths for the two materials, but also pronounced differences in the distribution of the spectral weight. In particuar, photoemission from the J_{eff}=1/2 states appears to be suppressed. Yet, it is found that the Sr3Ir2O7 data are in overall better agreement with band-structure calculations than the data for Sr2IrO4.
• ### Magnetically driven metal-insulator transition in NaOsO3(1202.1482)

The metal-insulator transition (MIT) is one of the most dramatic manifestations of electron correlations in materials. Various mechanisms producing MITs have been extensively considered, including the Mott (electron localization via Coulomb repulsion), Anderson (localization via disorder) and Peierls (localization via distortion of a periodic 1D lattice). One additional route to a MIT proposed by Slater, in which long-range magnetic order in a three dimensional system drives the MIT, has received relatively little attention. Using neutron and X-ray scattering we show that the MIT in NaOsO3 is coincident with the onset of long-range commensurate three dimensional magnetic order. Whilst candidate materials have been suggested, our experimental methodology allows the first definitive demonstration of the long predicted Slater MIT. We discuss our results in the light of recent reports of a Mott spin-orbit insulating state in other 5d oxides.
• ### Antiferromagnetic order and domains in Sr3Ir2O7 probed by x-ray resonant scattering(1201.1452)

Jan. 6, 2012 cond-mat.str-el
This article reports a detailed x-ray resonant scattering study of the bilayer iridate compound, Sr3Ir2O7, at the Ir L2 and L3 edges. Resonant scattering at the Ir L3 edge has been used to determine that Sr3Ir2O7 is a long-range ordered antiferromagnet below TN 230K with an ordering wavevector, q=(1/2,1/2,0). The energy resonance at the L3 edge was found to be a factor of ~30 times larger than that at the L2. This remarkable effect has been seen in the single layer compound Sr2IrO4 and has been linked to the observation of a Jeff=1/2 spin-orbit insulator. Our result shows that despite the modified electronic structure of the bilayer compound, caused by the larger bandwidth, the effect of strong spin-orbit coupling on the resonant magnetic scattering persists. Using the programme SARAh, we have determined that the magnetic order consists of two domains with propagation vectors k1=(1/2,1/2,0) and k2=(1/2,-1/2,0), respectively. A raster measurement of a focussed x-ray beam across the surface of the sample yielded images of domains of the order of 100 microns size, with odd and even L components, respectively. Fully relativistic, monoelectronic calculations (FDMNES), using the Green's function technique for a muffin-tin potential have been employed to calculate the relative intensities of the L2,3 edge resonances, comparing the effects of including spin-orbit coupling and the Hubbard, U, term. A large L3 to L2 edge intensity ratio (~5) was found for calculations including spin-orbit coupling. Adding the Hubbard, U, term resulted in changes to the intensity ratio <5%.
• ### Femtoscale magnetically induced lattice distortions in multiferroic TbMnO3(1110.2875)

Magneto-electric multiferroics exemplified by TbMnO3 possess both magnetic and ferroelectric long-range order. The magnetic order is mostly understood, whereas the nature of the ferroelectricity has remained more elusive. Competing models proposed to explain the ferroelectricity are associated respectively with charge transfer and ionic displacements. Exploiting the magneto-electric coupling, we use an electric field to produce a single magnetic domain state, and a magnetic field to induce ionic displacements. Under these conditions, interference charge-magnetic X-ray scattering arises, encoding the amplitude and phase of the displacements. When combined with a theoretical analysis, our data allow us to resolve the ionic displacements at the femtoscale, and show that such displacements make a significant contribution to the zero-field ferroelectric moment.
• ### Strong coupling of Sm and Fe magnetism in SmFeAsO as revealed by magnetic x-ray scattering(1107.1778)

The magnetic structures adopted by the Fe and Sm sublattices in SmFeAsO have been investigated using element specific x-ray resonant and non-resonant magnetic scattering techniques. Between 110 and 5 K, the Sm and Fe moments are aligned along the c and a directions, respectively according to the same magnetic representation $\Gamma_{5}$ and the same propagation vector (1, 0, 0.5). Below 5 K, magnetic order of both sublattices change to a different magnetic structure and the Sm moments reorder in a magnetic unit cell equal to the chemical unit cell. Modeling of the temperature dependence for the Sm sublattice as well as a change in the magnetic structure below 5 K provide a clear evidence of a surprisingly strong coupling between the two sublattices, and indicate the need to include anisotropic exchange interactions in models of SmFeAsO and related compounds.
• ### Comparative study of the phonons in non-superconducting BaC6 and superconducting CaC6 using inelastic x-ray scattering(1102.4767)

The low energy phonons of two different graphite intercalation compounds (GICs) have been measured as a function of temperature using inelastic x-ray scattering (IXS). In the case of the non-superconductor BaC6, the phonons observed are significantly higher (up to 20 %) in energy than those predicted by theory, in contrast to the reasonable agreement found in superconducting CaC6. Additional IXS intensity is observed below 15 meV in both BaC6 and CaC6. It has been previously suggested that this additional inelastic intensity may arise from defect or vacancy modes in these compounds, unpredicted by theory (d'Astuto et al, Phys. Rev. B 81 104519 (2010)). Here it is shown that this additional intensity can arise directly from the large disorder of the available samples. Our results show that future theoretical work is required to understand the relationship between the crystal structure, the phonons and the superconductivity in GICs.
• ### Phonons and superconductivity in YbC$_6$ and related compounds(1009.3056)

Sept. 15, 2010 cond-mat.supr-con
The out-of-plane intercalate phonons of superconducting YbC6 have been measured with inelastic x-ray scattering. Model fits to this data, and previously measured out-of-plane intercalate phonons in graphite intercalation compounds (GICs), reveal surprising trends with the superconducting transition temperature. These trends suggest that superconducting GICs should be viewed as electron-doped graphite.


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Keywords: Backpropagation, BP

## Speed Backpropagation up [1]

BP algorithm has been described in ‘An Introduction to Backpropagation and Multilayer Perceptrons’. And the implement of the BP algorithm has been recorded at ‘The Backpropagation Algorithm (Part I)’ and ‘The Backpropagation Algorithm (Part II)’. BP has worked in many applications, but there are too many drawbacks in the process. The basic BP algorithm is too slow for most practical applications that it might take days or even weeks in training. And these following 4 posts are some investigations to make the BP algorithm more practical and to speed it up.

In the post ‘Backpropagation, Batch Training, and Incremental Training’, the BP approximation example had shown that the algorithm converged very slowly. BP is a variation of LMS and LMS is a variation of ‘steepest descent’. So BP is a kind of steepest descent, and the difference between them is the calculation of derivatives. Steepest descent is the simplest and the slowest, while Newton and conjugate algorithms are faster. Then inspiration comes to us whether these algorithms can be used in speeding up the convergence of BP.

Research on faster algorithm falls on rough two categories and some directions would be discussed:

1. Development of heuristic techniques
• varying learning rate
• momentum
• rescaling variables
2. The standard numerical optimization technique
• find a numerical optimization technique already exists. ‘Reinvent the wheel’ is a good and bad idea.
• Levenberg-Marquardt algorithm

Backpropagation is called ‘back’ because in the calculation of the derivative of the sensitivities in the hidden layer are calculated by its next layer neurons that have connections with it. And the weights and biases updating process of BP is the same as the steepest descent. So we name the standard backpropagation algorithm steepest descent backpropagation and SDBP for short.

## Drawbacks of Backpropagation

LMS guarantee to converge that minimize the MSE under the condition that the learning rate $\alpha$ is small enough. MSE is a quadratic function that has always a single stationary point and constant Hessian. Because Hessian matrices of quadratic functions do not change, so the curvature of functions would not change and their contours are elliptical.

When BP is used in a layered network, it degenerates to the LMS algorithm. The MSE of the single-layer network is quadratic. So it has a single stationary point and constant curvature.

But when the network has more than one layer, MSE of it is no more quadratic. MSE of multiple layers network has many local minimum points and curvature varies widely in a different region of parameter space. Now let go to look at the surface of MSE of multiple layers network. The simplest network 1-2-1 would be our example and its abbreviated notation is:

the transfer functions of both the hidden layer and the output layer are log-sigmoid function. And in the following experiment the function to approximate has the same architecture of the 1-2-1 network and its parameters are:

\begin{aligned} \{&\\ &w^1_{1,1}=10,b^1_{1}=-5,\\ &w^1_{1,2}=10,b^1_{2}=5,\\ &w^2_{1,1}=1,w^2_{1,2}=1,b^2=-1\\ \}& \end{aligned} \tag{1}

Then in this task, the global minimum point is at equation(1). And in the interval $[-2,2]$ the target function looks like:

Because the target function to be approximated has the same architecture with our model, the 1-2-1 network can have the correct approximation where MSE is 0. Although this experiment is humble compared to practical applications, it can illustrate some important concepts.

To approximate the target function, we generate the inputs:

$\{-2.0,-1.9,\cdot,1.9,2.0\}$

with equivalent probability and the corresponding outputs. The performance index is the sum of square error which equals to MSE.

There are 7 parameters in this simple network model totally. However, we can not observe them all at one picture. We set $b^1_{1},w^1_{1,2},b^1_{2},w^2_{1,2},b^2$ to their optimum values given by equation(1) and leave $w^1_{1,1}$ and $w^2_{1,1}$ as variables. Then we get the contour map:

The performance index is not quadratic. Then it has more than one minimum, for instance, $w^1_{1,1}=0.88$ and $w^2_{1,1}= 38.6$ and other parameters are set as equation(1) is also a local minimum of the performance index. The curvature varies drastically over the parameter space and a constant learning rate can not suit the entire process. Because some regions are flat where a large learning rate is good, and some regions of curvature are high where a small learning rate is necessary. The flat region is a common condition when the transfer function of the network is sigmoid. For example, when the inputs are large, the surface of the performance index of the sigmoid network is very flat.

Because the 1-2-1 network has a symmetrical architecture, the surface of $b^1_1$ and $b^1_2$ is symmetric as well. and between these two local minimum there must be a saddle point which is at $b^1_1=0,b^1_2=0$:

So $b^1_1=0$ and $b^1_2=0$ are not good initial values. And if initial values of the parameters were large, the learning algorithm would start at a very flat region, this is also the nightmare for most algorithms. Trying several initial guesses is also a good method but when the whole training process needs days or weeks this method is impractical. A common method to initial parameters of networks is using small random numbers as a random number between $-1$ and $1$ with uniform distribution.

## Convergence Example

The batching method has been introduced in ‘Backpropagation, Batch Training, and Incremental Training’. It is a generalized method that uses the whole training set of the ‘The Backpropagation Algorithm (Part I)’ and ‘The Backpropagation Algorithm (Part II)’, which uses one point of training set a time. The following process is based on the batching method.

Now let’s consider the parameter $w^1_{1,1}$ and the $w^2_{1,1}$ while other parameters are set to optimum solution as in equation(1).

The first example is with initial guesses $w^1_{1,1}=-4$ and $w^2_{1,1}=-4$ whose trajectory is labeled as ‘a’:

It takes a long time during the flat region and the entire process takes more than 300,000 epochs. And the sum of the square error of the performance index is:

The flat region takes a great part of the whole process.

The second example is with initial guesses $w^1_{1,1}=-4$ and $w^2_{1,1}=10$ whose trajectory is labeled as ‘b’:

It converges to another local minimum point but not the global minimum. And the sum of squire error of the performance index is:

whose final point can not reduce error to 0.

As we have mentioned above, to the flat region a bigger learning rate is required. Now let’s start at $w^1_{1,1}=-4$ and $w^2_{1,1}=-4$ as well. But when we increase the learning rate from $1$ to $100$, the algorithm becomes unstable:

and it’s error is not decrease after some iterations:

After all the experiments above, we found that flat regions are everywhere then a larger learning rate is required. However, a large learning rate makes the algorithm unstable. What we do next is to make the algorithm stable and fast.

## References

1. Demuth, H.B., Beale, M.H., De Jess, O. and Hagan, M.T., 2014. Neural network design. Martin Hagan. ↩


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Now showing items 1-20 of 19963

• #### Characterizing Large-Scale Resting State Effective Connectivity Patterns with Functionally Constrained Priors in Individuals with a History of Major Depressive Disorder

Major depressive disorder (MDD) is a common mental health condition (Kessler & Bromet, 2013) and the 3rd leading cause of disability worldwide (James et al., 2018). MDD history is a significant risk factor for relapse and recurrence of depression (Buckman et al., 2018; Burcusa & Iacono, 2007). The current study investigated resting state effective connectivity among 13 brain regions from three resting state networks (i.e., default, salience, and central executive), which had been implicated in the pathophysiology of MDD from previous studies (Kaiser et al., 2015; Mulders et al., 2015). In the current study, both within- and between-networks effective connectivity were found to be different in those with a MDD history (N=29) compared to the healthy controls (N=28), through spectral dynamic causal modeling (Friston, Kahan, Biswal, et al., 2014), Bayesian model reduction (Friston et al., 2016), and parametric empirical Bayes (Zeidman, Jafarian, Seghier, et al., 2019) analyses. Of particular interest is the finding that there is more negative effective connectivity from right anterior insula to left dorsolateral prefrontal cortex and left inferior parietal lobe in MDD history. Previous studies have found less causal influence from anterior insula to prefrontal cortex in currently depressed individuals (Hyett et al., 2015; Iwabuchi et al., 2014; Kandilarova et al., 2018). Given the importance of anterior insular in interoception and subjective feelings (Craig & Craig, 2009), the current study provides some preliminary evidence that altered effective connectivity between anterior insula and prefrontal cortex may be related to MDD history as well.
• #### Trapping Sets of Iterative Decoders for Quantum and Classical Low-Density Parity-Check Codes

Protecting logical information in the form of a classical bit or a quantum bit (qubit) is an essential step in ensuring fault-tolerant classical or quantum computation. Error correction codes and their decoders perform this step by adding redundant information that aids the decoder to recover or protect the logical information even in the presence of noise. Low-density parity-check (LDPC) codes have been one of the most popular error correction candidates in modern communication and data storage systems. Similarly, their quantum analogues, quantum LDPC codes are being actively pursued as excellent prospects for error correction in future fault-tolerant quantum systems due to their asymptotically non-zero rates, sparse parity check matrices, and efficient iterative decoding algorithms. This dissertation deals with failure configurations, known as \emph{trapping sets} of classical and quantum LDPC codes when decoded with iterative message passing decoding algorithms, and the \emph{error floor phenomenon} - the degradation of logical error rate performance at low physical noise regime. The study of quantum trapping sets will enable the construction of better quantum LDPC codes and also help in modifying iterative quantum decoders to achieve higher fault-tolerant thresholds and lower error floors. Towards this goal, the dissertation also presents iterative decoders for classical and quantum LDPC codes using the \emph{deep neural network framework}, novel iterative decoding algorithms, and a decoder-aware \emph{expansion-contraction method} for error floor estimation. In this dissertation, we first establish a systematic methodology by which one can identify and classify \emph{quantum trapping sets} (QTSs) according to their topological structure and decoder used. For this purpose, we leverage the known harmful configurations in the Tanner graph, called \emph{trapping sets} (TSs), from the classical error correction world. The conventional definition of a trapping set of classical LDPC codes is generalized to address the syndrome decoding scenario for quantum LDPC codes. Furthermore, we show that the knowledge of QTSs can be used to design better quantum LDPC codes and decoders. In the context of the development of novel decoders, we extend the stochastic resonance based decoders to quantum LDPC codes, propose iteration-varying message passing decoders with their message update rules learned by neural networks tuned for low logical error rate, and present a syndrome based generalized belief propagation algorithm for tackling convergence failure of iterative decoders due to the presence of short cycles. Our analysis of TSs of a layered decoding architecture clearly reveals the dependence of the harmfulness of TSs (classical or quantum) on the iterative decoder, and thus on the error floor estimates. We present a computationally efficient method for estimating error floors of LDPC codes over the binary symmetric channel without any prior knowledge of its trapping sets. The sub-graph expansion-contraction method is a general procedure for TS characterization, which lists all harmful error patterns up to a given weight for the LDPC code and decoder. Based on this decoder-aware trapping set characterization for LDPC codes, we propose a model-driven deep neural network (DNN) framework that unfolds the decoding iterations, to design the \emph{decoder diversity of finite alphabet iterative decoders (FAIDs)}. Our decoder diversity DNN-FAID delivers excellent waterfall performance along with a low error floor.

• #### They See Me Different…Like an Immigrant Cause of How I Sound: Perceived Difference, Limitations, & Co-Naturalizations of Race and Language

Latinx English language learners (ELLs) have long been the intended targets of U.S. language planning and policy efforts that seek to manage both the use of Spanish and its speakers. Since 2000, Arizona has adopted some of the most restrictive educational policies that shape the schooling of its ELLs (e.g., Proposition 203 and House Bill 2064). Like other bilingual education policies, Arizona’s frame Latinx ELLs as needing linguistic remediation in order for ELLs to develop proficiency in academic English for them to be successful in the modern, global economy (Flores, 2016). Yet academic/home language distinctions have been shown to position multilinguals’ language practices as deficient compared to an unmarked norm even when ELLs ostensibly model language practices that are validated when produced by non-racialized individuals (Flores & Rosa, 2015; Rosa, 2016). What is not well-known is if/how multilinguals reconstruct raciolinguistic ideologies. This descriptive qualitative study is guided by the research question: In what ways do Latinx multilingual students reproduce raciolinguistic ideologies? To better understand the pervasiveness of raciolinguistic ideologies, I interviewed ten Latinx multilinguals from two high schools in southern Arizona and thematically analyzed the data (Braun & Clarke, 2006). The findings showed Latinx multilingual students reproducing raciolinguistic ideologies, particularly in relation to co-naturalizations of race and language, perceived linguistic limitations, and raciolinguistic difference. These findings suggest that multilinguals sometimes adopt the stances of white perceiving subjects that re/construct multilingual language practices as inferior (Flores & Rosa, 2015; Inoue, 2003; Rosa & Flores, 2017), and deviating from an idealized monolingual norm (Flores, 2013). I conclude that there is a need for practitioners to advance efforts to dismantle raciolinguistic ideologies, and that the interventions most needed by multilinguals are ones that challenge the ubiquity of raciolinguistic ideologies and contribute to their denaturalization.
• #### Coping with Complexity: Essays on Evolution and Institutions

Despite their disparate subjects, the following essays share a number of common themes. Chief among these are complexity, evolution, and institutions. The first two essays examine Hayek's social theory, an examination that brings to light two basic points about complex societies. First, they are difficult to predict and control. Second, they adapt to internal and external changes. These features lay the groundwork for section II, which examines the proper form of governance structures for a complex, adaptive society. The first essay of part II applies multilevel selection theory to the problem of governing complexity. It concludes that polycentric political organization, supplemented by a few additional design principles,'' facilitates a socially beneficial process of competition and evolution. The second essay of part II uncovers a related benefit of polycentric governance. Due to its decentralized and competitive nature and due to the vast amount of relevant and constantly changing information generated in a complex society, polycentric governance institutions utilize information more effectively than centralized modes of governance. There is a substantial welfare benefit to utilizing this information by implementing reforms that seek to address the concerns and satisfy the preferences of millions, or perhaps billions, of citizens. Moreover, centralized governance becomes increasingly difficult as increasing numbers of increasingly interdependent variables become relevant to any given problem. Polycentricity is an adaptation of the state in response to the problem of social complexity. Like biological adaptations, this adaptation may be blind and unintentional. It may even precede the phenomenon to which it proves adaptive. Yet, it is adaptive nonetheless, since it provides an effective response to the problems posed by its environment. Finally, part III begins to examine some of the normative, philosophical consequences of these social scientific investigations. If society is in a constant state of flux, if it is evolving in response to fluctuating variables, then the traditional task of political philosophy may stand in need of amendment. Philosophers from Plato to Rawls have attempted to characterize a conception of justice, a political summum bonum, that transcends the institutional variations of time and place. If justice is, at least in part, a project of reconciliation, and if the values held by citizens continue to evolve, then there may not be a stable conception of justice that transcends societal dynamism. We may, instead, need to content ourselves with identifying certain general desiderata that better enable society to coordinate on a shared conception of justice, however ephemeral this conception might prove to be.
• #### Moving Beyond Inclusive Excellence: Operationalizing Diversity, Equity, & Inclusion Through Organizational Alignment in Higher Education

When it comes to the implementation of diverse, equitable, and inclusive (DEI) behaviors, institutions of higher education are misaligned in their understanding and operation of what the work entails. In an effort to emphasize diversity, equity, and inclusion (DEI) in the larger Organizational Development process (OD), many institutions of higher education wind up focusing most, if not all, of their energy into areas of the work that does not allow for sustainable action. The ensuing research explores the relationship between strategic plans for diversity and inclusion (SPFDI) and the ways in which they are impacted by organizational design – specifically the Inclusive Excellence model. In addition to the SPFDI, I will explore two different action items, Diversity Focused Programming (DFP) and Equal Employment Opportunity Compliance (EEOC) as cooperating elements used to implement DEI. Both action items will be examined through the lens of Inclusive Excellence (IE) as they pertain to sustaining the behavior of diversity, equity, and inclusion in institutions of higher education. Where elements of the information pertaining to this particular study are extremely scarce in both research and practice in higher education, I use a multidimensional approach in order to compile the necessary data to support my study. A multidimensional approach is a research method that involves the examination of multiple fields of study in order to analyze and make a case for another. In this case, I review organizational behavior and organizational design as subsets of organizational development, as well as the hybrid Inclusive Excellence and strategic planning models, corporate diversity programming models, and federal/state equal employment requirements in order to answer how organizational design effects the behavior of diversity, equity, and inclusion in institutions of higher education. As a result, this multidimensional study was supported by using a mixed-methods approach to analyze the data I gathered from the study. I used a quantitative approach to showcase the amount of institutional strategic plans that were impacted by the Inclusive Excellence model and I used a qualitative approach to explain and highlight the challenges and successes the model itself has had on various institutions of higher education. Together, this study examines the ways in which a series of colleges or universities that have adopted the Inclusive Excellence model interpret diversity, equity, and inclusion based on their understandings of the definitions. The chief aim of this study was to discover how the Inclusive Excellence model, as an organizational design, defines, implements, and sustains behaviors of diversity, equity, and inclusion in institutions of higher education. This study applies organizational design and behavior as subsects of the larger organizational development process in order to illustrate their relationships with the Inclusive Excellence model (IE) and strategic plans for diversity and inclusion (SPFDIs).
• #### Cultural Sensitivity for Healthcare Providers on the Tohono O’odham Nation: A Quality Improvement Project

Purpose. The purpose of this quality improvement (QI) project was to develop and implement an accessible, culturally sensitive educational intervention, a brief PowerPoint presentation designed for healthcare providers and staff of the Sells Hospital ED who provide care to members of the Tohono O’odham Nation (TON).Background. In rural areas of the United States (US), many barriers are present that hinder and complicate access to quality and culturally sensitive healthcare. Within rural and remote settings, the Emergency Department (ED) often becomes the sole source of accessible medical care for a broad range of both acute and chronic healthcare needs. Although the ED is critical for ensuring emergency care for rural populations, it can be a fast-paced and intimidating clinical environment, making it difficult for patients to effectively advocate for their healthcare needs. The ED is focused on delivering acute, critical, vital and lifesaving interventions however, of equal importance is the delivery of culturally sensitive healthcare. Healthcare staff and providers employed in Native American (NA) healthcare settings must possess cultural sensitivity, interpersonal etiquette and be aware of the historical and present-day intergenerational impact of historical trauma experienced by Native communities across the US. Purpose. The purpose of this QI project was to collaborate with TON cultural experts to develop, implement, and evaluate the impact of an educational intervention designed for healthcare providers who provide care for the TON. Methods. This project utilized a descriptive quality improvement design. Results. The educational presentation was co-created with consultation from five (N=5) Tohono O’odham cultural members and experts. These results of the post survey demonstrated that the educational material had a positive and influential impact on six (N=6) healthcare providers who work in the Sells ED. Conclusions. Participatory co-creation of culturally aligned educational material was a valuable aspect of this project. The outcomes of this quality improvement project offer an exemplar of a co-created educational video designed for healthcare providers working on the TON. This project has the capacity to improve cultural sensitivity and enhance quality of patient care and patient outcomes in the Tohono O’odham Healthcare system.
• #### White Curricula Effect to White Replacement Anxiety, Status Quo Politics: Teacher Experience and Understanding in Culturally Responsive Professional Development

While the student demographic continues to shift in public education across the country, reflecting a more diverse classroom comprised of minoritized students, teacher preparation programs continue to espouse White middle-class values. As such, the education process continues to dehumanize minoritized students through socially acceptable discriminatory practices and policies. This approach to teacher preparation leaves teachers ill prepared to adequately teach minoritized students by not recognizing the resources that they bring to the classroom. To the contrary, minoritized students are expected to leave their culture and identity outside of the classroom. As the achievement gap is maintained, this study purposefully examines the process implemented to interrupt that disparity through in-service teacher professional development in culturally responsive teaching in a large urban school district. This grounded theory method study examines in-service teacher experience and understanding in culturally responsive professional development that tends to teacher bias thinking and critical awareness development. Teacher critical awareness development focuses in these four areas: ongoing effort to instructionally integrate students’ cultural knowledge, attention to the effects of explicit and implicit bias, ongoing effort to affirm students’ academic and ethnic identities, and heightened awareness to issues of social justice, teachers’ asset-based beliefs, teacher critical awareness, and student identity. The findings provide insight regarding the ways that in-service teachers experience and understand the culturally responsive professional development that encompass six themes: (a) Status Quo-White Curricula Effect, (b) Altruistic Reconciliation, (c) Pensive Practitioners, (d) Colorblind Liberal, (e) People of Color Apologetic Syndrome and White Replacement Anxiety, and (f) Practical Complacent Practitioners. The six emergent themes were further analyzed and categorized into three overarching categories: the Conventional Practitioners, the Dysconscious Racists, and the Equity Saboteurs. The results of this study serve to inform approaches to implement culturally responsive professional development to interrogate educational inequities and provide humanizing spaces of authentic learning for minoritized students.
• #### Synthesis, Comprehensive Characterization, and Development of Therapeutic Peptides and Glycopeptides for Targeted Respiratory Drug Delivery as Inhalation Aerosols

Central nervous system (CNS) disorders, including neurodegeneration and chronic pain, and many respiratory diseases would greatly benefit from the specific and potent peptide pharmaceuticals and their low inherent toxicity. The delivery of peptides to target the brain is challenging, principally due to peptides' low metabolic stability, which decreases their duration of action, poor penetration of the blood-brain barrier (BBB), and their incompatibility with oral administration, typically resulting in the need for parenteral administration. These challenges limit the clinical application of peptides and explain the interest for alternative routes of peptide administration, particularly: delivery to the respiratory tract (upper and lower). Upper to target the brain through the olfactory route bypassing the blood-brain barrier (BBB), i.e., needle-free nose-to-brain delivery (N-to-B), which offers protein and peptide drugs the possibility to reach the brain noninvasively. N-to-B delivery can be a convenient method for rapidly targeting the CNS, bypassing the BBB, and minimizing systemic exposure. In addition, delivery to the lower respiratory tract as inhalation aerosol offers attractive advantages in delivering the drug locally to treat lung diseases; and to the CNS to treat its disorders at a low dose while minimizing systemic adverse effects. The lung is a low metabolic organ compared to the gastrointestinal (GI) tract. It allows rapid and high drug absorption due to the large surface area, the high blood flow, and the absence of the first-pass metabolism. In this study, several peptides and glycopeptides with different pharmacological mechanisms were developed. Some of these compounds were synthesized using the SPPS strategy and formulated as dry powders with characteristics tailored to target the respiratory tract (upper and/or lower) to treat various CNS and lung diseases. Advanced organic closed mode spray drying technique was used to produce microparticulate/ nanoparticulate formulations utilizing sugar-based excipients. The solubility and lipophilicity of all included compounds were determined computationally using molecular operating environment (MOE) software and experimentally using the shake-flask method (SFM). The raw and formulated compounds were comprehensively characterized in the solid-state. The safety of all peptides and glycopeptides covered in this dissertation was evaluated in vitro using the human nasal, brain, and pulmonary cell lines. The in vitro aerosol dispersion of the raw and spray-dried compounds was tested using an FDA-approved human inhaler device, and the influence of spray drying process conditions on the aerosol dispersion was evaluated.
• #### Design, Synthesis, and Evaluation of Brain-Penetrant PACAP-Derived Glycopeptides for the Treatment of Neurodegeneration and Neuroinflammation

Neurodegenerative disorders negatively impact the health of millions of people worldwide each year, and current therapeutic strategies only alleviate symptoms and exhibit little to no curative potential. Peptides comprise an important class of biological regulatory molecules that may be able to meet these concerns. Many endogenous peptides act as hormones, neuromodulators, secretagogues, and regulators of the inflammatory response. Furthermore, peptides are highly selective for their target receptors, leading to reduced side effect profiles, and they are regarded as non-toxic due to their metabolism yielding innocuous amino acids. However, progress in developing peptide drugs is hampered by their poor in vivo pharmacokinetic profiles, limited membrane permeability, and low oral bioavailability. Several chemical strategies including cyclization, N-methylation, lipidation, PEGylation, and incorporation of unnatural amino acids have been largely successful in improving the stability of peptides, but generally don’t elicit membrane penetration. One such chemical modification that can address the membrane permeability problem is glycosylation. Glycosylation has been demonstrated to improve water solubility and in vivo stability of peptides, and dramatically enhance penetration across biological membranes, most notably the blood-brain barrier (BBB). We have applied our glycosylation methodology to a variety of endogenous peptides, and this work summarizes the glycosylation of PACAP, a potential candidate for treating neurodegenerative disorders. Overall, we found that our PACAP glycopeptides exhibited superior stability in vitro and in vivo compared to their non-glycosylated counterparts while maintaining the intrinsic efficacy and potency of native PACAP. Most importantly, we found that our PACAP glycopeptides were able to penetrate the BBB in physiologically relevant concentrations and elicit neuroprotective and anti-inflammatory activities in animal models of Parkinson’s disease, stroke, and traumatic brain injury.


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tw
Posts: 1053
Joined: May 10th, 2002, 3:30 pm

### Re: Need Help: Vegetarian Recipes

So this is what drives the stock market.
Fear and greed.   Same for all markets.
It must be a very stressful job.
Dunno. I have nothing to equities.
I am just bored at home at the moment.

katastrofa
Posts: 7960
Joined: August 16th, 2007, 5:36 am
Location: Alpha Centauri

### Re: Need Help: Vegetarian Recipes

Read a book, water the paving stones in your "garden", hug your wife, have a vegan burger, ... do something interesting, enriching, humanising, ... before your vacation is over!

katastrofa
Posts: 7960
Joined: August 16th, 2007, 5:36 am
Location: Alpha Centauri

### Re: Need Help: Vegetarian Recipes

I got in JIT
better JIT than J2L!

I had to minimise BYND regret so chucked out some 85 puts on the close, which expiry on Friday.
Nickels are so much sweeter in the shadow of the bulldozer. (but $2 seemed fairly chunky). Beyond Meat Option Buyer Makes Big Bet Ahead Of Earnings "The trader first made two identical large purchases of call options at a$110 strike price that expire on Friday. The 1,980 call options were purchased at the ask price of $2.40 and represent a$475,200 bullish bet at a break-even price of $112.40. The options only turn a profit if Beyond Meat shares finish Friday's session about 12.8 percent higher than where they were trading at around noon on Thursday. About two minutes later, likely the same trader bought another 503 Beyond Meat call options expiring on Friday. This time, the trader bought the$95-strike contracts at the ask price of $8.922. The second trade represented an additional$447,844 bullish bet.
Together, the three bullish trades represent an aggregate $923,084 bet that only pays off if Beyond Meat shares see a big post-earnings surge on Friday." They expanded to meet the demand from supermarkets and signed deals with some big food chains last year, so one can expect a riveting report. Given that the market experts are sceptical about BYND's future and most traders are pig-heads, I'm betting that the report should outgrow the expectations. tw Posts: 1053 Joined: May 10th, 2002, 3:30 pm ### Re: Need Help: Vegetarian Recipes I got in JIT better JIT than J2L! I had to minimise BYND regret so chucked out some 85 puts on the close, which expiry on Friday. Nickels are so much sweeter in the shadow of the bulldozer. (but$2 seemed fairly chunky).
"The trader first made two identical large purchases of call options at a $110 strike price that expire on Friday. The 1,980 call options were purchased at the ask price of$2.40 and represent a $475,200 bullish bet at a break-even price of$112.40. The options only turn a profit if Beyond Meat shares finish Friday's session about 12.8 percent higher than where they were trading at around noon on Thursday.
About two minutes later, likely the same trader bought another 503 Beyond Meat call options expiring on Friday. This time, the trader bought the $95-strike contracts at the ask price of$8.922. The second trade represented an additional $447,844 bullish bet. Together, the three bullish trades represent an aggregate$923,084 bet that only pays off if Beyond Meat shares see a big post-earnings surge on Friday."

They expanded to meet the demand from supermarkets and signed deals with some big food chains last year, so one can expect a riveting report. Given that the market experts are sceptical about BYND's future and most traders are pig-heads, I'm betting that the report should outgrow the expectations.
Yeah it looks like they made their estimates.
The IV should come closer to sane levels but  by seemingly 100% analyst consensus the stock is aggressively  overpriced so they can only come off so far
Plenty of opportunity yet!

But people seeming to be buying their product to some degree at least.
The days of the western world slavishly eating circular pieces of dead cow are numbered perhaps!

katastrofa
Posts: 7960
Joined: August 16th, 2007, 5:36 am
Location: Alpha Centauri

### Re: Need Help: Vegetarian Recipes

I personally doubt it will ever happen - people are too mindless and greedy. I wonder when the fear will lead them when the whole methane blows up in our faces. Anyway, it's probably too late to stop the global heating, so bet on and tuck in what you like

katastrofa
Posts: 7960
Joined: August 16th, 2007, 5:36 am
Location: Alpha Centauri

### Re: Need Help: Vegetarian Recipes

tw
Posts: 1053
Joined: May 10th, 2002, 3:30 pm

### Re: Need Help: Vegetarian Recipes

bearish
Posts: 4810
Joined: February 3rd, 2011, 2:19 pm

### Re: Need Help: Vegetarian Recipes

Nice list. My local Korean grocer usually has very large king oyster mushrooms for a reasonable price, so I may well try #1 (although I may substitute something else for the mint). The mushroom paella also looks intriguing. On account of a special on fresh coconut from our grocery delivery people, I am planning to make something along these lines in the coming week: Raw Vegan Thai Coconut Soup. You should be proud of me!

For clarity - that was meant as a reply to Kata's mushroom post.

katastrofa
Posts: 7960
Joined: August 16th, 2007, 5:36 am
Location: Alpha Centauri

### Re: Need Help: Vegetarian Recipes

Fantastic! Proud of you and happy for the tasters!
Raw veggies are a vitamin bomb - for healthy bones, teeth and mind! Not to mention home-made meals give extra powers for fighting monsters + perk "Daddy's girls!" in this case, to put it in the language of computer games

katastrofa
Posts: 7960
Joined: August 16th, 2007, 5:36 am
Location: Alpha Centauri

### Re: Need Help: Vegetarian Recipes

Diet vs risk of hemorrhagic stroke in women
“The main takeaway message should be to encourage the intake of legumes, nuts, vegetable fats, oils, and other foods from plant sources while the intake of animal fats, and particularly red and processed meat, should be discouraged,”

bearish
Posts: 4810
Joined: February 3rd, 2011, 2:19 pm

### Re: Need Help: Vegetarian Recipes

Fantastic! Proud of you and happy for the tasters!
Raw veggies are a vitamin bomb - for healthy bones, teeth and mind! Not to mention home-made meals give extra powers for fighting monsters + perk "Daddy's girls!" in this case, to put it in the language of computer games
So, after a slight work-related delay, I did actually make the soup tonight. Hacking through the coconut shell was more work than advertised, but I made it. I personally enjoyed the result, as did one of the other victims (tasters), but another one indicated that it was too much like chimichurri, i.e. more of a sauce than a soup. As it happened, that was Daddy's girl...

bearish
Posts: 4810
Joined: February 3rd, 2011, 2:19 pm

### Re: Need Help: Vegetarian Recipes

Diet vs risk of hemorrhagic stroke in women
“The main takeaway message should be to encourage the intake of legumes, nuts, vegetable fats, oils, and other foods from plant sources while the intake of animal fats, and particularly red and processed meat, should be discouraged,”
They say that, but there is also this statement dangling in the report: "Surprisingly, red meat-heavy diets appeared to lower cholesterol levels more than fish diets."

katastrofa
Posts: 7960
Joined: August 16th, 2007, 5:36 am
Location: Alpha Centauri

### Re: Need Help: Vegetarian Recipes

katastrofa
Posts: 7960
Joined: August 16th, 2007, 5:36 am
Location: Alpha Centauri

### Re: Need Help: Vegetarian Recipes

Fresh broccoli stems. Vegan ambrosia! Sadly, the local mosquitoes preferred to eat me

(Blame the fat thighs and big head on the perspective - in reality I'm perfect!)
Last edited by katastrofa on August 6th, 2019, 2:10 pm, edited 1 time in total.

bearish
Posts: 4810
Joined: February 3rd, 2011, 2:19 pm

### Re: Need Help: Vegetarian Recipes

I would think that any notion of those thighs being fat would indeed reflect a warped perspective. As the saying goes, those legs go all the way up!

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1. math help/algebra

social science in a town election the winning candidate has 220 more votes than the loser. if 810 votes were cast in all how many votes did each candidate receive?
i wrote 220 + x = 810
x=590
candidate one =590
candidate 2 = 220
am i correct this is an algebra question
show the equaiton correct me if need be thanks

2. Originally Posted by lizard4
social science in a town election the winning candidate has 220 more votes than the loser. if 810 votes were cast in all how many votes did each candidate receive?
i wrote 220 + x = 810
x=590
candidate one =590
candidate 2 = 220
am i correct this is an algebra question
show the equaiton correct me if need be thanks
Okay, call the number of votes for candidate 1 as x, and the number of votes for candidate 2 as y. I will presume candidate 2 wins so y > x. (It doesn't matter which candidate we pick as long as we pick one.) Then we know that
$x + y = 810$
and
$y - x = 220$

Can you solve this from here?

-Dan


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## Search for new physics in final states with a single photon and missing transverse momentum in proton-proton collisions at ?s=13 TeV

Abstract: A search is conducted for new physics in final states containing a photon and missing transverse momentum in proton-proton collisions at ?s=13 TeV, using the data collected in 2016 by the CMS experiment at the LHC, corresponding to an integrated luminosity of 35.9 fb?1. No deviations from the predictions of the standard model are observed. The results are interpreted in the context of dark matter production and models containing extra spatial dimensions, and limits on new physics parameters are calculated at 95% confidence level. For the two simplified dark matter production models considered, the observed (expected) lower limits on the mediator masses are both 950 (1150) GeV for 1 GeV dark matter mass. For an effective electroweak-dark matter contact interaction, the observed (expected) lower limit on the suppression parameter ? is 850 (950) GeV. Values of the effective Planck scale up to 2.85?2.90 TeV are excluded for between 3 and 6 extra spatial dimensions.

Otras publicaciones de la misma revista o congreso con autores/as de la Universidad de Cantabria

Fuente: Journal of High Energy Physics, Vol. 2019, Num. 02, Art. Num. 074

Editorial: Springer Verlag

Fecha de publicación: 01/02/2019

Nº de páginas: 48

Tipo de publicación: Artículo de Revista

ISSN: 1126-6708,1029-8479

Url de la publicación: https://doi.org/10.1007/JHEP02(2019)074

### Autores/as

SIRUNYAN, A. M.

PEDRO JOSE FERNANDEZ MANTECA

ANDREA GARCIA ALONSO

JUAN GARCIA FERRERO

MARIA AMPARO LOPEZ VIRTO

CEDRIC GERALD PRIEELS