text:
In my last post, I wrote about my first steps towards a 6502-based homebrew 8-bit computer. Since then I’ve added a 6522 Versatile Interface Adapter (VIA). More specifically, it is a W65C22S. The VIA has a number of functionalities (after all, it makes a claim to being versatile).

Most interestingly, it has two 8-bit wide I/O ports (PA and PB) and two timers (T1 and T2). The VIA is operated over 16 registers, which the system’s address decoder currently maps to 0xeff0 to 0xefff.

As a starting point, I hooked up 8 LEDs to PB. While the official data sheet implies that the device can’t drive the LEDs directly, I came across a few online resources that reported more optimistic real-world numbers. For a quick test, connecting the LEDs directly worked, but going forward, I’ll dig up some 74HC-series buffers left over from my VGA generator project.

Using the VIA as LED output has the advantage that the LEDs can be set over the data bus. The only extra GPIO pin of the FPGA that this setup uses is for a chip-select signal (since the address decoder is implemented on the FPGA). That is in contrast to the memory-mapped LEDs I used before, which use up one GPIO pin per LED (for a total of 8 pins).

The VIA also provides two timers that can trigger interrupts on the 6502. The Investigating Interrupts tutorial on 6502.org has been a great resource to get started with the timers. I’ve implemented the moving light shown in my last post using timer interrupts. The VIA implements the timers over 16-bit counters that are decremented at the rate of the CPU clock, and it allows configuring an interrupt signal when a counter reaches zero. Therefore, updating the LEDs on each interrupt would move the light too fast. Instead, the interrupt service routine only updates the light on every tenth interrupt. The following assembly makes it all happen:

Finally, below is an updated view of the breadboard. The VIA is in the top left with 8 green LEDs connected to PB. The 8 orange wires connect the device to the data bus and the 4 yellow wires connect the 4 lower address bus signals (A0 to A3) to the register select pins of the VIA. The memory mapped LEDs discussed in the last post are the yellow ones in the bottom right, connected to the FPGA board.


text:
# minte9 learningjourney

S R Q

### Euclidean distance

KNN uses proximity, Euclidean distance between two points. $$d(x,y) = \sqrt{\sum_{i=1}^{n} (x_i - y_i)^2}$$

""" K-Nearest Neighbors Algorithm

In ML, the computer uses data to learn the best f(x)
In classical algorithms, the f(x) is provided by the programmer

2. Select a value for k
3. Calculate distances to the new point
4. Select the k-nearest points
5. Get the most common class
6. Assign the new point to that class
"""

import numpy as np
import matplotlib.pyplot as plt

X = np.array([
[2, 2], [2, 2.5], [2.5, 2.5], [2.5, 2], [2.25, 2.25],
[3, 3], [3, 3.5], [3.5, 3.5], [3.5, 3], [3.25, 3.25],
[4, 4], [4, 4.5], [4.5, 4.5], [4.5, 4], [4.25, 4.25],
])
y = np.array([
1, 1, 1, 1, 1,
2, 2, 2, 2, 2,
3, 3, 3, 3, 3,
])

k = 3 # number of k-nearest neighbors to use
xA = np.array([3.6, 1.8]) # new point with unknown class

distances = np.sqrt(np.sum((X - xA)**2, axis=1)) # axis=1 means rows of X
keys = np.argsort(distances)
knn_keys = keys[:k]
knn_classes = y[knn_keys]
knn_most_common_class = np.bincount(knn_classes) # the number of occurrences
knn_class = knn_most_common_class.argmax() # max value in array

print("Distances: \n",distances)
print("Keys ordered by distances: \n", keys)
print("Nearest neighbors keys: \n", knn_keys)
print("Nearest neighbors classes: \n", knn_classes)
print("Algorithm class response: \n", knn_class)

"""
Distances:                  [1.61245155 1.74642492 1.30384048 ...
Keys ordered by distances:  [3  8  2  5  4  ...
Nearest neighbors keys:     [3 8 2]
Nearest neighbors classes:  [1 2 1]
Algorithm class response:   1
"""

# -----------------------------------------------
# Plotting

fig, ax = plt.subplots()
ax.set_xlabel('x1')
ax.set_ylabel('x2')

plt.scatter(X[:, 0], X[:, 1], c=y)
plt.scatter(xA[0], xA[1], marker='x', color='r', label='Class =%s' %knn_class)

for i in knn_keys:
plt.plot((xA[0], X[i][0]), (xA[1], X[i][1]), color='gray', linestyle='--')

plt.title('K-nearest Neigbors')
plt.xlim(0, 6)
plt.ylim(0, 6)
plt.legend()
plt.show()

Questions
Last update: 51 days ago

format: plain


text:
# how to draw multiple graphs next to each other with labels

How to draw multiple graphs next to each other in a document? Also, how to name each graph with a label? One more thing is I need to show an dashed edge to intersect the graph edge, in that case how the edge or dashed line should be represented?

\documentclass[a4paper,12pt]{article}
\usepackage{pstricks,pst-node,pst-tree}
\begin{document}
\pagenumbering{gobble}
$\psmatrix[colsep=2.5cm,rowsep=1.5cm,mnode=circle] &v_0&v_0\\ 0&&&0\\ &v_1&v_1 \ncline{->}{2,1}{1,2}^{0} \ncline{->}{1,2}{1,3}^{0} \ncline{->}{1,3}{2,4}_{0} \ncarc[arcangle=-10]{->}{1,2}{3,3}_{1} \ncarc[arcangle=10]{->}{3,2}{1,3}_{1} \ncarc[arcangle=-30]{->}{2,1}{3,2}_{1} \ncarc[arcangle=30]{->}{2,1}{3,2}_{2} \ncarc[arcangle=-30]{->}{1,3}{2,4}_{2} \ncarc[arcangle=30]{->}{1,3}{2,4}^{3} \ncline{->}{3,3}{2,4}_{1} \ncline{->}{3,2}{3,3}_{0} \endpsmatrix$
\vspace{1in}
\end{document}

Also, can I name these individual graphs with labels?

Since these graphs have to be included in an IEEE template I am planning to generate graphs in pstricks and then include the pdf with \includegraphics in LaTeX.

• For figures side-by-side and labelled subfigures, have a look at this question – Thruston Mar 23 '15 at 10:12
• Can you explain a bit more about the "dashed edge" - which of the graph edges should it intersect? – Thruston Mar 23 '15 at 10:14
• @HarishKumar its ok sir. I used pstricks so asked in it. if any other way possible please let me know. – pavan kumar Mar 25 '15 at 3:44
• @Thruston dashed edge in the sense \linestyle=dashed which produces a dashed edge. My question is can we intersect an edge with a dashed or dotted edge? – pavan kumar Mar 25 '15 at 3:45
• I think you can use automata from tikz. Please check the pgfmanual (texdoc pgfmanual from command prompt.) – user11232 Mar 25 '15 at 4:54


text:
# Arduino controlled PWM PC Fan

I am looking at getting 2 Evercool EC8015HH12BP 80x10mm (4-wire) PWM fans. However, I am looking at controlling the fan speed with the arduino via the PWM pins.

I found the following diagram that seems to be what I am looking for in order to hook the fan up to the Arduino:

The code that I think I can use is this:

int pwmPin = 9;      // digital pin 9
int pwmVal = 10;

void setup()
{
pinMode(pwmPin, OUTPUT);   // sets the pin as output
Serial.begin(9600);
}

void loop()
{
if (pwmVal != 255) {
analogWrite(pwmPin, pwmVal);
//pwmVal += 10;
Serial.print(pwmVal);  // Print red value
Serial.print("\n");    // Print a tab
} else {
Serial.print('at max high');  // Print red value
Serial.print("\n");    // Print a tab
}
delay(1000);
}

I gather that the PWM would be in the range of 0-255 when writing out to it from the ardunio? I will be using the DS18B20 Thermometer Temperature Sensor in order to see how fast I need to spin the fan.

However, the fan speed (max 12V right now) never slows down one bit.

I'm using D9 on the Arduino Nano ATmega 328.

The reference is here for the board (in case i have the board pin wrong): enter link description here

Any helpful feedback would be great!

• If I may without offending, one lovely thing about the Arduino platform is that you can simply try it and see if it works. Even better, modularize your problem, and test each individual subsystem. You will learn WAY MORE about how to approach problems like this by trying them than you ever will by asking "What do you think?" Nobody should help you debug your code before you try to debug it yourself. – Scott Seidman Mar 25 '13 at 23:13
• @ScottSeidman I have updated my OP with more information on my test. – StealthRT Mar 25 '13 at 23:47
• That's a hair better. What does your serial out tell you pwmVal is doing? – Scott Seidman Mar 25 '13 at 23:54
• @ScottSeidman Its just set to 10 right now over and over again.. which should slow the fan down but its still spinning MAX speed. – StealthRT Mar 26 '13 at 0:18
• PWM frequency needs to be between 21kHz and 28kHz according to formfactors.org/developer/specs/4_Wire_PWM_Spec.pdf . I don't know how to set PWM frequency on an Arduino, but I suspect it needs to be set – Scott Seidman Mar 26 '13 at 0:27

One thing to note is that

if (pwmVal != 255) {
pwmVal += 10;
...

is not going to stop at 255, since pwmVal will be 250, then 260, e.t.c. One way to fix this would be write

if(pwmVal < 255)
{
pwmVal += 10;
}
else
{
pwmVal = 255;
}

By the way your code is written, if DEBUG is set to 0, nothing will happen (pwmVal will be set to 0). If DEBUG is set to 1, the fan speed will increase at a rate set by "wait" (which isn't defined in this code), until it gets to it's maximum. The value will also be printed to the serial port.

• pwmVal=min(pwmVal, 245); pwmVal += 10; – Scott Seidman Mar 25 '13 at 23:23
• Thanks for the reply help, gbmhunter. I have updated my OP with more information from my current test. – StealthRT Mar 25 '13 at 23:48

PWM frequency needs to be between 21kHz and 28kHz according to formfactors.org/developer/specs/4_Wire_PWM_Spec.pdf . I don't know how to set PWM frequency on an Arduino, but I suspect it needs to be set.

The same doc suggests that you may have reversed your sense and PWM pins (though your diagram and photo show two different things!). I can't verify this or take responsibility for your fan if its wrong.

• The PWM frequency when using the analogWrite() function is about 490Hz, and this cannot be changed. However, you can manipulate the PWM registers directly (look at the ATmega datasheet or examples online), to set the PWM frequency to basically anything you want. – gbmhunter Mar 26 '13 at 19:43


text:
## The Annals of Probability

### A Remark on Convergence in Distribution of $U$-Statistics

#### Abstract

It is proved that, for $h$ measurable and symmetric in its arguments and $X_i$ i.i.d., if the sequence $\{n^{-m/2} \sum_{i_1,\ldots,i_m\leq n,i_j\neq i_k \text{if} j\neq k} h(X_{i_1},\ldots, X_{i_m})\}^\infty_{n=1}$ is stochastically bounded, then $Eh^2 < \infty$ and $Eh(X_1,x_2,\ldots,x_m) = 0$ a.s.

#### Article information

Source
Ann. Probab., Volume 22, Number 1 (1994), 117-125.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176988850

Digital Object Identifier
doi:10.1214/aop/1176988850

Mathematical Reviews number (MathSciNet)
MR1258868

Zentralblatt MATH identifier
0801.60015

JSTOR
Gine, Evarist; Zinn, Joel. A Remark on Convergence in Distribution of $U$-Statistics. Ann. Probab. 22 (1994), no. 1, 117--125. doi:10.1214/aop/1176988850. https://projecteuclid.org/euclid.aop/1176988850


text:
## Absolute Value Equations

Posted on Categories - GMAT Quant, GRE Quant

Many students are uncomfortable with the concept of absolute value. They often think of it as some magic trick that makes everything positive. In a sense this is correct, but if that’s how you think about absolute value, then solving absolute value equations and inequalities will just be more complicated magic tricks. In other words, this...


text:
# How to prove $(α·σ)(β·σ) = α·β +iα×β·σ$ (where, $α$ and $β$ are 3 dimensional vectors and $σ$ represents Pauli matrices)?

I tried to evaluate the LHS first and obtained the first term of RHS easily. Then i tried to use the commutation relations of $$\mathrm{SU}(2)$$ group to proceed further to obtain the second term of the LHS from remaining quantities but got stuck there. Can somebody show how it's done?

• WP. – Cosmas Zachos May 17 at 10:28
• Unless you know a smarter way, try writing out all of the components. – my2cts May 17 at 11:40

## 2 Answers

The commutation relation $$[\sigma_i,\sigma_j] = 2i\epsilon_{ijk}\sigma_k$$ is strictly insufficient for what you want to achieve, and it needs to be supplemented with the anticommutation relations between the Pauli matrices, $$\{\sigma_i,\sigma_j \} = 2\delta_{ij}.$$ As the Wikipedia page points out, adding those two will get you an expression for the individual products, $$\sigma_i\sigma_j = \delta_{ij} + i\epsilon_{ijk}\sigma_k,$$ and you can then contract this with the two relevant vectors on either side to get the expression you're after.

Write the expression in index notation. Use commutation relation of Pauli matrices to commute them. Than use anti-commutation relation to get them back in the same order as what you started with but with opposite sign. Now you can rearrange to get the desired answer.

Hope this helps.


text:
# Showing that a curve is not rectifiable if its arc length is not a continuous function

This is a (translated) proof from a textbook of the fact that arc length of a rectifiable curve is a continuous function.

Let $\phi:[T_0,T_1]\rightarrow\mathbb C$ be a function whose real part and imaginary part are continuous, and $C$ be a curve represented by $\phi$. Suppose $C$ is rectifiable. Define $f:[T_0,T_1]\rightarrow\mathbb R$ by $f(t) = L(C|[T_0,t])$, where $L(C|I)$ is the arc length of $C$ restricted to the interval $I$. To show by contradiction that $f$ is continuous, assume $f$ is not continuous at $t_0\in [T_0, T_1]$. Since $f$ is monotonously increasing, either of $\lim_{t\rightarrow t_0-0} f(t) < f(t_0)$ or $\lim_{t\rightarrow t_0+0} f(t) > f(t_0)$ holds. WLOG we may assume the former holds. Here $t_0 > t$. Let $\epsilon_0 = f(t_0) - \lim_{t\rightarrow t_0-0}f(t)$. By definition, there exists an infinite number of $t_j < \tilde{t_j} < t_{j+1} < \tilde {t}_{j+1}\quad(j = 1,2,\dots)$ s.t. $L(C|[t_j,\tilde{t}_j])>\epsilon_0/2$. Then we have $L(C) = +\infty$. Contradiction.

I can't figure out why the sentence that begin with "By definition" is true. Why are there such $t_j$'s?

EDIT: In the book, $L(C)$ is defined to be the supremum (possibly $+\infty$) of $\sum_{j=1}^{n}|\phi(s_j)-\phi(s_{j-1})|$ for any partition $T_0 = s_0 < s_1 < \dots < s_n = T_1$. $C$ is rectifiable iff $L(C) <\infty$.

-
this looks strange to me. Could you add the information how rectifiability and arc length are defined in that book? – user20266 Mar 25 '12 at 12:51
I added it to the question statement. – Pteromys Mar 26 '12 at 4:23
I don't see the reasoning either, maybe there is some more context that is missing. Anyway, continuity is not difficult to demonstrate by other means. Burago, Burago, and Ivanov do it nicely in a few lines in "A Course in Metric Geometry", p. 35 Proposition 2.3.4 (you can find it online). – yasmar Mar 26 '12 at 18:54


text:
# High Input BJT Differential Amplifier

This is a basic differential amplifier.

I want to modify it in order to have high input impedance (a few $M\Omega$ from DC to at least $200~kHz$)

I thought about replacing the CE pair input with a CC-CC cascade pair, or a Darlington pair, but I don't think they have good frequency response.

Any suggestion?

I don't really care about the gain, because I will use another stage for that purpose.

• What ideas do you have to increase the input impedance? Are you permitted to consider JFETs? – jonk Jul 8 '17 at 1:47
• Real spec? Z of 0.8 pF @ 200 kHz is 1MegOhm – sstobbe Jul 8 '17 at 1:56

a few ways:

1) reduce Ic;

2) increase current gain;

3) use positive feedback;

5) use fets;

...

You'll need to boot-strap the C_gate_drain of JFETs, to reach that Zin. Hence the drain of the diffpair cannot be attached to any gain-node.


text:
## Algebra 1

It is in the Square of Binomial form which is $a^{2}$ + 2ab + $b^{2}$ = $(a+b)^{2}$ This is because the first and last term are squared in the polynomial and the middle term is +2 times the first and last term. Thus it follows the rule of Square of Binomial.


text:
# A Discussion ofAdversarial Examples Are Not Bugs, They Are Features

### Affiliations

MIT

UC Berkeley

MIT

MIT

OpenAI & Harvard

MIT

MIT

MIT

Allen Institute for AI

Aug. 6, 2019

### DOI

10.23915/distill.00019

On May 6th, Andrew Ilyas and colleagues published a paper outlining two sets of experiments. Firstly, they showed that models trained on adversarial examples can transfer to real data, and secondly that models trained on a dataset derived from the representations of robust neural networks seem to inherit non-trivial robustness. They proposed an intriguing interpretation for their results: adversarial examples are due to “non-robust features” which are highly predictive but imperceptible to humans.

The paper was received with intense interest and discussion on social media, mailing lists, and reading groups around the world. How should we interpret these experiments? Would they replicate? Adversarial example research is particularly vulnerable to a certain kind of non-replication among disciplines of machine learning, because it requires researchers to play both attack and defense. It’s easy for even very rigorous researchers to accidentally use a weak attack. However, as we’ll see, Ilyas et al’s results have held up to initial scrutiny. And if non-robust features exist… what are they?

To explore these questions, Distill decided to run an experimental “discussion article.” Running a discussion article is something Distill has wanted to try for several years. It was originally suggested to us by Ferenc Huszár, who writes many lovely discussions of papers on his blog.

Why not just have everyone write private blog posts like Ferenc? Distill hopes that providing a more organized forum for many people to participate can give more researchers license to invest energy in discussing other’s work and make sure there’s an opportunity for all parties to comment and respond before the final version is published.
We invited a number of researchers to write comments on the paper and organized discussion and responses from the original authors.

The Machine Learning community sometimes worries that peer review isn’t thorough enough. In contrast to this, we were struck by how deeply respondents engaged. Some respondents literally invested weeks in replicating results, running new experiments, and thinking deeply about the original paper. We also saw respondents update their views on non-robust features as they ran experiments — sometimes back and forth! The original authors similarly deeply engaged in discussing their results, clarifying misunderstandings, and even running new experiments in response to comments.

We think this deep engagement and discussion is really exciting, and hope to experiment with more such discussion articles in the future.

## Discussion Themes

Clarifications: Discussion between the respondents and original authors was able to surface several misunderstandings or opportunities to sharpen claims. The original authors summarize this in their rebuttal.

Successful Replication: Respondents successfully reproduced many of the experiments in Ilyas et al and had no unsuccessful replication attempts. This was significantly facilitated by the release of code, models, and datasets by the original authors. Gabriel Goh and Preetum Nakkiran both independently reimplemented and replicated the non-robust dataset experiments. Preetum reproduced the $\widehat{\mathcal{D}}_{det}$ non-robust dataset experiment as described in the paper, for $L_\infty$ and $L_2$ attacks.
Gabriel repproduced both $\widehat{\mathcal{D}}_{det}$ and $\widehat{\mathcal{D}}_{rand}$ for $L_2$ attacks.
Preetum also replicated part of the robust dataset experiment by training models on the provided robust dataset and finding that they seemed non-trivially robust. It seems epistemically notable that both Preetum and Gabriel were initially skeptical. Preetum emphasizes that he found it easy to make the phenomenon work and that it was robust to many variants and hyperparameters he tried.

Exploring the Boundaries of Non-Robust Transfer: Three of the comments focused on variants of the “non-robust dataset” experiment, where training on adversarial examples transfers to real data. When, how, and why does it happen? Gabriel Goh explores an alternative mechanism for the results, Preetum Nakkiran shows a special construction where it doesn’t happen, and Eric Wallace shows that transfer can happen for other kinds of incorrectly labeled data.

Properties of Robust and Non-Robust Features: The other three comments focused on the properties of robust and non-robust models. Gabriel Goh explores what non-robust features might look like in the case of linear models, while Dan Hendrycks and Justin Gilmer discuss how the results relate to the broader problem of robustness to distribution shift, and Reiichiro Nakano explores the qualitative differences of robust models in the context of style transfer.

Distill collected six comments on the original paper. They are presented in alphabetical order by the author’s last name, with brief summaries of each comment and the corresponding response from the original authors.

### Affiliations

Justin and Dan discuss “non-robust features” as a special case of models being non-robust because they latch on to superficial correlations, a view often found in the distributional robustness literature. As an example, they discuss recent analysis of how neural networks behave in frequency space. They emphasize we should think about a broader notion of robustness. Read Full Article

#### Comment from original authors:

The demonstration of models that learn from only high-frequency components of the data is an interesting finding that provides us with another way our models can learn from data that appears “meaningless” to humans. The authors fully agree that studying a wider notion of robustness will become increasingly important in ML, and will help us get a better grasp of features we actually want our models to rely on.

### Affiliations

Gabriel explores an alternative mechanism that could contribute to the non-robust transfer results. He establishes a lower-bound showing that this mechanism contributes a little bit to the $\widehat{\mathcal{D}}_{rand}$ experiment, but finds no evidence for it effecting the $\widehat{\mathcal{D}}_{det}$ experiment. Read Full Article

#### Comment from original authors:

This is a nice in-depth investigation that highlights (and neatly visualizes) one of the motivations for designing the $\widehat{\mathcal{D}}_{det}$ dataset.

### Affiliations

Gabriel explores what non-robust useful features might look like in the linear case. He provides two constructions: “contaminated” features which are only non-robust due to a non-useful feature being mixed in, and “ensembles” that could be candidates for true useful non-robust features. Read Full Article

#### Comment from original authors:

These experiments with linear models are a great first step towards visualizing non-robust features for real datasets (and thus a neat corroboration of their existence). Furthermore, the theoretical construction of “contaminated” non-robust features opens an interesting direction of developing a more fine-grained definition of features.

### Authors

Reiichiro shows that adversarial robustness makes neural style transfer work by default on a non-VGG architecture. He finds that matching robust features makes style transfer’s outputs look perceptually better to humans. Read Full Article

#### Comment from original authors:

Very interesting results that highlight the potential role of non-robust features and the utility of robust models for downstream tasks. We’re excited to see what kind of impact robustly trained models will have in neural network art! Inspired by these findings, we also take a deeper dive into (non-robust) VGG, and find some interesting links between robustness and style transfer.

### Affiliations

Preetum constructs a family of adversarial examples with no transfer to real data, suggesting that some adversarial examples are “bugs” in the original paper’s framing. Preetum also demonstrates that adversarial examples can arise even if the underlying distribution has no “non-robust features”. Read Full Article

#### Comment from original authors:

A fine-grained look at adversarial examples that neatly our thesis (i.e. that non-robust features exist and adversarial examples arise from them, see Takeaway #1) while providing an example of adversarial examples that arise from “bugs”. The fact that the constructed “bugs”-based adversarial examples don’t transfer constitutes another evidence for the link between transferability and (non-robust) features.

### Affiliations

Eric shows that training on a model’s training errors, or on how it predicts examples form an unrelated dataset, can both transfer to the true test set. These experiments are analogous to the original paper’s non-robust transfer results — all three results are examples of a kind of “learning from incorrectly labeled data.” Read Full Article

#### Comment from original authors:

These experiments are a creative demonstration of the fact that the underlying phenomenon of learning features from “human-meaningless” data can actually arise in a broad range of settings.

## Original Author Discussion and Responses

MIT

### Citation Information

If you wish to cite this discussion as a whole, citation information can be found below. The author order is all participants in the conversation in alphabetical order. You can also cite individual comments or the author responses using the citation information provided at the bottom of the corresponding article.

### Editorial Note

This discussion article is an experiment organized by Chris Olah and Ludwig Schubert. Chris Olah facilitated and edited the comments and discussion process. Ludwig Schubert assisted by assembling the responses into their current presentation.

We’re extremely grateful for the time and effort that both the authors of the responses as well as the authors of the original paper put into this process, and the patience they had with the editorial team as we experimented with this format. Respondents were selected in two ways. Some respondents came to our attention because they were actively working on better understanding the Ilyas et al results. Other respondents were subject matter experts we reached out to.

Distill is also grateful to Ferenc Huszár for encouraging us to explore this style of article.

### References

1. Adversarial examples are not bugs, they are features[PDF]
Ilyas, A., Santurkar, S., Tsipras, D., Engstrom, L., Tran, B. and Madry, A., 2019. arXiv preprint arXiv:1905.02175.

If you see mistakes or want to suggest changes, please create an issue on GitHub.

### Reuse

Diagrams and text are licensed under Creative Commons Attribution CC-BY 4.0 with the source available on GitHub, unless noted otherwise. The figures that have been reused from other sources don’t fall under this license and can be recognized by a note in their caption: “Figure from …”.

### Citation

Engstrom, et al., "A Discussion of 'Adversarial Examples Are Not Bugs, They Are Features'", Distill, 2019.
@article{engstrom2019a,
}


text:
# Definition:Division Algebra/Definition 1

## Definition

Let $\left({A_F, \oplus}\right)$ be an algebra over field $F$ such that $A_F$ does not consist solely of the zero vector $\mathbf 0_A$ of $A_F$.

$\left({A_F, \oplus}\right)$ is a division algebra if and only if:

$\forall a, b \in A_F, b \ne \mathbf 0_A: \exists_1 x \in A_F, y \in A_F: a = b \oplus x, a = y \oplus b$

That is, for every pair of elements $a, b$ of the algebra where $b$ is non-zero, there exists:

a unique element $x$ such that $a = b \oplus x$
a unique element $y$ such that $a = y \oplus b$


text:
### Home > INT3 > Chapter 6 > Lesson 6.2.4 > Problem6-67

6-67.

Shift the graph of $y = \log(x)$ up $3$ units and to the right $6$ units. Graph both the original function and the transformed graph on the same set of axes and write the equation of the transformed graph.

$y=\log(x−h)+k$

Use the eTool below to shift the graph of y = log x.
Click the link at right for the full version of the eTool: INT3 6-67 HW eTool


text:
# How To Solve Three Variable Linear Equations

By Kathleen Knowles, 07 Oct 2020

An equation between two variables is known as a Linear equation. A Linear equation usually results in a straight line when plotted graphically. The variables, which on most occasions are real numbers, are considered the parameters of the equation.

There are several systems of linear equations involving the same set of variables. A system here refers to when you have two or more equations working together.

## Examples Relating to Three Variable Linear Equations

2X + Y=6

3X - Y= 4

X-2Y +3Z=9

-X+3Y-Z=-6

X+2Y+3Z=-7

2X-3Y-5Z=9

-6X-8Y+Z=-22

### Using the Elimination Method to Solve a Three Variable Linear Equation

A three-variable linear equation is a bit more difficult to solve compared to equations with two variables. This complexity is a result of the additional variable.

Although there are several methods for solving this type of equation, the elimination method remains the most straightforward.

Follow the procedure below to use the elimination method in solving three variable linear equations:

1. Put all the equations in standard form, avoiding decimals and fractions.

2. Select a suitable variable to eliminate.

3. Choose any two of the three equations and eliminate the selected variable.

4. Select a different set of the two equations and eliminate the same selected variable.

5. Solve the two equations in steps three and four for the two variables they contain.

6. Substitute the answers in step five into any equation that has the remaining variable.

7. Check to prove the solution with all the three original equations.

#### Example 1

Task: Solve the following system of equations using the elimination method.

X-2Y +3Z=9 ______________(1)

-X+3Y-Z=-6_______________ (2)

2X-5Y+5Z=17_____________ (3)

#### Solution

In this case, you realize that the system is already in standard form; therefore, choose the variable to eliminate, for instance, X. You should then select two equations with which to eliminate X. For this example, pick (1) and (2).

Thus;

X-2Y +3Z=9

-X+3Y-Z=-6

__________________

Y +2Z=3__________(4)

You should then select a different set of two equations, in this case, equations (1) and (3) to eliminate the same variable.

Thus;

X-2Y+3Z=9___________(1)

2X-5Y +5Z=17_________(3)

To eliminate X, multiply equation (1) with (-2) or any other suitable constant.

Thus;

-2X +4Y -6Z = -18

2X-5Y+5Z=17

____________________

-Y-Z=-1__________(5)

You can now solve equation (4) and (5) .

Y+2Z=3

-Y-Z=-1

__________________

Z=2

Now substitute Z=2 in any of the created 2×2 system, that is (4) or (5). In this case pick equation (5).

-Y-Z=-1

-Y-2=-1

Thus Y=-1

Use the answers obtained to substitute into any equation involving the remaining variable. In this case pick X-2Y+3Z=9___________(1)

X-2Y+3Z=9___________(1)

X-2(-1)+3(2)=9

X+2+6=9

X+8=9

X=1

Therefore the solution is X=1, Y =-1 and Z = 2.

#### Example 2

Task: Solve the following system of equations using the elimination method.

X=3Z-5

2X+2Z=Y +16

7X-5Z= 3Y +19

Solution

First, write all the equations in standard form.

Thus;

X -3Z = -5____________(1)

2X-Y+2Z=16_________(2)

7X-3Y-5Z=19_________(3)

Next, choose a suitable variable to eliminate. In this case, select Y since it is missing in equation (1). Then, select equation (2) and (3) to eliminate Y.

2X-Y +2Z=16__________(2)

7X-3Y -5Z=19__________(3)

Please, multiply equation (2) by a suitable constant,say ( -3) to get:

-6X+3Y-6Z= 48

Then, eliminate Y.

-6X+3Y-6Z= 48

7X-3Y -5Z=19

_____________________

X-11Z=-29_________________(4)

It would be best if you then solved equation (1) and (4) since they are 2×2 system linear equation by subtracting.

Thus;

X -3Z = -5_________________(1)

X-11Z=-29_________________(4)

______________________

8Z=24

Therefore Z=3

You can then substitute Z=3 into equation (4)

X-11Z=-29_________________(4)

X-11(3)=-29

X-33=-29

X=4

Then, submit X=4 and Z=3 into equation 3 to get the value of Y.

7X-3Y -5Z=19__________(3)

7(4)-3Y-5(3)=19

28-3Y-15=19

-3Y=6

Therefore Y=-2

Here's the solution: X=4,Y=-2 and Z=3

### Consider the Gaussian Elimination Method in Solving Three Variable Linear Equations.

The Gaussian Elimination Method is the best method for solving three (or more) variable equations. However, the Gaussian Elimination Method is generally for experts, as it involves a bit of set up work. You don't have to worry though, because once you have the system set up, the equation is straightforward to solve.

To use the Gaussian Elimination Method, you have to translate your equations into a matrix using placeholder zeros and ones, where necessary. You should then set up the matrix by manipulating it through basic application of the properties of matrixes. You should then add, subtract, multiply and divide the rows in the matrix to make ones and zeros in specific locations.

#### Examples

Solve the following equation using the Gaussian Elimination Method

system of equations.

–3x + 2y – 6z = 6

5x + 7y – 5z = 6

x + 4y – 2z =8

#### Solution

You realize that in this problem, no expression for a variable is solved. It means you'll have to do the multiplication and addition tasks to simplify the system.

First, do away with the leading x terms in any of the two rows. To begin, simply pick any two rows you find easy to clear out before switching the rows later to have the system in the upper triangular form.

Since there is no existing rule limiting you to pick the x term starting from the first row, pick the simpler x term in the third row which gives a simple coefficient of multiply the third row by 3 then add it to the first row. If you find this difficult, you can do the calculations on paper.

Thus;

-3X + 2Y-6Z=6

5X + 12Y-6Z=24

14Y - 12Z=30

You should now write the results in this format:

7Y- 6Z= 15

5X +7Y- 5Z= 6

X + 4Y -2Z= 8

Whereas in solving two variable expressions, you are allowed to multiply a row, there is no provision for this in three variable linear equations. It is therefore suggested that you work it out on a scratch paper. You should get this result:

14Y -12Z= 30

5X +7Y - 5Z= 6

X + 4Y - 2Z= 8

Next, multiply the first row by one- half to get smaller values for coefficients.

Thus;

7Y - 6Z = 15

5X + 7Y -5Z= 6

X +4Y - 2Z= 8

Now that you have the value of Z, divide the first row by 43. Next, arrange the rows in the upper triangular format:

Thus;

43Z = 43

Y- 7Z= -4

X +4Y- 2Z= 8

Multiply the first row by 1/43 to get:

Z= 1

Y-7Z=- 4

X+ 4Y-2Z= 8

X+ 4Y-2Z=8

Y-7Z=-4

Z=1

Please use the back solving process to get the values of Y and Z:

Y – 7(1) = –4

Y – 7 = –4

Y = 3

X + 4(3) – 2(1) = 8

X + 12 – 2 = 8

X + 10 = 8

X = –2

Thus the solution is:

X = - 2

Y= 3

Z = 1

### Try Other Methods of Solving Three Variable Linear Equation.

The remaining methods of solving three variable linear equations are the substitution method and the graphical method. In substitution, the equation can quickly be written with a single variable, as the subject is identified. The identification is made by solving the equation of the variable. Next, substitution is done to the expression in which the variable appears as well as the two other equations. You will, therefore, come up with a system with fewer variables. After you have solved the smaller system, either through substitution or any other method, substitute the solutions you have found for the variables back into the first right-hand side of the expression.

Consider this example:

Solve the following three variable linear equations by the substitution method.

3X +2Y-Z= 6

-2X+2Y +Z=3

X+Y+2=4

The coefficient of Z is already Z in equation (1). Therefore, solve for Z to get:

Z= 3X+2Y-6

You can now substitute for Z in equation (2) and (3).

Thus;

-2X + 2Y +(3X+2Y-6)=3

X+Y+(3X+2Y-6)=4

You can then simplify the new system to:

X+4Y=9

4X+3Y=10

Now solve for Z in equation ( 1)

X=9-4Y

Substitute the expression X=9-4Y in equation (3).

Thus;

4(9-4Y)+3Y=10

36-16Y+3Y=10

13Y=26

Y=3

With Y=2, work back the equation X=9-4Y.

Thus,

X=9-4Y

X=1

You can now find Z's value by substituting X=1 and Y= 2 in equation (2).

Z=3X +2Y-6

Z=3(1)+2(1)-6

Z=1.

Therefore X= 1,Y=2 and Z=1.

### Conclusion

Knowledge of three variable linear equations has actual real-life applications. In tackling life's challenges, many situations can be converted into mathematical expressions to illustrate the relationship between variables, otherwise known as linear equations.

Finally, knowledge of three variable equations is useful in supply and demand economics.

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# Tag Info

The answer to your question is the contents of section 1.3.2, titled "[w]hen $\mathcal{P}_{p,r}$ is known to be difficult". (Here $\mathcal{P}_{p,r}$ is the problem of computing the norm $\|A\|_{p,r} = \sup_{\|x\|_p=1} \|Ax\|_r$.) According to that section, the only cases which are known to be difficult are $\mathcal{P}_{\infty,1},\mathcal{P}_{\infty,2},\... 6 I don't know of any function with communication much higher than the$\gamma_2$bound. However, my intuition of why it is not tight is because the$\gamma_2$-norm is also a lower bound for QCMA communication. See this paper by Klauck for the definition of QCMA communication. To prove the lower bound on QCMA communication using the$\gamma_2$-norm you can ... 3 The norms are the usual norms of a ket vector, i.e.$|||a\rangle||^2 = \langle a|a\rangle$. What did we do on the bottom of page 3? It is really running the argument from the An Analog Analogue paper backwards. Imagine we start from the state$|g_x\rangle$(a particular ground state of the final Hamiltonian$H_{P}$, related to$|x\rangle$), and evolve ... 3 The spectral norm$||H||$determines the maximum energy involved in driving the evolution of the quantum system and thus the quantum computation. Any quantum evolution could be sped-up by a factor of$\lambda$by simply driving the system with Hamiltonian$\lambda H\$ as a simple consequence of Schrödinger's equation. The energy involved is simply another ...


text:
We saw that, depending on the parameter, the Mandelbrot law can either "explode" when iterated or reach a steady state. It would be interesting to see for which parameters an "explosion" (a.k.a. a "divergence") happens. However, the parameter can be a complex number, so we need two dimensions to describe all possible parameters (e.g. x axis for the real component of the number and y axis for the imaginary component of the number). Then in color we can mark whether (or when) the iterations of the Mandelbrot law diverge. Such a type of 2D maps is called "heat maps", similar to the ones used in weather forecasts.

Side note: The colors attributed to different values are arbitrary. Above we picked blue for cold and red for hot, but we could have picked anything we want. The particular choice is called "the color map" or "the color scheme" of the plot (it has nothing to do with geographical maps). Later today we will see how to use custom color maps.

Below we give you the code that can be used to plot the heat map of "divergence of the Mandelbrot law versus parameter used in its evaluation". Let us play with it before trying to explain exactly how it works.

In [1]:
using Plots

function mandelbrot_law(current_state, parameter)
next_state = current_state^2+parameter
return next_state
end

function mandelbrot_when_explodes(parameter, length)
current_state = 0
for i in 2:length
new_state = mandelbrot_law(current_state, parameter)
if abs(new_state) > 20
return i
else
current_state = new_state
end
end
return length
end

function get_grid_of_coordinates(rmin,rmax,imin,imax,step)
real_coordinate = rmin:step:rmax
imag_coordinate = imin:step:imax
grid_of_complex_coordinates = zeros(ComplexF64, length(imag_coordinate), length(real_coordinate))

for i_real in 1:length(real_coordinate)
for i_imag in 1:length(imag_coordinate)
grid_of_complex_coordinates[i_imag,i_real] = real_coordinate[i_real] + 1im * imag_coordinate[i_imag]
end
end
return grid_of_complex_coordinates
end

function plot_mandelbrot(rmin,rmax,imin,imax,step,length)
grid_of_complex_coordinates = get_grid_of_coordinates(rmin,rmax,imin,imax,step)
heatmap(rmin:step:rmax,imin:step:imax, mandelbrot_when_explodes.(grid_of_complex_coordinates, length), ratio=1)
end


text:
Enter the volume measured density and the number of grains into the calculator to determine the number of cubic centimeters (CCs).

Grain To CC Formula

The following equation is used to calculate the number of cubic centimeters from grains.

CC = gr * VMD
• Where CC is the cubic centimeter (CC)
• gr is the grains
• VMD is the volume measured density

To calculate CCs from gains, multiply the grains by the volume measured density.

What is a grain?

Definition:

A grain is a unit of weight equal to .065 grams.

How to Calculate Grain To CC?

Example Problem:

The following example outlines the steps and information needed to calculate cc from grains.

First, determine the number of grains. In this example, the number of grains is 40.

Next, determine the volume measured density. In this example, this is determined to be .06479791.

Finally, calculate the CC from grains using the formula above:

CC = gr * VMD

CC = 40 * .06479791

CC = 2.591 cm^3


text:
# Fermi Gas Model

• I
lukka98

In the fermi gas model, there is assumption that there is a 3D potential well, but there is "energetic degeneration" for each three index "nx, ny, nz".
Now the problem is with that image, if there is degeration, for some level En there may be 10 distinctive state with same energy, so there is 20 proton and 20 neutron for Pauli exclusion in that state, why in the image there are only two particle for each state?

Is because is a 1D potential well, just for simplify?

thanks


text:
A. Two Semiknights Meet
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

A boy Petya loves chess very much. He even came up with a chess piece of his own, a semiknight. The semiknight can move in any of these four directions: 2 squares forward and 2 squares to the right, 2 squares forward and 2 squares to the left, 2 squares backward and 2 to the right and 2 squares backward and 2 to the left. Naturally, the semiknight cannot move beyond the limits of the chessboard.

Petya put two semiknights on a standard chessboard. Petya simultaneously moves with both semiknights. The squares are rather large, so after some move the semiknights can meet, that is, they can end up in the same square. After the meeting the semiknights can move on, so it is possible that they meet again. Petya wonders if there is such sequence of moves when the semiknights meet. Petya considers some squares bad. That is, they do not suit for the meeting. The semiknights can move through these squares but their meetings in these squares don't count.

Petya prepared multiple chess boards. Help Petya find out whether the semiknights can meet on some good square for each board.

Please see the test case analysis.

Input

The first line contains number t (1 ≤ t ≤ 50) — the number of boards. Each board is described by a matrix of characters, consisting of 8 rows and 8 columns. The matrix consists of characters ".", "#", "K", representing an empty good square, a bad square and the semiknight's position, correspondingly. It is guaranteed that matrix contains exactly 2 semiknights. The semiknight's squares are considered good for the meeting. The tests are separated by empty line.

Output

For each test, print on a single line the answer to the problem: "YES", if the semiknights can meet and "NO" otherwise.

Examples
Input
2......................#.K..##..#.......#...##..#......#.K.........................#.......#..#....####.....##...............K#K#
Output
YESNO
Note

Consider the first board from the sample. We will assume the rows and columns of the matrix to be numbered 1 through 8 from top to bottom and from left to right, correspondingly. The knights can meet, for example, in square (2, 7). The semiknight from square (4, 1) goes to square (2, 3) and the semiknight goes from square (8, 1) to square (6, 3). Then both semiknights go to (4, 5) but this square is bad, so they move together to square (2, 7).

On the second board the semiknights will never meet.


text:
# Homework Help: Spring Constant Question: Need Help

1. Jun 6, 2010

### Paymemoney

Spring Constant Question:URGENT Need Help!!

Hi

I am having trouble with this question can someone solve it for me, I have a test tomorrow i really need to get this done.

1. The problem statement, all variables and given/known data
A person building a seismograph (for detecting earthquakes) needs a heavy mass suspended by a long spring. He constructs the long spring from 8 identical short springs connected together end to end( in series). He attaches one end of this long spring to the roof and hangs a 10.25 kg mass from it. The resonant frequency of this system is exactly 1.26Hz

a) What is the spring constant of this long spring?

b) What is the long spring extension when the mass is attached to it?

c) What is the spring constant of each short spring?

2. Relevant equations
F=-kx

$$T=2\pi\sqrt{\frac{m}{k}}$$

3. The attempt at a solution

a) 642.429

b) not sure

c) i tried to use the $$\frac{1}{k_t} = \frac{1}{k_1} + \frac{1}{k_2}$$

P.S
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Jun 6, 2010

### Redbelly98

Staff Emeritus
Re: Spring Constant Question:URGENT Need Help!!

(a) Looks good.
(b) The F=-kx equation is helpful here. Hint: F is the weight of the mass.
(c) That approach should work. Of course, there are 8 individual springs, not just 2.

3. Jun 6, 2010

### Paymemoney

Re: Spring Constant Question:URGENT Need Help!!

c) so i have done it for 8 strings and is still not correct.

i get $$\frac{4}{321}$$

4. Jun 6, 2010

### Redbelly98

Staff Emeritus
Re: Spring Constant Question:URGENT Need Help!!

Last edited: Jun 6, 2010
5. Jun 6, 2010

### Paymemoney

Re: Spring Constant Question:URGENT Need Help!!

$$\frac{1}{642} * 8$$

6. Jun 9, 2010

### Redbelly98

Staff Emeritus
Re: Spring Constant Question:URGENT Need Help!!

Sorry about not replying sooner, somehow I missed that you had responded. Not sure if you still want to work this out, but here goes...
Not quite. Let's look at the equation you wrote earlier:
kt is the 642 N/m you found for part (a).

The right-hand-side of this equation would be, for 8 springs,
(1/k1) + (1/k2) + ... + (1/k8)

7. Jun 9, 2010

### Paymemoney

Re: Spring Constant Question:URGENT Need Help!!

so to start off would it be something like this:
$$642 =(1/k_1)+(1/k_2)+(1/k_3)+(1/k_4)+(1/k_5)+(1/k_6)+(1/k_7)+(1/k_8)$$

8. Jun 9, 2010

### Redbelly98

Staff Emeritus
Re: Spring Constant Question:URGENT Need Help!!

Not quite. The left-hand side should be 1/kt, not simply kt.

Another hint: as it says in the problem statement, the 8 individual springs are identical.

9. Jun 9, 2010

### Paymemoney

Re: Spring Constant Question:URGENT Need Help!!

so it would be like this:

$$\frac{1}{642} = \frac{1}{k_n}$$

10. Jun 9, 2010

### louza8

Re: Spring Constant Question:URGENT Need Help!!

If the springs are identical and you've calculated that in series they have a spring constant of k = 642, shouldn't each individual spring have a spring constant of 642? What am I missing in this problem?

11. Jun 9, 2010

### Paymemoney

Re: Spring Constant Question:URGENT Need Help!!

no, because the 642 is the spring constant for the long spring which is constructed of 8 short springs.

And the thing i am trying to find is the spring constant for each short spring.

12. Jun 9, 2010

### louza8

Re: Spring Constant Question:URGENT Need Help!!

But the short springs are identical. When they're linked in series, the spring constant won't change.

Eg. if I have two identical springs with k=16N/m^2 for each then when they are in series the 'new spring' has a spring constant of 16N/m^2. However, if they are in parallel the spring constant would be considered to be 32N/m^2.

Applying this to your problem considering the springs are in series and identical, then each individual spring should have 642N/m^2??

13. Jun 10, 2010

### Paymemoney

Re: Spring Constant Question:URGENT Need Help!!

well thats not what my answer says.

It is 5139.2N/m

14. Jun 10, 2010

### louza8

Re: Spring Constant Question:URGENT Need Help!!

that would be the answer if they were in parallel, but they're in series.

15. Jun 10, 2010

### Redbelly98

Staff Emeritus
Re: Spring Constant Question:URGENT Need Help!!

This is simply not true. The spring constant does indeed change for springs in series. For the same amount of applied force, each spring stretches by a smaller amount than the entire assembly. So the spring constant must be different.

Uh, no, it would be
1/642 = 1/kn + 1/kn + 1/kn + 1/kn + 1/kn + 1/kn + 1/kn + 1/kn
Use basic algebra to solve that equation for kn.

Since I have probably given enough hints now, and you have the final answer to check your work, I'll leave you on your own to finish this one off. Good luck!

16. Jun 10, 2010

### louza8

Re: Spring Constant Question:URGENT Need Help!!

sorry for the misinformation!

17. Jun 10, 2010

### Paymemoney

Re: Spring Constant Question:URGENT Need Help!!

yep i got the answr, thanks for the help


text:
## Precalculus

Calculate. I want to know how to get to the solution. (Below the problem is the solution)

$$[f(x^{2}-1)]^{3}$$

$$\frac{1}{x^{2}-1}$$

• Anonymous commented

rate all answers :) thank you


text:
# Nuclear and astrophysics aspects for the rapid neutron capture process in the era of multimessenger observations

Europe/Rome
Meeting room (ECT* - Trento)

### Meeting room

#### ECT* - Trento

Strada delle Tabarelle, 286 38123 - Villazzano (TN) Italy
, , , ,
Description

Nuclear and astrophysics aspects for the rapid neutron capture process in the era of multimessenger observations

The rapid-neutron capture process (r-process) is responsible for producing around half of all nuclides heavier than iron. One site for the r-process was recently confirmed: the advanced LIGO and Virgo detectors observed two neutron stars merging and immediate follow-up observations were compatible with a kilonova, a thermal “afterglow” powered by radioactive decay of newly synthesized r-process material. Moreover, the observations indicated that neutron-star mergers produce a blue lanthanide-free signal followed by a red lanthanide-rich component, contrary to expectations. Although neutron-star mergers are now known to be r-process element factories, this might not be the only r-process site, and a comprehensive understanding and description of the r-process is still lacking.

This workshop will bring together theorists and experimentalists to address the many aspects of nuclear physics and astrophysics that must be considered and properly understood in order to model the r-process.

Main Topics:

• Astrophysical site(s) of the rapid neutron capture process (r process)
• Observational data related to the r process
• Galactic chemical evolution and the r process
• Sensitivity studies for the r process
• Theoretical nuclear physics inputs for the r process
• Nuclear physics experiments for the r process

Keynote participants:

Andreas Bauswein (Heidelberg ITS), Gabriele Cescutti (Osservatorio di Trieste, INA), Benoit Côté (Konkoly Observ.), Tobias Fischer (Univ. Wroclaw), Oliver Just (RIKEN), Stephan Rosswog (Stockholm Univ.), Marius Eichler (TU Darmstadt), Carla Fröhlich (NC State Univ.), Gail McLaughlin (NC State. Univ.), Marco Pignatari (Univ. Hull), Stylianos Nikas (TU Darmstadt), Rebecca Surman (Univ. Notre Dame), Friedrich-Karl Thielemann (Univ. Basel), Jutta Escher (Lawrence Livermore), Jérôme Margueron (IPN Lyon), Matthew Mumpower (Los Alamos), Leo Neufcourt (NSCL), Frédéric Nowacki (Univ. of Strasbourg/CNRS), Nils Paar (Univ. of Zagreb),  Marco La Cognata (INFN-LNS), Iris Dillmann (TRIUMF), Dennis Mücher (Univ. Guelph), Shunji Nishimura (RIKEN), Artemis Spyrou (NSCL, MSU)

ChETEC events are community events intended for networking and collaboration as well as learning. We value the participation of every attendee and want all attendees to have an enjoyable and productive experience. Accordingly, all attendees are expected to show respect and courtesy to other attendees throughout the workshop and to abide by the following Code of Conduct. Any participant who wishes to report a violation of this policy is encouraged to speak to Anu Kankainen or Ann-Cecilie Larsen, as they have agreed to serve as a point of contact (or if desired, to another member of the organizing team). Thank you for helping make this a welcoming, friendly event for all.

Code of conduct:

ChETEC-supported events are committed to providing a harassment-free environment for everyone, regardless of gender, sexual orientation, disability, physical appearance, body size, race, nationality, or religion. Harassment includes offensive verbal comments or jokes related to gender, sexual orientation, disability, physical appearance, body size, race, religion, sexual images in public spaces, deliberate intimidation, stalking, following, harassing photography or recording, sustained disruption of talks or other events, inappropriate physical contact, and unwelcome sexual attention. All communication should be appropriate for a professional audience including people of many different backgrounds. Be kind to others. Do not insult or put down other attendees. Behave professionally. Participants asked to stop any harassing behavior are expected to comply immediately. Attendees violating these rules may be asked to leave the event at the sole discretion of the conference organizers.

Secretariat - Ines Campo
• Monday, July 1
• 8:45 AM 9:15 AM
Registration 30m
• 9:15 AM 9:25 AM
Welcome
• 9:25 AM 10:45 AM
Session
• 9:25 AM
Neutron capture elements in the Early Universe 35m

In the last years, the search for the oldest stars has started to investigate the central region of our Galaxy and its outskirts with ultra-faint galaxies.
Both Galactic bulge and ultra-faint galaxies host extremely old stars, with ages compatible with the ages of the oldest halo stars. The data coming from these recent observations present new signatures in neutron capture elements. Our study, based on stochastic chemical evolution models, shows how this new fundamental information can improve the constraints on the nature of the first sources of neutron
capture elements: the r-process events and the first massive stars.
Our findings support a scenario where at least a fraction of r-process events
has exploded in a very short timescale and where the first stellar generations have been fast rotators. We also predict the existence
of Eu-free stars due to the rarity of the r-process events.

Speaker: Gabriele Cescutti (Osservatorio Astronomico di Trieste, INAF)
• 10:00 AM
Galactic Chemical Evolution of r-Process Elements 35m

Galactic chemical evolution simulations are powerful tools to reconstruct the evolution of the elements across cosmic time. In this talk, I will present how we can use these simulations to investigate the properties of r-process sites (e.g., frequency and mass ejected). Chemical evolution predictions should not be seen as the final answer, but rather as a complementary piece of puzzle that must be combined with the messages sent by other fields of research. In particular, I will present the connection made between galaxy simulations and the gravitational wave detection GW170817, I will highlight what can we learn about the delay time of neutron star mergers by looking at the chemical evolution trends of r-process elements in the disk of the Milky Way, and how we can use hydrodynamic simulations of the early Universe to address the chemical signatures left by r-process events on the surface of old metal-poor stars during the first billion years of galactic evolution.

Speaker: Benoit Côté
• 10:45 AM 11:10 AM
Coffee break 25m
• 11:10 AM 12:30 PM
Session
• 11:10 AM
Improving the nuclear energy density functionals: constraints from the ground state and collective excitations 35m

Over the past years the energy density functionals have been extensively used in nuclear physics and astrophysics research; there are more than 240 nonrelativistic Skyrme parametrizations and 260 relativistic-mean-field (RMF) models introduced so far. However, all of them are optimized mainly by the nuclear ground state data, often supplemented with pseudo-observables in order to set the nuclear matter (equation of state) properties. Recently a novel relativistic energy density functional has been constrained not only by the ground state properties of nuclei but also with the isoscalar giant monopole resonance energy and dipole transition strength in nuclei, i.e. dipole polarizability in 208Pb [1]. A unified framework of the relativistic Hartree-Bogoliubov model, random phase approximation, and $\chi^2$ minimization protocol, based on the relativistic density-dependent point coupling interaction has been established in order to determine the DD-PCX parameterization [1]. The implementation of the experimental data on nuclear excitations allows improving the isovector channel of effective interaction as well as constraining the symmetry energy and nuclear matter incompresibility by using genuine observables on finite nuclei in the minimization protocol to constrain the effective interaction. The effective interaction DD-PCX accurately describes the nuclear ground state properties including the neutron-skin thickness, as well as the isoscalar giant monopole resonance excitation energies and dipole polarizabilities and open perspectives for further applications.

[1] E. Yuksel , T. Marketin, N. Paar, Phys. Rev. C 99, 034318 (2019)

Speaker: Nils Paar (Faculty of Science University of Zagreb)
• 11:45 AM
How to deal with neutrinos in simulations of neutron-star mergers and core-collapse supernovae? 35m

Among the most difficult ingredients in models of neutron star mergers and core-collapse supernovae is the treatment of neutrinos. In this talk I will briefly summarize our understanding of the most important neutrino effects in the context of r-process nucleosynthesis and I will discuss a few recently proposed schemes and their pros and cons.

Speaker: Oliver Just (RIKEN Japan)
• 12:30 PM 2:30 PM
Lunch 2h
• 2:30 PM 4:00 PM
Session
• 2:30 PM
Supernovae, neutron stars, and chemical evolution 35m

One of the open question of the r-process is whether neutron star mergers are the only site or whether there is an additional (rare) r-process site, possibly related to supernovae. In this talk, I will discuss neutron star and black hole distributions from core-collapse supernovae and how they may fit in with the notion of an additional rare r-process site.

Speaker: Carla Froehlich (North Carolina State University)
• 3:05 PM
Neutron star mergers: neutrinos and r-process nucleosynthesis 35m
Speaker: Gail McLaughlin (North Carolina State University)
• 4:00 PM 4:30 PM
Coffee break 30m
• 4:30 PM 5:45 PM
Session
• 4:30 PM
Discussion 35m
• Tuesday, July 2
• 9:00 AM 10:30 AM
Session
• 9:00 AM
r-process contributions from massive star explosions triggered by the hadron-quark phase transition 35m

Canonical core-collapse supernova explosions driven by the neutrino-heating mechanism are presently ruled out as nucleosynthesis site for the production of heavy r-process elements with A ~ 195 (third r-process peak). Detailed numerical studies, with accurate neutrino transport and a sophisticated treatment of weak processes included, have shown that the ejected material yields neither sufficiently high entropies nor large neutron excess [1] for the production of elements with atomic numbers greater than 32 < Z < 50 [2], known as light neutron-capture elements. Here, a review of this caveat will be presented. Based on new insights, a possibility will be revisited that a few rare supernova explosion events can account for a strong r-process, i.e. the production of elements up to mass numbers of A ~ 195. Therefore, it has been shown recently that the appearance of exotic phases of hot and dense matter, associated with a 1st-order phase transition from ordinary nuclear matter to the quark-gluon plasma at the supernova interior, can trigger the onset of energetic supernova explosions of massive stars with zero-age main sequence masses of 40–50 solar masses  [3]. Surprisingly, these events yield a strong r process, details of which will be presented and discussed in this talk.

References

[1] G. Mart??nez-Pinedo, T. Fischer, A. Lohs, and L. Huther, "Charged-Current Weak Interaction Processes in Hot and Dense Matter and its Impact on the Spectra of Neutrinos Emitted from Protoneutron Star Cooling," Phys. Rev. Lett. 109, 251104, 2012.
[2] G. Mart??nez-Pinedo, T. Fischer, and L. Huther, "Supernova neutrinos and nucleosynthesis," J. Phys. G Nuc. Phys. 41, 044008, 2014.
[3] T. Fischer, N.-U. F. Bastian, M.-R. Wu, S. Typel, T. Klahn, and D. B. Blaschke, "Quark deconfinement as a supernova explosion engine for massive blue supergiant star", Nat. Astron. 2, 980

Speaker: Tobias Fischer (University of Wroclaw)
• 9:35 AM
Microscopic description of fission for the r-process in neutron-star mergers ejecta 35m

Nuclear fission is known to be of fundamental importance in many applications, for example for energy production applications, such as nuclear power reactors or nuclear waste recycling. In astrophysics, nuclear fission plays a significant role during the rapid neutron-capture process (r-process) of stellar nucleosynthesis by recycling the matter during the neutron irradiation occurring in a neutron star merger ejecta [1,2]. The recent observation of gravitational waves and its optical counterpart from a binary neutron-star merger proves that such events can provide a viable site for the production of heavy (and potentially super-heavy) nuclei by the r-process nucleosynthesis. During the r-process, heavy neutron-rich nuclei are produced and decay or fission. A reliable description of nuclear fission is needed to explain the fission of such heavy neutron-rich nuclei.

The description the nuclear fission is a theoretical challenge because the many-body problem has to be solved with an interaction between nucleons that is known in a phenomenologically way only. In addition of these static considerations there are dynamical effects which leads to the splitting of the nucleus. There are four major aspects that need to be described during the fission process, namely i) the fissioning nucleus formation, ii) the fission barrier penetration and transmission, iii) the fission fragment formation, and iv) the fission fragment de-excitation. Fissioning nucleus can be formed by neutron (neutron-induced fission), gamma capture (photofission), or beta decay (beta-delayed fission). The fission barrier can be crossed by tunnel effect like in spontaneous fission or be crossed over if the nucleus is sufficiently excited like in neutron/gamma-induced fission. When the barrier is crossed, nucleus can be splitted in many ways with different probabilities, called the fission yields. Finally fission fragments de-excite mainly by neutron and gamma evaporation.

All these aspects have to be properly and microscopically described for nucleosynthesis applications since they involve exotic neutron-rich nuclei that cannot be produced experimentally. The most recent theoretical and computational developments need to be considered for a reliable estimate. In the present paper, we will describe our effort to provide updated state-of-the-art models for the description of the fission process by exotic neutron-rich nuclei.
Concerning the fission path, new calculations have been performed, based on newly computed potential energy surfaces (PES) on the basis of Gogny HFB-calculations with beyond-mean-field corrections [3]. Results for all the 500 even-even nuclei from Th to Ds lying between the proton and the neutron drip lines will be compared with predictions obtained within the Skyrme-HFB or liquid-drop approaches. Moreover, through the determination of the inertia tensor at each point of the PES, the least action path can be determined and spontaneous fission half-lifes deduced and compared with available experimental data [4]. Based on these new non-trivial fission paths, all fission transmission coefficients have to be computed considering competition between fission and others possible channels to deduce fission cross sections. Recent results along those lines will be presented
Finally we will present the scission-point model, called SPY [5], developed to estimate yields and kinetic energies of the fission fragments. To improve the description of the fissioning system at the scission point, microscopic state densities, proton and neutron distributions as well as potential energy surfaces of each fragments are now considered within the mean-field approach. We will show that these new developments have a significant impact on the predictions of fission yields and fragment excitation energies. Implications for the r-process nucleosynthesis will be discussed.

[1] S. Goriely et al, Phys. Rev. Lett 111, 242502 (2013)
[2] S. Goriely, Eur. Phys. J. A 51, (2015)
[3] N. Dubray et al, Phys. Rev. C 77, 014310 (2008)
[4] J.-F. Lemaı̂tre et al, Phys. Rev. C 98, 024623 (2018)
[5] J.-F. Lemaı̂tre et al, Phys. Rev. C 99, 034612 (2019)

Speaker: Dr jean-françois Lemaître (université libre de Bruxelles)
• 10:30 AM 11:00 AM
Coffee break 30m
• 11:00 AM 12:30 PM
Session
• 11:00 AM
Nuclear reaction theory for the era of multi-messenger observations: capture cross sections from indirect measurements 35m

Obtaining cross sections for neutron-induced reactions on unstable isotopes is challenging, but critical for astrophysics simulations. Various indirect methods have been proposed to address this problem. The ‘surrogate reaction method’ [1] uses inelastic scattering or transfer (‘surrogate’) reactions to produce the compound nucleus of interest and measure its subsequent decay. When combined with a proper theoretical description of the surrogate reaction mechanism, this data provides constraints for the models describing the decay of the compound nucleus, which dominate the uncertainties of the cross section calculations. I will present applications of the method to recent measurements of the (p,d) and (d,p) transfer reaction in the Zr-Y-Mo region. The procedure for obtaining constraints for unknown capture cross sections is illustrated and results for both known (benchmark) and unknown capture reactions are presented [2,3]. The method makes no use of auxiliary constraining quantities, such as neutron resonance data, or average radiative widths, which are not available for short-lived isotopes; thus it can be applied to isotopes away from stability, including those of relevance to astrophysics simulations.

[1] Escher et al, Rev. Mod. Phys. 84, 353 (2012).
[2] Escher et al, PRL 121, 052501 (2018).
[3] Ratkiewicz et al, PRL 122, 052502 (2019).

• This work is performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. Support from the Laboratory Directed Research and Development Program at LLNL, Projects No. 16-ERD-022 and 19-ERD-017, is acknowledged.
Speaker: Jutta Escher
• 11:35 AM
The creation of the first r-process peak in neutron star mergers, impact of nuclear masses and beta decay rates. 35m

The observation of the electromagnetic counterpart of GW170817 gravitational wave hinted the production of r-process elements in the aftermath of neutron star mergers. The color of the electromagnetic counterpart suggests there are at least two different contributions of electron fraction ($Y_e$) distributions, one moderately high, reproducing the light r-process elements, and one $<0.25$ reproducing heavier nuclei including the lanthanide elements. We present a study for the creation of the first r-process peak using astrophysical conditions matching the ones speculated for neutron star mergers. We identify the range of $Y_e$ that can reproduce the first r-process peak and the effect of specific nuclear masses and beta decay rates on it.

Speaker: Stylianos Nikas (Techniche Universitat Darmstadt / GSI)
• 12:30 PM 2:30 PM
Lunch 2h
• 2:30 PM 4:00 PM
Session
• 2:30 PM
Nuclear astrophysics in the era of multi-messenger observations at INFN-LNS 35m

Gravitational waves detection in neutron mergers and the parallel observations in the visual and IR spectrum have triggered a new era in astronomy, the so-called multi-messenger era, where information of astrophysical significance is carried by different messengers. The possibility to identify a source and follow its time evolution has opened a new window on exotic phenomena, allowing us to pinpoint a realistic site for the r-process.
Such more in-depth analysis of the astrophysical scenarios calls for a parallel comprehensive study of the nuclear processes powering them. In this contribution I will review the research activity that is presently carried out and it is under development at the INFN-Laboratori Nazionali del Sud (Italy). It can be broadly divided into three categories: (i) constraining the r-process through a better understanding of the s-process; (ii) the study of nuclear reactions involved in the r-process; (iii) studying the opacity of a plasma made up of lanthanides.
Understanding the s-process nucleosynthesis plays a pivotal role since abundances of r-nuclei are deduced by subtracting the calculated s-process yields from the galactic chemical abundances. Therefore, uncertainties on s-elements production directly reflects on the r-process yields. Now, while the 13C(a,n)16O neutron source is well constrained, the 22Ne(a,n)25Mg one, supplying a larger neutron flux than 13C(a,n)16O, is still affected by large uncertainties, calling for further studies to better constrain the s-process and so the r-process. Also, the investigation of neutron-capture cross sections, especially in the case of branch point nuclei, can help constraining the r-process nucleosynthesis. With this respect, the Trojan horse method (THM) is an indirect approach developed at LNS making it possible to study reactions of astrophysical importance (also neutron-induced) at the corresponding Gamow energies.
Such studies are important for point (ii) as well. In this case, other processes such as the study of the 12C+12C fusion reactions are very important. In fact, the cross section influences the rate of core collapse supernovae and, consequently, the neutron star birth rate. This is also independently determined from 26Al galactic abundance, so the reactions responsible from the production and destruction of 26Al plays an important role to cast light on the neutron star formation rate. With this respect, 26Al (n,p) and (n,a) reactions on the ground and isomeric state have a strong influence on the 26Al yield from core-collapse supernova explosion, and their study will be performed through the THM in the near future.
Also beta decay of r-nuclei has a great relevance in determining the abundance pattern deduced from the galactic material. In particular, beta-delayed neutron emission (βn) is a form of radioactive decay in which an electron, an anti-neutrino and one or more neutrons are emitted. The initial abundance distribution is shaped by the decay half-life T1/2, but the neutron emission affects the final abundances in two ways: on the one hand it shifts the decay path to lower masses and on the other hand it provides a source of neutrons for late captures that shift masses in the opposite way. Thus, a good knowledge of Pn and T1/2 values of the nuclei between the valley of stability and the r-process path is needed for a correct understanding of the observed abundances. The availability of FRIBS radioactive ion beams (and of the forthcoming separator FRAISE) and of the polycube neutron counter at LNS will make it possible to perform high accuracy studies of βn processes.
The third point is also extremely important, since along with a gravitational-wave signal and a short burst of γ-rays, neutron star mergers give rise to a transient optical–near-infrared (kilonovae). Unlike supernova absorption lines, the identification of kilonova atomic species is not secure. Therefore, the identification of r-nuclei in the ejecta is achieved by investigating the transient light curves, the maximum being directly connected with the optical thickness of the ejecta. The measured light curves suggest that the opacity is dominated by transitions from the lanthanides. However, predictions of the transient light curves and spectra suffer from the uncertain optical properties of heavy ions. At LNS we will have the unique opportunity to produce a controlled lanthanides plasma, with more accurate determination of temperature and density with respect to laser induced plasmas. The possibility to produce such stable and controlled plasmas is under study at LNS (Pandora project).

Speaker: Marco La Cognata (INFN-LNS)
• 3:05 PM
Constraining neutron-capture reactions for the r process 35m

In this talk I will discuss experimental constraints to neutron-capture reactions far from stability. These reactions are a critical part of the r process, and to date are almost completely unconstrained experimentally. Measuring direct neutron-capture reactions on short-lived nuclei is extremely challenging, and therefore one has to rely on indirect constraints. I will discuss the $\beta$-Oslo method, which was developed for this purpose by a Michigan State University and University of Oslo collaboration. I will present resent results on neutron-rich nuclei around mass 70, and also future plans for expanding to heavier r-process nuclei.

Speaker: Artemis Spyrou (Michigan State University)
• 4:00 PM 4:30 PM
Coffee break 30m
• 4:30 PM 5:50 PM
Session
• 4:30 PM
Nuclear fission for the r-process in the era of multi-messenger observations 35m
Speaker: Matthew Mumpower
• 5:05 PM
New Approach for Determination of Stellar Nucleosynthesis Abundances 25m

The recent observation of neutron stars merger by the LIGO collaboration and the measurements of the event’s electromagnetic spectrum as a function of time for different wavelengths, have altered profoundly our understanding of the r-process site, as well as considerably energized nuclear astrophysics research efforts. R-process abundances are a key element in r-process simulations, as a successful calculation must account for these abundances in the final debris of a stellar cataclysmic event. In this presentation, mankind’s complete knowledge of neutron cross sections obtained in the last 80 years, as encapsulated in the latest release of the Evaluated Nuclear Data File (ENDF/B) library, is used to obtain solar r-process abundances in a novel way. ENDF/B cross sections has been successfully used for decades in nuclear power and defense applications and are now used to obtain r-process abundances in a fully traceable, documented and unbiased way.

Speaker: Dr Boris Pritychenko (Brookhaven National Laboratory)
• Wednesday, July 3
• 9:00 AM 10:30 AM
Session
• 9:00 AM
SHELL MODEL FAR FROM STABILITY: ISLANDS OF INVERSION MERGERS 35m

In this presentation, I will expose some of the last developments in microscopic nuclear structure calculations for exotic nuclei far from stabilitity in the vicinity of $^{78}$Ni, in a key region needed for understanding nucleosynthesis paths of gold and some of the most heavy elements.

In a first part, I will expose recent study on the development of collectivity in neutron-rich nuclei around N=40, where recent experimental evidence suggest a rapid change from the spherical to rotational regime, in analogy to the island of inversion known at N=20 [1,2] and extension of the island of collectivity towards N=50 [3].
In a second part, our recent algebraic Nilsson SU3 self-consistent model [6] will be used to describe the intruder relative evolution in the vicinity of $^{78}$Ni. The spectroscopy of the exotic nucleus $^{78}$ performed at the RIKEN-RIF laboratory in Japan has been recently published in Nature [1]. The results support the doubly magic character N=50, Z=28, of the heaviest nickel isotope, that is spherical in its ground state. In addition they have detected the presence at very low energy (2.5 MeV) of another facet of the same nucleus which is radically different, characterized by its spheroidal shape. This atypical phenomenon of coexistence, more germane to molecular systems, was predicted by the Configuration-Interaction (LSSM) calculations of the Strasbourg-Madrid collaboration in 2016 [6].
The model predicts as well the vanishing of the magic closure at N=50 for the
more exotic isotones of Chromium and Iron which should be deformed in
their ground states, leading to the idea of merging islands of collectivity from N=40 to N=50, as already observed from N=20 to N=28 [3]. Core excitations and their impact on moments in Cu and Zn isotopic chains will be discussed.
Finally, discussion of the underlying mecanism in terms of Spin-Tensor components will be exposed and compared to other neutron-rich regions of the nuclear chart.

[1] E. Caurier, F. Nowacki, A. Poves, Phys. Rev. C 90, 014302 (2014)
[2] S. Lenzi et al., Phys. Rev. C 82, 054301 (2010)
[3] C. Santamaria et al., Phys. Rev. Lett. C 115, 192501 (2015)
[4] A. P. Zuker et al., Phys. Rev. C 92, 024320 (2015)
[5] R. Tanushui et al., Nature 569, 53-58 (2019)
[6] F. Nowacki, A. Poves, Phys. Rev. Lett. {\bf 117}, 272501 (2016)

Speaker: Frederic NOWACKI (IPHC Strasbourg)
• 9:35 AM
Towards a better understanding of dense matter with gravitational waves 35m

The observation of the tidal deformability extracted from GW170817 have been analyzed by many teams, leading to boundaries of the NS radius. In our analysis, we contrast continuous EoS with EoS with strong first order phase transitions showing that these two cases induce different constrain on global NS properties. We also explore the impact of low density neutron matter predictions from chiral EFT approach, and we show that our current nuclear physics knowledge is still a bit more constraining than GW170817 tidal deformability. We also analyze the required accuracy for the tidal deformability which can make it compete with nuclear knowledge and the one which could shed light on the presence of phase transition in the core of NS.

Speaker: Jérôme Margueron (IPN Lyon)
• 10:30 AM 11:00 AM
Coffee break 30m
• 11:00 AM 12:30 PM
Session
• 11:00 AM
Beta-delayed neutron studies with the BRIKEN setup 35m

Beta-delayed neutron-emission will be the dominant decay mechanism for almost all new neutron-rich nuclei that are to be discovered in the next decades with the new generation of radioactive beam facilities. Despite that, the present status and understanding of beta-delayed neutron emitters is surprisingly poor. Since the first observation of this decay process 80 years ago (R. B. Roberts et al., Phys. Rev. 55, 664 (1939)) for only half of the identified 621 beta-delayed neutron emitters a measurement of the one-neutron branching ratio has been carried out, and many of these measurements are rather uncertain.

40 years ago beta-delayed two-neutron emission was detected in 11Li, closely followed by the detection of the three-neutron emission in the same nucleus (R. Azuma et al., Phys Rev. Lett. 43, 1652 (1979), R. Azuma et al., Phys. Lett. B 96, 31 (1980)). And in 1988 the only beta-delayed four-neutron emitter, 17B, was detected (J.P. Dufour et al., Phys. Lett. B 206, 195 (1988)).

Despite this long history, the competition between neutron emission and de-excitation via gamma-decay, and the emission of several neutrons is not yet fully understood and has - until recently- been neglected in theoretical models. This leads to large discrepancies for the calculation of even more neutron-rich nuclei and hampers the accuracy of r-process model calculations since beta-delayed neutrons modify the r-process abundance distribution at late phases when emitted during the freeze-out while material is decaying back to stability.

Since 2016 the BRIKEN project (“Beta-delayed neutron measurements at RIKEN for nuclear structure, astrophysics, and applications”) focusses on the most exotic beta-delayed neutron-emitters which can presently be produced. The setup combines the most efficient neutron detection array in the world with a state-of-the-art implantation detector and two clover detectors. Several experiments have been carried carried out so far and covered >250 neutron-rich nuclei in the region between 64Cr and 170Gd. For many of these isotopes, the neutron-branching ratios have been measured for the first time, e.g. for the doubly-magic 78Ni. In addition also about 50 new beta-decay half-lives have been deduced. More experiments for A>150 and A<60 will be carried out in the upcoming 2 years.
Apart from the remeasurement of a large number of beta-delayed neutron-emitters, approximately 150 new emitters will be added to the list of ~300 known beta-delayed neutron emitters. Also the number of measured multi-neutron emitters will be largely expanded. The results from the BRIKEN campaigns will help to improve the theoretical understanding of this complex decay mechanism tremendously, and help towards a better reproduction of the r-process abundance distribution in astrophysical network calculations.

Speaker: Iris Dillmann (TRIUMF)
• 11:35 AM
r-process studies at RIBF 35m
Speaker: Shunji Nishimura (RIKEN Nishina Center)
• 12:30 PM 2:30 PM
Lunch 2h
• 2:30 PM 4:00 PM
Session
• 2:30 PM
Multimessenger area: Opportunities for future experiments at ISAC-II, TRIUMF 35m

The recent observation of neutron star mergers indicate the presence of the r-process in those events, but the precise elemental composition cannot be deduced from the multimessenger observations. Detailed information about the heavy, neutron-rich nuclei involved are needed in order to pin down the origin of heavy elements in the universe. The next-generation radioactive ion beam facility ARIEL at TRIUMF soon will start delivering intense and clean post-accelerated RIBs.

The new TI-STAR silicon tracker detector, under development in an international collaboration at the University of Guelph and TRIUMF, is designed for experiments with heavy, exotic beams at the future ARIEL facility. TI-STAR will contain a hydrogen, deuterium or helium gas target to gain a factor 20-100 in luminosity for direct reaction experiments compared to experiments using target foils. One major goal of TI-STAR is constraining neutron-capture rates of r-process nuclei in the key A=130 region around 132Sn. Calculations indicate that uncertainties of neutron capture rates are typically one order of magnitude, and can be responsible for current disagreements between predicted and measured abundance distributions. TI-STAR coupled to the TIGRESS array of HPGe detectors and the new EMMA recoil separator will offer populating the r-process nuclei via one-neutron transfer reactions. Reconstruction of excitation energies and gamma ray decay scheme will allow to determine the neutron capture rates via the Oslo method. I will present the status of our experimental program related to Oslo-type experiments at TRIUMF and will discuss the challenges and opportunities of the ARIEL and TI-STAR projects.

Speaker: Dennis Muecher (University of Guelph)
• 3:05 PM
Bayesian extrapolation of nuclear observables towards the neutron drip line 35m

Quantifying the mass, or nuclear binding energy, of atomic nuclei is fundamental for understanding the origin of elements in the universe. The astrophysical processes responsible for the nucleosynthesis in stars often take place far from the valley of stability, where experimental masses are not known. Taking advantage of the information contained in mass model residuals, where the experimental information exists, we utilize Bayesian machine learning techniques to provide the missing nuclear information using extreme extrapolations of theoretical predictions.

Our methodology was developed on the two-neutron separation energies S2n of even-even nuclei, where we consider 10 global models. Quantified emulators of S2n residuals are constructed using Bayesian Gaussian Processes (GP) and Bayesian neural networks of which we assess respectively predictive power and honesty of credibility intervals with rms deviation and empirical coverage probability, using the AME2003 dataset for training and a testing dataset at its external boundary composed of all ulterior measurements. While both statistical models reduce the rms deviation from experiment significantly, GP offers a better and much more stable performance. After statistical corrections all models display similar rms deviations on the testing dataset.

This methodology is applied to the one- and two-neutron separations energies of the nuclei in the region of heavy calcium isotopes, which is at the frontier of experimental and theoretical nuclear structure research. The recent discovery of the extremely neutron-rich nuclei around 60Ca and the experimental determination of masses for 55-57Ca provide unique information about the binding energy surface in this region. To assess the impact of these recent discoveries on the nuclear landscape, we compute the posterior probability for nuclides between Si and Ti to be bound to neutron emission. We find that extrapolations for drip-line locations are consistent across the global mass models used, in spite of significant variations between their raw predictions. In particular we predict that 68Ca has an average posterior probability pex ≈ 76% to be bound to two-neutron emission while 70Ca is a threshold system with pex ≈ 57%; 61Ca is expected to decay by emitting a neutron (pex ≈ 46%). This analysis is finally extended to the full nuclear landscape.

Speaker: Leo Neufcourt (Michigan State University)
• 4:00 PM 4:30 PM
Coffee break 30m
• 4:30 PM 5:50 PM
Session
• 4:30 PM
Mass measurements in the vicinity of the N=40 subshell closure 35m

Sensitivity studies have shown the predominant role of 67Fe and 69Co on the weak r-process abundance pattern [1]. The individual photodissociation rates in the r-process path depend exponentially on the reaction Q-values. The Q-value for 67Fe(n,γ)68Fe and 68Co(n,γ)69Co reactions are based directly on the masses of 67Fe and 69Co. The double Penning trap JYFLTRAP [2] at the University of Jyväskylä has been successfully used to measure masses of both 67Fe and 69Co influencing the astrophysical weak r-process. The long-living state of 70Co was also measured during the same experiment. The isotopes of interest were produced via proton-induced fission on a natural uranium target at the IGISOL facility [3]. The Time-of-flight Ion Cyclotron Resonance (TOF-ICR) technique [4] and the Ramsey’s method of time-separated oscillatory field [5] were used for the mass measurements. The measured nuclei lie beyond the N=40 subshell closure, and provide information about the nuclear structure and mass surface in this region which is known for deformation and shape coexistence. In this talk, the experimental methods, the results and their impact on astrophysics and nuclear structure in the N=40 region will be discussed.

Speaker: Laetitia Canete (university of Jyväskylä)
• Thursday, July 4
• 9:00 AM 10:30 AM
Session
• 9:00 AM
r-Process Sites, their Ejecta Composition, and their Imprint in Galactic Chemical Evolution 35m

From low metallicity stars and the presence of radioactive isotopes in deep-sea sediments we know that the main r-process, producing the heaviest elements, is a rare event. The question remains whether neutron star mergers, via GW170817 the only proven r-process site, are the only contributors or also (a rare class of) supernovae, hypernovae/collapsars, as well as neutron star - black hole mergers qualify as candidates. Early galactic evolution as well as variations in nucleosynthesis signatures, e.g. actinide boost stars, might indicate the need for such other sites. We discuss and present the possible options (a) with respect to possible differences in ejecta amount and composition, and (b) in terms of their timing (onset and frequency) during galactic evolution.

Speaker: Friedrich-K. Thielemann (University of Basel and GSI Darmstadt)
• 9:35 AM
Mass ejection from neutron star mergers 35m

The very first detection of gravitational waves from a neutron-star merger and accompanying electromagnetic emission has provided a wealth of information on astrophysics and nuclear physics. In particular, these observations have established that neutron star mergers play an important role for the Galactic enrichment by r-process elements. We will provide a general overview on neutron star mergers and will discuss the mass ejection from these events.

Speaker: Andreas Bauswein (GSI Darmstadt)
• 10:30 AM 11:00 AM
Coffee break 30m
• 11:00 AM 12:30 PM
Session
• 11:00 AM
The unknown site of actinide nucleosynthesis – clues from extraterrestrial Pu-244 in deep-sea archives 35m

Half of the heavy elements are produced in r-process nucleosynthesis, which is exclusively responsible for actinide production. The abundance of long-lived actinides in today’s interstellar medium (ISM) results from the interplay between production and decay. Their presence would establish that their production was recent.
The solar system moves through the ISM and collects ISM dust particles. Direct detection of freshly produced radionuclides ‘live’ on Earth, i.e. before decaying, provides thus direct insight into recent and nearby nucleosynthetic activity. In particular $^{244}$Pu (t$_{1/2}$=81 Myr) can place strong constraints on r-process frequency and production yields over the last few 100 Myr [1,2]. In our work, we searched for such ISM radionuclides incorporated into terrestrial archives.
Detection of ISM-$^{244}$Pu in deep-sea archives complements the positive detection of interstellar and supernova-produced $^{60}$Fe (t$_{1/2}$=2.6 Myr) [3-6]. However, the low concentrations measured previously suggest a low abundance of interstellar Pu [7]. It signals actinide r-process nucleosynthesis is rare, which is incompatible with the rate and expected yield of supernovae as the predominant actinide-producing sites, but compatible with high yield - low rate scenarios, such as e.g. neutron-star mergers.
Here we present new results for $^{244}$Pu measured with a new facility at ANSTO (Sydney) with unprecedented sensitivity and background-free detection of Pu. We will report on the first time detection of a quantitative influx of the r-process nuclide $^{244}$Pu onto Earth and link this to a concomitant influx of $^{60}$Fe and supernova-activity. These data provide also new insights into their ISM concentrations [8].
[1] M. Paul et al. ApJL 558 (2001)
[2] C. Wallner et al. New Astr. Rev. 48 (2004)
[3] K. Knie et al., PRL 83 (1999); PRL 93 (2004)
[4] A. Wallner et al., Nature 532 (2016)
[5] L. Fimiani et al., PRL 116 (2016)
[6] P. Ludwig et al., PNAS 113 (2016)
[7] A. Wallner et al., Nature Comm. 6 ‘(2015)
[8] A. Wallner et al., submitted, in review (2019)

Speakers: Anton Wallner (The Australian National University), Michaela Froehlich (ANU), Norikaru Kinoshita, Michael Hotchkis, Stefan Pavetich, Stephan Tims
• 11:35 AM
Nucleosynthetic signatures of astrophysical r-process sites 35m

The first observation of a kilonova (or macronova) in the aftermath of
a gravitational wave signal has confirmed neutron star mergers (NSMs) as
a major source of heavy r-process nuclei in the universe. However, some
observational data of r-process elements in the galaxy seemingly cannot be
explained if NSMs are assumed to be the only r-process site. Theoreti-
cal models show that the heaviest r-process nuclei can possibly be produced
also in other astrophysical scenarios, such as magneto-rotationally driven su-
pernovae (MRSNe) or disks forming around collapsars. Distinguishing these
scenarios by means of their nucleosynthetic signatures proves extremely chal-
lenging, since the properties of the neutron-rich nuclei involved are unknown,
in addition to the uncertainties in hydrodynamical conditions of the ejecta.
Most models, however, agree that the ejecta from NSMs include com-
ponents that are neutron-rich enough for fission cycling, while simulated
outflows from MRSNe are generally less neutron-rich. This talk aims to
outline possible differences in abundance patterns originating from this dif-
ference and to discuss uncertainties in nucleosynthesis calculations.

Speaker: Marius Eichler
• 12:30 PM 2:30 PM
Lunch 2h
• 2:30 PM 4:00 PM
Session
• 2:30 PM
Looking for what is not s process 35m
Speaker: Marco Pignatari
• 3:05 PM
The solar r-process residual distribution 35m

Theoretical r-process models still suffer for severe uncertainties, regarding in particular the physical conditions characterizing the hosting site and the adopted nuclear inputs.
For this reason, the contribution of the r-process to the solar distribution is commonly derived by subtracting the contribution coming from the slow neutron capture process (s-process), as r=1-s.
This curve provides, together with low metallicity stars heavy element distributions, the point of reference for r-process nucleosynthesis calculations. I will show the r-process residuals distribution we recently derived with a Galactic Chemical Evolution model including recent Asymptotic Giant Branch stars and rotating massive stars yields.

Speaker: Dr Sergio Cristallo (INAF - Osservatorio Astronomico d'Abruzzo)
• 4:00 PM 4:30 PM
Coffee break 30m
• 4:30 PM 5:50 PM
Session
• 4:30 PM
The nuclear physics of r-process abundance patterns 35m

The properties of thousands of nuclear species far from stability set abundance patterns and other observables from r-process events. We will describe recent efforts to forge explicit links between the details of the r-process isotopic abundance pattern and specific nuclear properties, here focusing on masses and spallation cross sections. We will discuss future prospects given the anticipated capabilities of the next generation of radioactive beam facilities.

Speaker: Rebecca Surman (University of Notre Dame)
• 5:05 PM
Stellar Models for R-process Nuclear Astrophysics 25m

Abstract: One of the primary mechanisms for guiding experimental research in nuclear astrophysics is the sensitivity study. In a broad sense, these studies involve a stellar model in which various quantities related to nuclear reactions are varied to examine the effects. These variables can include a single, or multiple, reaction rates, Q-values, nuclear masses, and others. Subsequently, various aspects of the model are examined, such as elemental abundances, thermodynamics, and astronomical observables and compared with theory and observations. This talk will examine the underlying stellar models, their strengths and limitations both broadly and as it applies to R-process, and discuss the findings of the most recent works, as well as improvements that must be made in the future in order to improve the accuracy of the results of the sensitivity study.

Speaker: Amber Lauer (Triangle Universities Nuclear Laboratory)
• Friday, July 5
• 9:00 AM 10:30 AM
Session
• 9:00 AM
Pygmy Modes and Astrophysical Reaction Rates 25m

The new low-energy dipole and quadrupole modes in charge-asymmetric nuclei have been studied in a EFT-based approach by HFB and extended QRPA methods, accounting for anharmonicities by the coupling to up to 6 quasiparticle (QP) configurations. The spectroscopy of pygmy dipole (PDR) and quadrupole (PQR) states is discussed with focus on the region of N=50,82 isotones and the Z=50 Sn-isotopes. Multi-QP coupling is found to provides the proper energy shifts and fragmentation pattern of experimentally observed strength distributions. The spectroscopic results are used in calculations of astrophysical reaction rates. The pygmy modes lead to a significant enhancement of (n,g) capture rates, thus altering the nucleo-synthesis scenarios.

Speaker: Horst Lenske (U. Giessen)
• 9:25 AM
Electron capture on nuclei at finite temperature based on relativistic density functional 25m
Speaker: Ante Ravlic (University of Zagreb)
• 9:50 AM
Studying the structure of the A=98 decay products 25m

A series of experiments have been planned to study the neutron rich A=98 chain of decay products, starting from the decay of $^{98}$Kr. Following systematic mass and charge radii studies of Rb, Sr and Y, the A=98 isotopes have displayed unique properties. These properties will be discussed and related to the motivation for the planned experiments to showcase a thorough study of the Kr,Rb, Sr and Y decay chain.

Speaker: Mustafa Rajabali (Tennessee Technological University)
• 10:30 AM 11:00 AM
Coffee break 30m
• 11:00 AM 12:00 PM
Session
• 11:00 AM
R-process experiments with fast ion beams at the NSCL and FRIB 25m

Fragmentation beam facilities provide an efficient way to produce neutron-rich isotopes, and study the evolution of nuclear structure away from beta-stability. I will present recent work on time-of-flight mass measurement experiments at the National Superconducting Cyclotron Laboratory, aimed at extending the reach of this sensitive mass measurement technique to isotopes relevant to r-process nucleosynthesis models. I will also discuss the perspectives for r-process experiments at the future Facility for Rare Isotope Beams (FRIB).


text:
Tags
#causality #statistics
Question
If there is a directed path that starts at node 𝑋 and ends at node 𝑌 , 𝑌 is [...] of 𝑋
a descendant

Tags
#causality #statistics
Question
If there is a directed path that starts at node 𝑋 and ends at node 𝑌 , 𝑌 is [...] of 𝑋
?

Tags
#causality #statistics
Question
If there is a directed path that starts at node 𝑋 and ends at node 𝑌 , 𝑌 is [...] of 𝑋
a descendant
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If there is a directed path that starts at node 𝑋 and ends at node 𝑌 , 𝑌 is a descendant of 𝑋

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