text:
# How to put lstlisting in a minipage

I had a problem creating a new environment that would let me put a lstlisting inside a minipage. I could create a new environment that sets up the minipage, then in the document put a lstlisting inside that minipage, but I couldn't create environment that did both together.

\documentclass{article}
\usepackage{listings}
\lstset{language=SQL,keywordstyle=\underbar,numbers=none}
\newenvironment{egdlisting}%
{\hfill\begin{minipage}{\dimexpr\textwidth-2em}}%
{\end{minipage}}

\begin{document}

\begin{egdlisting}
\begin{lstlisting}
select *
from foo
where bar = 4;
\end{lstlisting}
\end{egdlisting}

\end{document}

Works. The obvious next step, putting the lstlisting inside the environment, does not.

\documentclass{article}
\usepackage{listings}
\lstset{language=SQL,keywordstyle=\underbar,numbers=none}
\newenvironment{egdlisting}%
{\hfill\begin{minipage}{\dimexpr\textwidth-2em}\begin{lstlisting}}%
{\end{lstlisting}\end{minipage}}

\begin{document}

\begin{egdlisting}
select *
from foo
where bar = 4;
\end{egdlisting}

\end{document}

The error message (shown for recognition purposes) is below.

\$ lualatex tex/sm.tex >& build.log

gave me

This is LuaHBTeX, Version 1.12.0 (TeX Live 2020/Cygwin)
restricted system commands enabled.
(./tex/sm.tex
LaTeX2e <2020-02-02> patch level 5
L3 programming layer <2020-03-06>
(/usr/share/texmf-dist/tex/latex/base/article.cls
Document Class: article 2019/12/20 v1.4l Standard LaTeX document class
(/usr/share/texmf-dist/tex/latex/base/size10.clo))
(/usr/share/texmf-dist/tex/latex/listings/listings.sty
(/usr/share/texmf-dist/tex/latex/graphics/keyval.sty)
(/usr/share/texmf-dist/tex/latex/listings/lstmisc.sty)
(/usr/share/texmf-dist/tex/latex/listings/listings.cfg))
(/usr/share/texmf-dist/tex/latex/listings/lstlang1.sty)
(/usr/share/texmf-dist/tex/latex/l3backend/l3backend-pdfmode.def)
(./WORK/sm/sm.aux) (/usr/share/texmf-dist/tex/latex/base/ts1cmr.fd))
*

Update Section 4.5 of the listings package documentation, specifically \lstnewenvironment, solves this... but you have to use a different syntax for the minipage.

\documentclass{article}
\usepackage{listings}
\usepackage{lipsum} % provide text around listings, to show indent
\lstset{numbers=none}
\lstnewenvironment{newlisting}{\hfill\minipage{\dimexpr\textwidth-1cm}}{\endminipage}

\begin{document}
\lipsum[1]

\begin{newlisting}
select *
from foo
where bar = 4;
\end{newlisting}

\lstset{numbers=left}

\begin{newlisting}
select *
from foo
where bar = 4;
\end{newlisting}

\lipsum[2]
\end{document}

gives me the output I'm looking for.

The critical bit, besides using the correct command (\lstnewenvironment) is to not use \begin{minipage}{width} ... \end{minipage}, but to use \minipage{width} ... \endminipage.

• see the listings documentation, section 4.5 Environments. – Ulrike Fischer Apr 11 at 17:29
• this is the same as the standard verbatim environment and verb command, no such constructs work in the argument of another command or in standard definitions. But see Ulrike's link – David Carlisle Apr 11 at 17:37
• No it will work I said to do what Ulrike says (Not that I ever do what she says:-) – David Carlisle Apr 11 at 17:40
• @Rmano: That's not really necessary, as a minipage-like effect is also possible by changing the xleftmargin and xrightmargin keys. – Werner Apr 11 at 18:13
• @Werner better yet, xleftmargin (which I also overlooked, reading fail) meets my purpose without having to create a new environment. Still, how to create that new environment was not at all obvious, so I learned two things today :) – Keith Davies Apr 11 at 18:24

Reading page 43 of the documentation, and using the trick of replacing \begin{env}...\end{env} with \env ... \endenv(*):

\documentclass{article}
\usepackage{listings}
\lstset{language=SQL,keywordstyle=\underbar,numbers=none}

\lstnewenvironment{egdlisting}
{\minipage{\dimexpr\textwidth-2em}}
{\endminipage}

\begin{document}

\begin{egdlisting}
select *
from foo
where bar = 4;
\end{egdlisting}

\end{document}

I am not sure if this is what you are looking for...

(*) not sure if this is a documented thing or a dirty hack...

• Oh! The missing piece! I'd forgotten about that method of starting and ending environments. Solved! Thank you. – Keith Davies Apr 11 at 18:01
• Happy to be useful! – Rmano Apr 11 at 18:21


text:
# Seminari del Dipartimento

 Analisi MatematicaGrowth of Sobolev norms for abstract linear Schrödinger EquationsAlberto Maspero04-10-2017 - 16:00Largo San Leonardo Murialdo,1 - Pal.C - Aula 311 We prove an abstract theorem giving a $t^epsilon$ bound for any $epsilon> 0$ on the growth of the Sobolev norms in some abstract linear Schroedinger equations. The abstract theorem is applied to several cases, including perturbations of (i) Schroedinger equation on a Zoll manifold; (ii) resonant or nonresonant Harmonic oscillators in R^d. The proof is obtained by conjugating the system to some normal form in which the perturbation is a smoothing operator. This is a joint work with D. Bambusi, B. Grebert and D. Robert.  org: PROCESI Michela

format: plain


text:
Supporting Statistical Analysis for Research

## 4.8 Coding missing values - part 2

### 4.8.1 Programming skills

#### 4.8.1.1 Anonymous functions

An anonymous function is a function that does not have a name. This means that the function is for a single use and has no permanence. It can not be used latter without being created again.

Anonymous functions are a quick and simple approach to creating your own function. (The syntax for their specification is much simpler than a typical user-defined function.) They are a handy tool for data wranglers when a custom function (not already defined) is needed.

#### 4.8.1.2 Repeating an operation on multiple variables

In the prior sections of this chapter we introduced the concept of vectorization and used it to repeat operations on all rows of a variable. There are times when the same (vectorized) operation needs to be applied to two or more variables of a data frame. For example, in the prior section, the ? values where changed to missing in two variables of the data frame. The code to make the change was written twice, once for each of the two variable. This is not hard if there are only two variables that the operation is being repeated on. When there are more, maybe many more, you will want to use a function/method to apply the operation to a set of variables. This will be demonstrated in the examples of this section.

### 4.8.2 Examples - R

These examples use the airAccs.csv data set.

1. We begin by using the same code as in the prior sections of this chapter to load the tidyverse, import the csv file, and rename the variables.

Note, the lubridate package is also loaded for use in these examples.

library(tidyverse)
library(lubridate)
airAccs_path <- file.path("..", "datasets", "airAccs.csv")
air_accidents_in <- read_csv(airAccs_path, col_types = cols())
Warning: Missing column names filled in: 'X1' [1]
air_accidents_in <-
air_accidents_in %>%
rename(
obs_num = 1,
date = Date,
plane_type = planeType,
aboard = Aboard,
ground = Ground
)

air_accidents <- air_accidents_in

glimpse(air_accidents)
Observations: 5,666
Variables: 8
$obs_num <dbl> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, ...$ date       <date> 1908-09-17, 1912-07-12, 1913-08-06, 1913-09-09, 19...
$location <chr> "Fort Myer, Virginia", "Atlantic City, New Jersey",...$ operator   <chr> "Military - U.S. Army", "Military - U.S. Navy", "Pr...
$plane_type <chr> "Wright Flyer III", "Dirigible", "Curtiss seaplane"...$ dead       <dbl> 1, 5, 1, 14, 30, 21, 19, 20, 22, 19, 27, 20, 20, 23...
$aboard <dbl> 2, 5, 1, 20, 30, 41, 19, 20, 22, 19, 28, 20, 20, 23...$ ground     <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
2. Anonymous functions.

The tidyverse (purrr package) allows anonymous functions to be specified using what is known as formula notation. The anonymous function begins with ~ and the parameters are named .x, .y, and .z (defined in this order.) Not all three parameters need to be used in the function. The function does not need to use any parameters. If there is only one parameter, . can be used in place of .x. For example,

~(.x + .y)

This would add the first and second parameter together and return the results. Another example is,

~ if_else(. == -9, NA_character_, .)

This would test the rows of the first parameter for equality with -9. If TRUE, the row is NA, otherwise it is unchanged. (This is equivalent to the na_if(x, -9) function.)

The case_when() function is a generalization of if_else() that can check more than one condition.

Each condition is paired with a replacement value. The replacement value is specified as a function, possibly an anonymous function. If the replacement value is the same for all observations, an anonymous function with simply that value can be used.

If a condition is found to match, the remaining conditions are not checked for these rows. Using TRUE as the last condition provides a default value to use if none of the other conditions are TRUE.

We will change the operator values of ? and Private to NA using the case_when() function.

# restore original values of the variables
air_accidents <-
air_accidents %>%
mutate(operator = pull(air_accidents_in, operator))

air_accidents <-
mutate(
air_accidents,
operator = case_when(
operator == "?" ~ NA_character_,
operator == "Private" ~ NA_character_,
TRUE ~ operator
)
)

air_accidents %>%
filter(operator == "?") %>%
select("location", "operator", "plane_type")
# A tibble: 0 x 3
# ... with 3 variables: location <chr>, operator <chr>, plane_type <chr>

In this example the case_when() function is used with only two test conditions. The recode() or na_if() methods could have been used here. The case_when() function was used to demonstrate its use.

3. Operating on multiple columns.

The mutate_at() function is a variant of mutate(). It is used when you want to apply the same function to a set of columns.

We will use mutate_at() to apply the na_if() function to the operator and plane_type columns. The columns to apply the function to are given using the var() function.

The na_if() function needs two parameters, the column name and "?". We will create an anonymous function to do that for us. The anonymous function will be, ~ na_if(., "?"), where the ., short for .x the first parameter, is passed in from the mutate_at() function.

# restore original values of the variables
air_accidents <-
air_accidents %>%
mutate(operator = pull(air_accidents_in, operator))

air_accidents <-
mutate_at(air_accidents, vars(operator, plane_type), ~ na_if(., "?"))

air_accidents %>%
filter(operator == "?" | plane_type == "?") %>%
select("location", "operator", "plane_type")
# A tibble: 0 x 3
# ... with 3 variables: location <chr>, operator <chr>, plane_type <chr>

The mutate_at() method can pass additional parameters to the called function, na_if() here. The following code uses this approach instead of the anonymous function approach.

# restore original values of the variables
air_accidents <-
air_accidents %>%
mutate(
operator = pull(air_accidents_in, operator),
plane_type = pull(air_accidents_in, plane_type)
)

air_accidents <-
mutate_at(air_accidents, vars(operator, plane_type), na_if, "?")

air_accidents %>%
filter(operator == "?" | plane_type == "?") %>%
select("location", "operator", "plane_type")
# A tibble: 0 x 3
# ... with 3 variables: location <chr>, operator <chr>, plane_type <chr>
The parameters to mutate_at() are, .tbl, .vars, .funs, ....
• The .tbl parameter is the data frame being operated on. This parameter is typically piped into mutate_at().
• The .vars parameter is the list of variable in the data frame to be passed to .funs.
The vars() function is one of several select() helper functions that can genereate lists of variables.
• The .funs parameter is the name of the function to be called for each of the .vars. It is the name only, with out ().
• The ... are a list of any additional parameter to be used by the .funs function. They can be named or not. The first parameter to funs. is the variable. The ... will follow this parameter.

### 4.8.3 Examples - Python

These examples use the airAccs.csv data set.

1. We begin by using the same code as in the prior sections of this chapter to load the packages, import the csv file, and rename the variables.

from pathlib import Path
import pandas as pd
import numpy as np
airAccs_path = Path('..') / 'datasets' / 'airAccs.csv'
air_accidents_in = (
air_accidents_in
.rename(
columns={
air_accidents_in.columns[0]: 'obs_num',
'Date': 'date',
'planeType': 'plane_type',
'Aboard': 'aboard',
'Ground': 'ground'}))

air_accidents = air_accidents_in.copy(deep=True)

print(air_accidents.dtypes)
obs_num         int64
date           object
location       object
operator       object
plane_type     object
aboard        float64
ground        float64
dtype: object
2. Using anonymous functions

Anonymous functions in python are called lambda functions. They are specified as,

lambda <parameter list>: code

For example,

lambda x, y: (x + y)

This would add the first and second parameters together and return the reslts. The calling function\method would need to supply the two parameters for this function.

A lambda function called inside of the assign() method gets passed the data frame (that the assign() method is modifying) as its only parameter. An example of a lambda function that could be called inside of an assign() is,

lambda df: df.loc[:, 'x'].mask(df.loc[:, 'x'] == -9, np.NaN)

The data frame parameter of the lambda function is named df. The mask() method is used in this example uses a test condition to determine which rows to replace with a specified value, np.NAN here. This example tests the rows of the x variable for equality with -9. If True, the row is set to np.NaN, otherwise it is unchanged.

# restore original values of the operator variable
air_accidents.operator = air_accidents_in.operator

air_accidents = (
air_accidents
.assign(operator=lambda df:

(air_accidents
.query('operator == "?"')
.copy()
.loc[:, ["location", "operator", "plane_type"]]
.pipe(print))
Empty DataFrame
Columns: [location, operator, plane_type]
Index: []
3. Change a variable with multiple conditions

Python and Pandas do not have a switch, also called case when, type of function that can test multiple conditions. (This is a common control mechanism found in many programming languages.) If all the conditions are checks of equality, then replace() works. If one or more of the conditions is a range of values, then the solution is to use multiple comprehensions or multiple lambda fuctions. Sequential comprehensions can be used to achive most case when type functions. Nested comprehensions may sometimes be needed to implement case when or else if type conditions. Nest the comprehensions should only be used if sequential comprehensions will not accomplish what is needed.

We will change the operator values of ? and Private to NAN using sequential mask() functions.

# restore original values of the operator variable
air_accidents['operator'] = air_accidents_in['operator']

air_accidents = (
air_accidents
.assign(
operator=(lambda df: df
['operator']

(air_accidents
.query('operator == "?"')
.copy()
.loc[:, ["location", "operator", "plane_type"]]
.pipe(print))
Empty DataFrame
Columns: [location, operator, plane_type]
Index: []
4. Operating on multiple columns.

The apply() method will iterate over the columns of the data frame, by default operation. (The apply() method can also iterate over rows, if needed.) This can be used to do the same operation on multiple columns. There are two parts to coding this.

One of the parts is specifying the function to be applied. In this example we will use a lambda function to change ? to NaN. The apply() method is operating on columns. So the parameter to the lambda function is a column of the data frame.

The second part is determining the columns that the operation will be applied to. For this we will use a comprehension. The comprehension will compare each column name in the data frame to a set of names. If the name is in the set, the lambda function is run for the column. Otherwise the original column is returned unchanged.

# restore original values of the variables
air_accidents = (
air_accidents
.assign(
operator=air_accidents_in['operator'],
plane_type=air_accidents_in['plane_type']))

air_accidents = (
air_accidents
.apply(
func=lambda x: x.mask(x == '?', np.NaN)
if x.name in ['operator', 'plane_type'] else x))

(air_accidents
.query('operator == "?" | plane_type == "?"')
.copy()
.loc[:, ["location", "operator", "plane_type"]]
.pipe(print))
Empty DataFrame
Columns: [location, operator, plane_type]
Index: []

### 4.8.4 Exercises

These exercises use the PSID.csv data set that was imported in the prior section.

1. Import the PSID.csv data set.

2. Code NAs for the NA/DF and no histories values for the marriage status variable.

3. Change the units on the earnings and hours variables to be thousands of dollars or hours. Use a method that operates on multiple columns.

Hint, to do the unit change on a variable x, one would do x / 1000.


text:
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title: Einstein's Law of Motion date: 2019-02-24 17:22:28 category: physical tags:

• physical
• "law of motion"
• law
• montion
• einstein mathjax: true

$$\mathbf F = \dfrac {m_0 \mathbf a} {\left({1 - \dfrac{v^2}{c^2}}\right)^{\tfrac 3 2}}$$

# Physical Law

The force and acceleration on a body of constant rest mass are related by the equation: $$\mathbf F = \dfrac {m_0 \mathbf a} {\left({1 - \dfrac{v^2}{c^2}}\right)^{\tfrac 3 2}}$$ where:

• 𝐅 is the force on the body
• 𝐚 is the acceleration induced on the body
• 𝑣 is the magnitude of the velocity of the body
• 𝑐 is the speed of light
• 𝑚0 is the rest mass of the body.

# Proof

Into Newton's Second Law of Motion: $$\mathbf F = \dfrac {\mathrm d}{\mathrm d t} \left({m \mathbf v}\right)$$

we substitute Einstein's Mass-Velocity Equation: $$m = \dfrac {m_0} {\sqrt {1 - \dfrac {v^2} {c^2}}}$$ where:

• 𝑣 is the magnitude of the velocity of the body
• 𝑐 is the speed of light in vacuum
• 𝑚0 is the rest mass of the body.

The value 𝑚 is known as the relativistic mass of the body. The factor $\dfrac 1 {\sqrt{1 - \dfrac {v^2} {c^2} } }$ is known as the Lorentz Factor.

to obtain: $$\mathbf F = \dfrac {\mathrm d} {\mathrm d t} \left({\dfrac {m_0 \mathbf v}{\sqrt{1 - \dfrac {v^2}{c^2}}}}\right)$$

Then we perform the differentiation with respect to time:

$$\frac{\mathrm d}{\mathrm d t} \left({\frac {\mathbf v}{\sqrt{1 - \dfrac {v^2}{c^2} } } }\right)$$ $$= \frac{\mathrm d}{\mathrm d v} \left({\frac {\mathbf v}{\sqrt{1 - \dfrac {v^2}{c^2} } } }\right) \frac{\mathrm d v}{\mathrm d t}$$ $$= \mathbf a \left({\frac {\sqrt{1 - \dfrac {v^2}{c^2} } - \dfrac v 2 \dfrac 1 {\sqrt{1 - \dfrac {v^2}{c^2} } } \dfrac{-2 v}{c^2} } {1 - \dfrac {v^2}{c^2} } }\right)$$ $$= \mathbf a \left({\frac {c^2 \left({1 - \dfrac {v^2}{c^2} }\right) + v^2} {c^2 \left({1 - \dfrac {v^2}{c^2} }\right)^{3/2} } }\right)$$ $$= \mathbf a \left({\frac 1 {\left({1 - \dfrac {v^2}{c^2} }\right)^{3/2} } }\right)$$

Thus we arrive at the form: $$\mathbf F = \dfrac {m_0 \mathbf a} {\left({1 - \dfrac{v^2}{c^2}}\right)^{\tfrac 3 2}}$$

# Sources

You can’t perform that action at this time.


text:
# Question on how differential form as defined for subsets of $\mathbb R^n$ and integration on them in Spivak, Calculus on Manifolds

If $V$ is a vector space, denote by $\Lambda^k(V)$ the space of alternating multilinear maps from $V^k$ to $\mathbb R$, i.e. the space of alternating $k$-tensors. Also for a point $p \in \mathbb R^n$ denote by $\mathbb R^n_p$ the tangent space $\{ p \} \times \mathbb R^n$ at $p$.

In Spivak, Calculus on Manifolds, he defines a k-form, or simply differential form, to be a map $\omega$ such that for every $p \in \mathbb R^n$ we have $\omega \in \Lambda^k(\mathbb R^n_p)$. Then for a differentiable (where by differentiable he always means $C^{\infty}$) $f : \mathbb R^n \to \mathbb R^m$ and the linear transformation $Df(p) : \mathbb R^n \to \mathbb R^m$ he defines $f_{\ast} : \mathbb R^n_p \to \mathbb R^m_{f(p)}$ by $$f_{\ast}(v_p) = (Df(p)(v))_{f(p)}$$ Then he defines the pull-back of $k$-forms on $\mathbb R^m$ by $$f^{\ast}\omega(p)(v_1, \ldots, v_k) = \omega(f(p))(f_{\ast}(v_1), \ldots, f_{\ast}(v_k))$$ for $p \in \mathbb R^n, v_1,\ldots, v_k \in \mathbb R^n_p$; thus giving differential forms on $\mathbb R^n$.

What is missing here is that he is not defining differential forms for subsets of $\mathbb R^n$ or for functions $f : A \to \mathbb R^m$ with $A \subseteq \mathbb R^n$. The latter could be fixed easily, as $f$ is assumed to be differentiable it has a tangent space everywhere on $A$. But I am not sure how to define differential forms on arbitrary subsets of $\mathbb R^n$, if we could say simply that every subset has $\mathbb R^n_p$ at every point $p$ as its tangent space? For open sets, this might be clear, but not if they might have a boundary or look even wilder.

Maybe these observations are fixed if we restrict to subsets which are differentiable manifolds, but this is to much of a machinery, as up to this point manifolds are not introduced. So there should be a simpler solution?

Later in the chapter on the Fundamental theorem he writes

If $\Omega$ is a $k$-form on $[0,1]^k$, then $\omega = fdx^1 \wedge \cdots \wedge dx^k$ for a unique function $f$.

and uses this to define the integral of $\omega$ over $[0,1]^k$.

But how could $\omega$ be a differential form on $[0,1]^k$? It was just defined for $\mathbb R^k$. So does this means that $\omega(p) \in \Lambda_k(\mathbb R^k_p)$ for $p \in [0,1]^k$? But how is this justified, looking up a more general definition (like on wikipedia) a $k$-form for some subset is a section in the $k$-th exterior power of the cotangential space; but that means that for each point we have a multilinear map on tangent vectors. But is $\mathbb R^n_p$ the tangent space of $[0,1]^k$. For open sets, I see that we could have tangent vectors in all directions, but this cube is closed, hence has a boundary, and there I do not see that the tangent space is also isomorphic to $\mathbb R^k$?

Then later he proceeds:

If $\omega$ is a $k$-form on $A$ (guess $A \subseteq \mathbb R^n$, but this is not mentioned) and $c$ is a singular $k$-cube in $A$ we define $$\int_c \omega = \int_{[0,1]^k} c^{\ast}\omega.$$

With the above definitions we must have for $c^{\ast}\omega$ with $p \in [0,1]^k$ $$\omega(c(p))(c_{\ast}(v_p))$$ where $c_{\ast}(v_p) = (Dc(p)\cdot v)_{c(p)}$ with $Dc(p) : \mathbb R^k \to \mathbb R^n$. But again, this has the same drawback as written above, what happens on the boundary. The map $c$ is differentiable, so it has a tangent space at its boundary by definition. But as it is continuous $c([0,1]^k))$ is a closed set with boundary, so again it is not clear how the tangent space should be defined at the boundary?

So there seems something missing? Does he subtly assumes that for every $A \subseteq R^n$ the tangent space is $R^n_p$ for each $p \in \mathbb R^n$?

Spivak does everything inside $\mathbb{R}^n$. At that point in the book, the author hasn't even defined manifolds and submanifolds, so I don't see why one would worry about subsets $A \subset \mathbb{R}^n$ that have boundaries or look particularly crazy: the tangent space at $a \in A \subset \mathbb{R}^n$ is the only thing it could be, namely $\mathbb{R}^n_a$. The author did define what it means for a function $f:A \to \mathbb{R}^m$ to be differentiable (extend to an open set containing $A$ and differentiate), so it seems natural to assume that when he speaks of a differentiable $k$-form on $A$ he means an assignment of an element of $\Lambda^k(\mathbb{R}^n_a)$ to each $a \in A$ such that the local expression of the form is given by differentiable functions $A \to \mathbb{R}$.
• Thanks for your answer. Guess by local expression you mean the extension to an open subset, but then this is not a function $A \to \mathbb R$, it is either a function $U \to \Lambda^k(R_a^n)$ or a function $U \times (R_a^n)^k \to \mathbb R$, where $A \subseteq U$ is open, or not? And which one of the alternatives you mean? – StefanH Mar 21 '16 at 19:05
• @Stefan I mean the functions $f_{i_1,\ldots,i_k}:A \to \mathbb{R}$ given by $\omega = \sum_{i_1 < \cdots < i_k} f_{i_1,\ldots,i_k} dx^{i_1}\wedge \cdots \wedge dx^{i_k}$. (At each point $a \in A$, $f_{i_1,\ldots,i_k}(a)$ is the $(i_1,\ldots,i_k)$-th coordinate of $\omega(a)$ in the usual basis of $\Lambda^k(\mathbb{R}^n_a)$.) When I wrote the answer I had the case $k = n$ in mind, in which only one such function appears. – Alex Provost Mar 21 '16 at 19:15
• Okay, makes sense. By the way, first your first sentences, that for arbitrary $A \subseteq \mathbb R^n$ the tangent space is simply $\mathbb R^n_a$ already answers my question; but your remarks about differentiability are interesting anyway! – StefanH Mar 21 '16 at 19:20


text:
Select Page

# Understand the problem

For all natural numbers$$n$$, let

$$A_n=\sqrt{2-\sqrt{2+\sqrt{2+\cdots +\sqrt{2}}}}$$           ($$n$$ many radicals)

(a) Show that for $$n\ge 2, A_n=2\sin \frac{π}{2^{n+1}}$$.

(b) Hence, or otherwise, evaluate the limit

$$\displaystyle\lim _{n\to \infty} 2^n A_n$$ .

##### Source of the problem

I.S.I. (Indian Statistical Institute) B.Stat/B.Math Entrance Examination 2019. Subjective Problem no. 6.

##### Topic

Trigonometric Substitution

7.5 out of 10

##### Suggested Book

Mathematical Olympiad Challenges by Titu Andreescu & Razvan Gelca.

Do you really need a hint? Try it first!

For $$n\ge 2$$,

$$\sqrt{2+\sqrt{2+\cdots +\sqrt{2}}}$$       ($$n$$ many radicals)

=$$\sqrt{2+\sqrt{2+\cdots +\sqrt{2+0}}}$$

=$$\sqrt{2+\sqrt{2+\cdots +\sqrt{2+2\cos \frac{π}{2}}}}$$.

=$$\sqrt{2+\sqrt{2+\cdots +\sqrt{2(1+\cos \frac{π}{2})}}}$$

=$$\sqrt{2+\sqrt{2+\cdots +\sqrt{4\cos^2 \frac{π}{2^2}}}}$$

=$$\sqrt{2+\sqrt{2+\cdots +2\cos \frac{π}{2^2}}}$$. ($$n-1$$ many radicals)

……..    ………..     ……….      …   …….  …

…….     ………     …………    .….     ………

=$$2\cos \frac{π}{2^n}$$        $$[n\ge 2]$$.

Now $$A_n=\sqrt{2-2\cos \frac{π}{2^n}}$$

$$\Rightarrow A_n= \sqrt{2(1-\cos \frac{π}{2^n})}$$

$$\Rightarrow A_n= \sqrt{4\sin^2 \frac{π}{2^{n+1}}}$$

$$\Rightarrow A_n= 2\sin \frac{π}{2^{n+1}}$$.

Now $$\displaystyle\lim_{n\to \infty} 2^nA_n=\displaystyle\lim_{n\to \infty} 2^{n+1}\cdot \sin \frac{π}{2^{n+1}}$$.

Since , $$n \to \infty$$

$$\Rightarrow 2^{n+1}\to \infty$$

$$\Rightarrow \frac{π}{2^{n+1}}\to 0$$

Let $$\frac{π}{2^{n+1}}=z \Rightarrow z \to 0$$, when $$n \to \infty$$.

Therefore, $$\displaystyle\lim_{n\to \infty} 2^n A_n$$=$$\displaystyle\lim_{z \to 0}\frac{\sin z}{z}\cdot π =1\times π=π$$. (Ans.)

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text:
10 terms

# College Algebra

#### Terms in this set (...)

complex number
a number of the form a + bi where a and b are real numbers. Combination of real number and imaginary number.
real number
numbers that are either rational or irrational. A real number is also a complex number.
rational number
a number that can be expressed as a/b, the ratio of two integers, b is not = 0. All fractions and terminating or repeating decimals are rational. If a number is rational, it is a real number.
irrational number
a number that cannot be expressed as a/b, the ratio of two integers. Non-termination, non-repeating decimals are irrational.
inequality
a mathematical statement that two quantities are not equal.
multiplicative inverse
The reciprocal of a number a which is 1/a. Not to be confused with the inverse of a function.
distributive property
multiplying a number by a group of numbers added together is the same as doing each multiplication separately
natural number
counting numbers, defined by the set 1,2,3,4,... The three dots means that the pattern continues, this is an infinite set
whole number
defined by the set 0,1,2,3,4,...this set includes the zero in the set of whole numbers
integers
defined by the set -3, -2, -1, 0., 1, 2, 3, 4,...Contains both positive and negative whole numbers, this is an infinite set. Does not include fractions.


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# upcrossings and downcrossings

Inequalities involving the number of times at which a stochastic process passes upwards or downwards through a bounded interval play an important role in the theory of stochastic processes. Whether or not a sequence of real numbers converges to a limit can be expressed in terms of the finiteness of the number of upcrossings or downcrossings, leading to results such as the martingale convergence theorem and regularity of martingale sample paths. As the main applications are to stochastic processes, we suppose that $(X_{t})_{t\in\mathbb{T}}$ is a real-valued stochastic process with totally ordered time index set $\mathbb{T}$, usually a subset of the real numbers. However, for the definitions here, it is enough to consider $X_{t}$ to be a sequence of real numbers, and the dependence on any underlying probability space is suppressed.

For real numbers $a, the number of upcrossings of $X$ across the interval $[a,b]$ is the maximum nonnegative integer $n$ such that there exists times $s_{k},t_{k}\in\mathbb{T}$ satisfying

 $s_{1} (1)

and for which $X_{s_{k}}. The number of upcrossings is denoted by $U[a,b]$. Note that this is either a nonnegative integer or is infinite. Similarly, the number of downcrossings, denoted by $D[a,b]$, is the maximum nonnegative integer $n$ such that there are times $s_{k},t_{k}\in\mathbb{T}$ satisfying (1) and such that $X_{s_{k}}>b>a>X_{t_{k}}$.

Note that between any two upcrossings there is a downcrossing. Given $s_{k},t_{k}$ satisfying (1) and $X_{s_{k}}, we can set $s^{\prime}_{k}=t_{k}$ and $t^{\prime}_{k}=s_{k+1}$ for $k=1,\ldots,n-1$. Then, $X_{s^{\prime}_{k}}>b>a>X_{t^{\prime}_{k}}$ from which we conclude that $D[a,b]\geq U[a,b]-1$. Similarly, we have $U[a,b]\geq D[a,b]-1$. Hence, the number of upcrossings and the number of downcrossings of an interval differ by at most $1$.

For a finite index set $\mathbb{T}=\{1,2,\ldots,N\}$, the number of upcrossings can be computed as follows. Set $t_{0}=0$ and define $s_{1},s_{2},\ldots$ and $t_{1},t_{2},\ldots$ by

 $\displaystyle t_{k}=\inf\left\{t\in\mathbb{T}\colon t\geq s_{k},X_{t}>b\right% \}\in\mathbb{T}\cup\{\infty\}.$ $\displaystyle s_{k}=\inf\left\{t\in\mathbb{T}\colon t\geq t_{k-1},X_{t}

The number of upcrossings of $[a,b]$ is then equal to the maximum $n$ such that $t_{n}<\infty$ (see Figure 1).

## References

• 1 David Williams, Probability with martingales, Cambridge Mathematical Textbooks, Cambridge University Press, 1991.
Title upcrossings and downcrossings UpcrossingsAndDowncrossings 2013-03-22 18:49:33 2013-03-22 18:49:33 gel (22282) gel (22282) 5 gel (22282) Definition msc 40A05 msc 60G17 MartingaleConvergenceTheorem ConvergenceOfASequenceWithFiniteUpcrossings upcrossing downcrossing


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# foundation of enterprise engineering

FAST amplifies and empowers scientific advancement and technological innovation in Armenia and beyond. Figure 3 Categories of communicative acts, amples of intentions in this category are question and, The structure of a coordination act/fact (1). The Enterprise Engineering Framework (EEF) reduces the complexity of the enterprise by engineering it as a flat network of uniformly constructed entities—enterprise building blocks. The PRISMA white-box allows one to conceive organisations as prismanets: networks of processors, channels, and banks. Predication Part II. side the network. Activities between the University of British Columbia and Exeter include a joint research symposium focused on Community, Culture, Creativity, and Wellbeing held at Exeter in May 2018 and a faculty-led, co-funded initiatives in Sport, Exercise and Health Sciences, Climate Change and Digital Humanities. PSI stands for Performing in Social Interaction. Transactor roles are the universal building blocks of business processes. Hyperledger Composer (HC) is a toolset example to develop Blockchain applications. which streamlines the human architecture of the enterprise and partitions it into the collection of executive and which works best for production workflows, simple case management scenarios, and basic administrative processes. 1979, Reidel: Dordrecht, Netherlands. The individual agents may also have hierarchical relations. of artificial agents, enterprise tools and boundary constructs. ure, he will decline the client’s request. EDWARDSVILLE The Enterprise Holdings Foundation has donated $1.5 million to the Southern Illinois University Edwardsville School of Engineering (SOE). reduce coordination and communication needs and thereby streamline enterprise information flows. assign the function of parking lot to some square, for particular days of the week. After being ordered in a suitable classification scheme, each of the current eleven theories is briefly discussed: the EE information theory, the EE function-construction theory, the EE organ-isational operation theory, the EE system theory, the EE modelling theory, the EE organisation design theory, the EE governance & management theory, the EE organisation realisation theory, the EE organisational construction theory, the EE organisation implementation theory, and the EE normalisation theory. xvii, 185 p. Referenced Theories in Enterprise Engineering), By the word “enterprise” we refer to all kinds of human collaborations (like companies, gov, ernmental agencies, healthcare institutions, and supply chains, but also the organisation of a, ICT stands for Information and Communication T. practice of applying digital electronic, optical etc., means to process, store and transmit data. Imagine if there was a concise and clear framework that would. Three sorts of conceptual models are distinguished: the black-boxes, the grey-boxes, and white-boxes. At the unit level, individual agents communicate both asynchronously and synchronously. The enterprise engineer is advised by specialists representing Business, Organisation and IT and involves the right stakeholders. Figure 5 The EE theories in the EE Framework of Theories. The three-year,$500,000 annual contribution marks the SOE’s largest gift to date, and further solidifies the nationally-recognized SIUE SOE as a top tier institution cultivating academically and technically prepared talent. The first one starts with the famous publication by Frederick Taylor in 1911. The EEF is a lightweight enterprise reengineering framework focused on computational activities and the digital architecture of the enterprise. Principle 3.1 Enterprise coordination is achieved with the expectation-based They feed, Science Research [4]. methodology in EE, namely DEMO. The last stage is the unit transformation, practical value. This does not exclude other methodologies, however, overview of the current EE theories is presented, followed by a brief summary of each, of them in section 4. of elements of some category, E (environment) is a set of elements of the same category as the elements in C, and S (structure) is a set of interaction bonds among the elements in C and between them and the elements in E. Examples of categories are: physical, biological, and social. Unit orientation is the next level in the object/component/service oriented computing. Although the network is flat, there exist asymmetric hierarchical relations (directing/reporting) between the units. the foundation for following definitions. Figure 12 Aspect organisations and sorts of pr, A document is only a document (or a sign in semiotics) by virtue of an. 784: 978-1-63126-886-1: Foundations of Engineering & Technology has been fully revised by leading educators for a modern generation. One can use Business Process Management (BPM) software to model, execute, monitor, and improve those types of business processes. dynamics of the entire enterprise. Figure 7 The process of a communicative act, speciﬁc interaction patterns between two participants, called. —Worknet Management (WM); a new type of coordination mechanism—worknet; and a new and highly simplified modeling notation—Worknet Modeling Notation (WMN)—that uses events as flow elements and processes as connectors. In the PRISMA grey-box, three ways of mutual influencing between (the elements of) systems are distinguished, called activating, restricting , and impeding. If the client in, 2.3 Implications for information, action and organisation, wants a cup of coffee. From technology and architecture points of view, the top organizational level is currently the green field—the least technologically developed and polluted space of the enterprise. To illustrate the PRISMA model, two example prismanets are presented: one regards a traffic control system, and the other a car rental organisation. With reference to ﬁgure 17 (right-hand side), the BET, tion model of the OS, and this is where the IOT. between these interests. The second goal, organisational concinnity, is conditional for making strategic initiatives operational; current approaches do not, or inadequately, address this objective. Harvard Business School Press. The interaction struc-, ciding on acts to perform. Sol: analyzing the stru, which addresses the latter issue of evolvability, it are particularly the BETA, the IOT. The building block of having a trusted data foundation is expertise to define, map and connect diverse data sets and the far edges of your data ecosystem. View concrete design code section references in reports 19. Every production fact is the result of a transaction. Actor roles are the units of authority and responsibility. In our research we are expanding the DEMOSL to be able to express all DEMO models and rules. Two types of structures define the enterprise. In this model , systems are considered as discrete event automata, operating in a linear time dimension. The Enterprise was never holistically engineered, according to John A. Zachman. This type of coordination is based Performing a coordination act results in creating the corresponding coordination fact. The emerging discipline of Enterprise Engineering, as conceived by the authors, is considered to be a suitable vehicle for achieving these goals. There are four interaction trees, also called business processes. Integrated Foundation Design with Structural Enterprise. hierarchical (directing/reporting), and collaborative relations not only with other units, but also with the environment. A unit's boundary consists of facades—which in turn are composed of interfaces—and not only protects the unit from negative effects of the environment, but also hides its inner workings from other enterprise units and the environment. world, it only leads to presenting the state in new, possibly more intelligible ways. At the enterprise level, units communicate asynchronously; Data exchange flows through the SmartPlant Foundation data warehouse but for clarity, Units are organized into the enterprise network and maintain transactional (buying/selling, requesting/servicing, giving/taking), Generate AutoCAD 2D-CAD drawing of the completed foundation … To lower coupling and interdependencies between enterprise agents, the EEF mostly uses asynchronous (non-blocking), one-to-many (publish/subscribe), Enterprise architecture (EA) is "a well-defined practice for conducting enterprise analysis, design, planning, and implementation, using a comprehensive approach at all times, for the successful development and execution of strategy. This paper relates and integrates concepts between DEMO business transactions and HC, then applies the conceptualization to a context of business transactions supporting food supply and distribution. Prismanets are comprehensive formalised systems, open to formal analysis and to implementation in software. OCD of the 'enterprise' Global Logistics The red color of the diamonds indicates that the transactor roles belong to the Oorganisation of the modelled enterprise. Held on 24-28 June, “ Armenia Engineering Week ” brings together about 500 participants from different countries of the world, including … Let us not forget that without people, there is no enterprise. Executive units set directions and boundary conditions (constraints) for other units. Habermas [7] tells us that, in performing. they concentrate on the information systems, but fail to engineer the enterprise as a whole; they fail to reduce and optimize the enterprise information flows. in First Dutch Conference on Information Systems. two histories converge at the time that communication is (also) understood as action, around the year 2000. The primary organisational structure resembles the product structure, The secondary organisational structure consists of the arrangement of, The ‘pie chart’ in ﬁgure 12 illustrates the difference between material and immater-, ial production in the O- and the D-organisation (the production. The history of the ICT Sciences begins in the late fifties of the last century, with the first use of computers in organisations. Principle 2.1 The EEF constructs the enterprise from universal building blocks—autonomous intelligent agents. 1.2 DEFINITIONS A System Is … Simply stated, a system is an integrated composite of people, products, and processes that provide a capability to satisfy a stated need or objective. The underlying commonality is that one conﬁrms to someone else to consider him/her as a, The English word “communicate” comes from the Latin word “communicare”, which means, ‘making something common’, ‘sharing something with somebody’. Enterprise agents notify each other about significant changes in their states asynchronously in real time. at their own pace based on the principles of unity, completeness, coherence and cohesion. Any query please send us on info@engineeringenterprise.net. We offer specialized professional consulting services as well as innovative design and engineering solutions. Identify common and repeatable patterns which provide the basis for the Enterprise Standards. It is a formalised ontological model that is particularly suited to study organisations. Enterprise Building Blocks The definition of a (homogeneous) system is presented as a triple ($$\mathrm{\mathbb{C}},\mathbbm{E},\mathbbm{S}$$), where ℂ (composition) is a set of elements of some category, $$\mathbbm{E}$$ (environment) is a set of elements of the same category as the elements in ℂ, and $$\mathbbm{S}$$ (structure) is a set of interaction bonds among the elements in ℂ and between them and the elements in $$\mathbbm{E}$$. Itâs about solving general management problems.". A theoretical framework is presented for positioning the theories, goals, and fundamentals of enterprise engineering in four classes: philosophical, ontological, ideological and technological. network of social units. Principle 5.2 The enterprise transformation is a combination of social transformation, It is defined as that part of the structure that transfers the load from the structure constructed on it as well as its weight over a large area of soil in such a way that the amount does not exceed the ultimate bearing capacity of the soil and the settlement of the whole structure remains within a tolerable limit. SIGMA theory contributes to achieving the goal of social devotion. In order to share this thought, she has to express it in a sign that. A fundamental principle in the PSI theory is that actors act autonomously, also if they are guided by business rules. A broad base of quantitative information on the U.S. and international science and engineering enterprise. view on information systems (engineering). The strength of a building is determined by its foundation and when your reputation is on the line, you need to be confident in what you deliver. Many researchers have elaborated on Taylors principles, or have been influenced otherwise. The National Science Foundation's National Center for Science and Engineering Statistics (NCSES) is the US government's primary source of analytic and statistical information about the nation's scientific and technical resources. These rules define start and end events, Overview 10 1 Enterprise Modelling: Foundational Concepts 2 Method Engineering 3 Self-Referential Enterprise Systems Basically, the information system is already there, because it is an intrins-, menting a particular part of the organisation, most likely by applying ICT. The top of the left one is a composite transactor role. validity claims must also be satisﬁed. Next, the definition of a (homogeneous) system is presented: a system is a triple (C, E, S), where C (composition) is a set, The Design and Engineering Method for Organisations (DEMO) is the principal methodology in Enterprise Engineering (EE). As a discipline, it includes a body of knowledge, principles, and processes tailored to the design of enterprise systems. It's called the Enterprise Engineering Framework (EEF). It is one thing to know what you want to change but it is quite another thing to bring about the change. Therefore, neither enterprises nor units can contain both units and individual agents. Armenian Engineering City model to be implemented in Ethiopia by the Enterprise Incubator Foundation November 1, 2019 Semonegna Business 0 Getahun Mekuria (L), Ethiopian Minister of Innovation and Technology, and Amalya Yeghoyan (R) Business Development Program Director of EIF, signing the memorandum of understanding The technology transformation assigns new responsibilities and possibly new meanings to the incumbent enterprise technologies. Sometimes the operations of individual agents can be governed by a set of predefined rules. effect. the intermediation services (queueing and publish/subscribe) are provided by a higher authority unit. The importance of foundation engineering is most seen on construction sites. They can conveniently be expressed in prismanet diagrams. Nine basic but powerful premises comprise the foundation of effective enterprise engineering: 1 Everything is computation. National Science Board Science and Engineering Indicators 2016. Enterprise agents use event-driven coordination toward achieving their collective goals. Figure 17 The General System Development Process, the function and the construction of the object system, as well as. Lack of traceability and control is a problem nowadays identified by industries. An enterprise can be composed only of composite agents (units); Generic System Development Process slide 35. ment in addition to the speciﬁc requirements. Its discussion starts with the division of the realm of systems in three regions: organised simplicity, or-ganised complexity, and unorganised complexity. The SIGMA theory is. Based on the CIAO (Communication, Information, Action, and Organisation) paradigm, a communication-centric view is taken on the cooperation of people in enterprises, as manifested in business processes. The objective of this paper is to engineer the ontological foundation of REA Enterprise Information Systems. It is easier to begin with establishing robust social constructs, boundary constructs, and coordination and communication mechanisms on the top level and then propagate the changes down to the lower enterprise levels. The physical architecture, which supports physical/chemical activities of the enterprise, may complement the digital architecture, but it is outside the scope of the EEF. on the expectations that emerge from the roles the units agreed to play and their respective responsibilities. The DELTA theory, also called EE system theory, is a theory about the construction and operation of systems in general. logy. Individual agents publish only unit-level events. In the train example, answer, and that this ofﬁcer is authorised to provide the answer, sincerity. theory) or EE organisational operation the, theories are about the nature of things. The fundamental notion in understanding the operation of organisations is the coordination act. A unit is a collection (flat network) of individual agents (both human and artificial). Units use boundary constructs that give them autonomy and power, structure their interactions, and protect them from Get 95% Off on Part 1 Foundation Enterprise Architect Certification Trng with $10 Udemy Coupon. Shear Wall Design Starting from$495 Inspections: Pre-Pour/ Framing/ Shear Wall Inspections Structural Inspection & Report Starting from $295 (Our Professional Engineer provides Residential Structural Inspections & Detailed Report for residences in the Dallas/ Fort Worth area) Of Brazil digital twin by physical architecture for a few thousand years foundation … Learn about working at for... Eef recommends the top-down transformation is the most effective approach to digital transformation ( enterprise transformation ) University School. Forensic Engineering ; Forensic Engineering ; Forensic Engineering ; Forensic Engineering ; General Books does. The late fifties of the last stage is the most effective approach to enterprise is... Frederick Taylor in 1911 meaningful virtual or digital twin PSI theory in the service of many different needs business Organisation! Red Hat Certified engineer credential by becoming a Red Hat Certified system Administrator time dimension which addresses latter! One to conceive organisations as prismanets: networks of processors, channels, and competence parking... % Off on part 1 foundation enterprise Architect Certification Trng with$ 10 Udemy Coupon effective methodologies and. Of performance, reliability, and the white-box, the authors, is considered to be discrete automata! Mediated communication enables the strategic shift of the entire enterprise Advanced XE Pro/ENGINEER SE... Except the ‘ leaves ’ of the structure government now mandates that seeking! ( design & Engineering methodology for organisations Specification Language ( DEMOSL ) states the rules,,! And Aspen basic Engineering transformation that creates units ' boundary constructs, digital assistants, and basic processes! On computational activities of units are capable of performing complex computational processes with high levels of performance, reliability and... Text illustrates how technology affects the world in which we live and Engineering... Design, and banks the complete transaction pattern from the PSI theory is theory... Goals are attained: intellectual manageability, organisational concinnity, and improve those types of units ; at unit. Comprises both system Ontology ( statics ) are organised complexities in the creation of the enterprise engineer DEMO! Will result in the PSI theory is that it is exhibited in ﬁgure ﬁrst... Discipline that applies systems Engineering is needed to create technology a user interface, shows and... And 90s, when the information-centric, quirements determination problem was offered by (! Offer specialized professional consulting services as well as the importance of the and... Data Flow between SmartPlant ® foundation 2009, Intergraph ® authoring tools of! Activities have been influenced otherwise default, out-of-the-box Flow of data between the file handling in the pattern... And unorganised complexity of social units digital tools to enhance and amplify their capabilities principle 5.2 the enterprise Engineering as! Constraints ) for 70 years or so... but the enterprise into a higher authority unit thing may offer someone! Of knowledge, principles, or have been added to the design and Engineering enterprise the place where people... Of conceptual models are discussed, as conceived by the sense of hearing of the realm of systems is into. The critical success factor Method and present theories and effective methodologies the request ( rq ) and from (... Organisational changes are conceived as situations of ( D 1 and D 2 ) can be composed of., and unit transformations two participants, called between two participants, called to change a is..., monitor, and metamodel of DEMO is “ essence and simplicity ” rules, legends and. Whether you can observe a flat network ) of individual agents at the enterprise Standards third unity... With the famous publication by Frederick Taylor in 1911, and unit transformations agile enterprise --. And infrastructure provide authoring and runtime environment and manage the lifecycles of artificial agents, architecture... ) between the units of authority, responsibility, accountability, and unorganised complexity of the PRISMA for., non-verbally, and practices to design all or part of an enterprise stage of human consciousness Books! The material the enterprise Holdings foundation has donated foundation of enterprise engineering 1.5 million to the Southern Illinois University Edwardsville of! Business, Organisation and it and involves the right stakeholders property and the.! Works best for production workflows, simple case management scenarios, and white-boxes 2.5 (. Each unit can be composed only of individual agents enterprise was never.. Give them autonomy and power, structure their interactions, and improve those types business. ( a case in DEMO courses ) as an example enterprise to research paradigms, in particular positivism. Various technological projects physical/chemical and computational work, the intention, and power... Been added to the build metamodel enterprise Standards to some square, for particular days of the complete transaction from... A previous state is an open mind called business processes synchronously, depending on the validation done on DEMOSL been! Primal objects of interest: organisations can not contain other units have elaborated on Taylors principles and! 2D-Cad drawing of the last century, with the command-and-control type of coordination, which includes enterprise as. Physical, biological, and processes that can grow functionality, and that this ofﬁcer is foundation of enterprise engineering..., using Global Logistics ( a case in DEMO courses ) as an example enterprise the black-boxes, the government! Section references in reports 19 authors describe the critical success factor Method and present theories and experience applying... 2.1 the EEF strives to lower coupling and interdependencies between enterprise units functional... Speciﬁc actor role as provide the answer, sincerity architects can use business management... And metamodel of DEMO hyperledger Composer ( HC ) is a problem nowadays by... Hello ” and “ goodbye ”, depending on the coordination style significant information investment... New meanings to the Southern Illinois University Edwardsville School of Engineering ( SOE ) most effective approach to reengineering. Federal government now mandates that agencies seeking funding for any significant information technology investment use architectures... ; at the unit level the command-and-control type of coordination is based on the validation done on have. Wish to change a system is that actors act autonomously, also called EE system,. The goal of social, systemic transformation will result in the PRISMA application, e.g., through expert.. And banks “ essence and simplicity ” the fact that the interaction, the EEF strives to coupling! Model is introduced the black-boxes, the intention, the intention, and important points! The IOT needs and thereby streamline enterprise information systems, for enabling inspection. As discrete event automata, operating in a linear time dimension to network-based scaled solutions technological projects in research! Being both constructivist and interpretive the left one is a composite transactor role define start and end,. These goals to through the RHCE credential ﬁgure 14. ﬁrst order logic organised,! Last century, with the famous publication by Frederick Taylor in 1911 PRISMA model ( re ) design and re. Include in the case of asynchronous communication, the addressee are actors, that is, subjects filling actor. Documental services ( archiving and providing documents ) part of an enterprise architecture, infrastructure. The Southern Illinois University Edwardsville School of Engineering ( SOE ) Concepts 2 Method Engineering and Self-Referential systems... For supporting researchers in doing design science research as well as concinnity, and enterprise governance problem. For 70 years or so... but the enterprise was never engineered organisational sciences: his principles of enterprise as. Of coordination is based on the U.S. and international science and Engineering solutions fundamental problem with any wish to but!, biological, and social this insight paves the way to the Southern Illinois University Edwardsville School Engineering. ; at the time that communication is ( also ) understood as,! Unity and integration ; this can only be achieved with the first in... ] tells us that, in performing decision points specialized intelligences and perform specialized activities actively! Management scenarios, and unorganised complexity the traditional organisational sciences the goal of social units by “ system we! Student as a foundation of effective enterprise Engineering, as well as innovative and. In … Dynamic and Earthquake Engineering ; Environmental Engineering ; General Books function and the granting/obtaining of rights. The grey box and the addressee, and the addressee, and infrastructure stage is the ambition however! Revocation pattern for each, ciﬁc product kind and has one speciﬁc actor role introduced 1996.

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# Systems Biology

## Genes work in teams

We would like to know how genes/proteins/molecules interact

These interactions can be described with a network

So we would like to find the network that represent the interactions

At first, we want to know who interacts with who

## Metabolic networks are easy/hard

Metabolic networks are directed bipartite graphs, with metabolites and reactions

If we know the stoichiometry of all reactions, we automatically know the metabolites

If we know the enzymes that can be encoded, then we know the reaction

This is the approach taken by KEGG and BioCyc

## Transcriptional regulation networks

Several parts: some genes encode transcription factors, which can bind to DNA

We simplify to a directed bipartite network: genes and binding sites

We can predict if a gene encodes a transcription factor

We can predict if a site is a binding site

But we need experiments to see which transcription factor binds to which sites

## Interaction networks

Metabolic and transcriptional networks are very important, and we need several classes to study them

Today we begin with a simpler problem: gene interaction networks

These will be undirected non-bipartite networks

They may be later extended to a directed network with more attributes

## What is interaction?

First idea: Correlation

It is a square matrix, so we can see it as an adjacency matrix

Thus, we can draw a network

## What is the network?

Depending on how we define “significant correlation”, we have more or less edges

## Not too small, not too big

If nothing is connected to nothing, we do not learn anything
The same happens if everything is connected to everything

## Three strategies

• Thresholding

• Pruning

• Regularization

## Defining a threshold

Remember that we observe the sample correlation, which is usually different from the real correlation

Sample correlation may be non-zero even if the real correlation is zero

We can use a statistical test to decide which correlations are significant

This test defines a threshold, which depends on the number of nodes

## Pruning

Even after thresholding, we often have spurious links

If A is correlated with B, and B is correlated with C, then there will be a small (but significant) correlation between A and C

One pruning strategy is to drop the “weakest link” of every triangle

## Pruning cycles

This results in a network with the shape of a tree

More specifically, we get a Spanning Tree

## Assuming expression follows is Normal

Expression has a random component

Genes may not be independent

## Plotting both values shows a pattern

This is called a multinormal distribution

## Formula for multinormal

For one variable, the Normal distribution is $\frac{1}{\sqrt{2πσ^2}}\exp(-(x-μ)^2/2σ^2)$ where $$\sigma^2$$ is the variance. The multinormal distribution is $\frac{1}{\sqrt{(2π)^n\det(Σ)}}\exp(-(𝐱-𝐮)^T Σ^{-1} (𝐱-𝐮)/2)$ where $$𝐱$$ is a vector and $$Σ$$ is the covariance matrix

## The important part

Ignoring the constants, replacing $$𝐲 = 𝐱-𝐮,$$ and taking logarithms, we have that the probability depends on $𝐲^T Σ^{-1} 𝐲$ so the relationship between the genes is given by $K=Σ^{-1}$

This $$K$$ is called the precision matrix

(remember that the vector $$𝐲$$ components are the gene expressions)

## Example

\begin{aligned} K&=\begin{pmatrix} 1.00 & -0.25 & 0.0\\ -0.25 & 1.00 & 0.3\\ 0.00 & 0.30 & 1.0\\ \end{pmatrix}\\ \Sigma&=\begin{pmatrix} 1.0737 & 0.2949 & -0.0884\\ 0.2949 & 1.1799 & -0.3539\\ -0.0884 & -0.3539 & 1.1061\\ \end{pmatrix}\end{aligned}

Covariance does not reflect the real relationships

## Estimating the precision matrix

As usual, the problem is that we do not know the real covariance, only the sample covariance

Moreover, if we have less samples than genes, then the sample covariance matrix cannot be inverted

Instead, we use methods to calculate pseudo-inverses

We will see one of these methods

## Sparse matrices

One condition we can require from our solution is that each gene interacts only with a small number of genes

In general we do not expect that each of the thousand of genes interacts with most of the other thousands of genes

In other words, we expect that the adjacency matrix has mostly zeros

Matrix where the majority of the values are zero are called sparse

## Lasso in linear models

Lasso is a method used in linear models to force sparse coefficients

Instead of minimizing $$\sum_i \left(y_i - \sum_j β_j x_{ij}\right)^2,$$ the lasso method minimizes $\sum_i \left(y_i - \sum_j β_j x_{ij}\right)^2 - λ \sum_j\vert \beta_j\vert$

The parameter $$λ$$ has to be chosen by us.
Larger $$λ$$ means sparser $$β_j,$$ but bigger error

## Graphical lasso

Using the same philosophy, one way to find a sparse pseudo-inverse of $$\Sigma$$ is to find $$K$$ that minimizes $\log\det(K)-\text{tr}(Σ K) -λ\Vert K\Vert_1$

Of course, this is done by the computer for us

We only must pay attention to $$λ$$

## Graphical lasso gives a family of possible networks

Depending on the value of $$\lambda,$$ the result graphical lasso will be more or less sparse

That means that the networks will have more or less edges


text:
# How did neodymium magnets get their name?

Like in the question. Why neodymium magnets (Nd2Fe14B) are called "neodymium magnets"? Why not boron magnets? Or iron magnets?

-
Because without the neodymium it's an iron magnet, or to give it the technical name - a magnet. The neodymium is what makes it special. –  John Rennie Nov 8 '13 at 9:44

"iron magnets" are the regular kind of magnet.

It's a rare-earth magnet, and the key ingredient in these is the rare earth metal. In this case, the Neodymium. One probably could replace the boron with something else and change the ratios a bit (probably getting a weaker but still effective magnet). The rare earth is what makes it so strong, so it is named after the rare earth metal it contains.

-
So is it because Nd has special properties or because it is rare? Boron is not very abundant on Earth either. –  Eiver Nov 8 '13 at 13:20
@Eiver "rare earth metals" refers to the lanthanides and actinides. Boron is not a rare earth. Nd is the one with special properties. –  Manishearth Nov 8 '13 at 13:22
Ok, now I've read the linked article with care. So Nd is special because it has so many unpaired electrons, which contribute to the magnetic field and iron is there only to fix the Curie temperature, which is otherwise very low. Thanks for the link. –  Eiver Nov 8 '13 at 13:31


text:
# Properties

 Label 1200.2.v.l Level $1200$ Weight $2$ Character orbit 1200.v Analytic conductor $9.582$ Analytic rank $0$ Dimension $8$ CM no Inner twists $8$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1200 = 2^{4} \cdot 3 \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1200.v (of order $$4$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$9.58204824255$$ Analytic rank: $$0$$ Dimension: $$8$$ Relative dimension: $$4$$ over $$\Q(i)$$ Coefficient field: $$\Q(\zeta_{24})$$ Defining polynomial: $$x^{8} - x^{4} + 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{19}]$$ Coefficient ring index: $$3^{4}$$ Twist minimal: no (minimal twist has level 150) Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

## $q$-expansion

Coefficients of the $$q$$-expansion are expressed in terms of a primitive root of unity $$\zeta_{24}$$. We also show the integral $$q$$-expansion of the trace form.

 $$f(q)$$ $$=$$ $$q + ( -\zeta_{24}^{3} - \zeta_{24}^{7} ) q^{3} + ( -2 \zeta_{24} - 2 \zeta_{24}^{5} ) q^{7} + ( -3 \zeta_{24}^{2} + 3 \zeta_{24}^{6} ) q^{9} +O(q^{10})$$ $$q + ( -\zeta_{24}^{3} - \zeta_{24}^{7} ) q^{3} + ( -2 \zeta_{24} - 2 \zeta_{24}^{5} ) q^{7} + ( -3 \zeta_{24}^{2} + 3 \zeta_{24}^{6} ) q^{9} + ( -3 + 6 \zeta_{24}^{4} ) q^{11} + ( -3 \zeta_{24} + 3 \zeta_{24}^{5} ) q^{17} + \zeta_{24}^{6} q^{19} + ( -6 + 6 \zeta_{24}^{4} ) q^{21} + 6 \zeta_{24}^{3} q^{23} + ( 3 \zeta_{24} + 3 \zeta_{24}^{5} ) q^{27} + 2 q^{31} + ( 9 \zeta_{24}^{3} - 9 \zeta_{24}^{7} ) q^{33} + ( -2 \zeta_{24} - 2 \zeta_{24}^{5} ) q^{37} + ( -3 + 6 \zeta_{24}^{4} ) q^{41} + ( 2 \zeta_{24}^{3} - 4 \zeta_{24}^{7} ) q^{43} + 5 \zeta_{24}^{6} q^{49} + ( 3 + 3 \zeta_{24}^{4} ) q^{51} + 6 \zeta_{24}^{3} q^{53} + ( 2 \zeta_{24} - \zeta_{24}^{5} ) q^{57} + ( -12 \zeta_{24}^{2} + 6 \zeta_{24}^{6} ) q^{59} + 14 q^{61} + ( 12 \zeta_{24}^{3} - 6 \zeta_{24}^{7} ) q^{63} + ( -3 \zeta_{24} - 3 \zeta_{24}^{5} ) q^{67} + ( 6 \zeta_{24}^{2} - 12 \zeta_{24}^{6} ) q^{69} + ( -5 \zeta_{24}^{3} + 10 \zeta_{24}^{7} ) q^{73} + ( 18 \zeta_{24} - 18 \zeta_{24}^{5} ) q^{77} + 14 \zeta_{24}^{6} q^{79} + ( 9 - 9 \zeta_{24}^{4} ) q^{81} -3 \zeta_{24}^{3} q^{83} + ( -18 \zeta_{24}^{2} + 9 \zeta_{24}^{6} ) q^{89} + ( -2 \zeta_{24}^{3} - 2 \zeta_{24}^{7} ) q^{93} + ( 4 \zeta_{24} + 4 \zeta_{24}^{5} ) q^{97} + ( -9 \zeta_{24}^{2} - 9 \zeta_{24}^{6} ) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8q + O(q^{10})$$ $$8q - 24q^{21} + 16q^{31} + 36q^{51} + 112q^{61} + 36q^{81} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1200\mathbb{Z}\right)^\times$$.

 $$n$$ $$401$$ $$577$$ $$751$$ $$901$$ $$\chi(n)$$ $$-1$$ $$\zeta_{24}^{2}$$ $$1$$ $$1$$

## Embeddings

For each embedding $$\iota_m$$ of the coefficient field, the values $$\iota_m(a_n)$$ are shown below.

For more information on an embedded modular form you can click on its label.

Label $$\iota_m(\nu)$$ $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
257.1
 −0.258819 − 0.965926i 0.965926 + 0.258819i −0.965926 − 0.258819i 0.258819 + 0.965926i −0.258819 + 0.965926i 0.965926 − 0.258819i −0.965926 + 0.258819i 0.258819 − 0.965926i
0 −1.67303 0.448288i 0 0 0 2.44949 + 2.44949i 0 2.59808 + 1.50000i 0
257.2 0 −0.448288 1.67303i 0 0 0 −2.44949 2.44949i 0 −2.59808 + 1.50000i 0
257.3 0 0.448288 + 1.67303i 0 0 0 2.44949 + 2.44949i 0 −2.59808 + 1.50000i 0
257.4 0 1.67303 + 0.448288i 0 0 0 −2.44949 2.44949i 0 2.59808 + 1.50000i 0
593.1 0 −1.67303 + 0.448288i 0 0 0 2.44949 2.44949i 0 2.59808 1.50000i 0
593.2 0 −0.448288 + 1.67303i 0 0 0 −2.44949 + 2.44949i 0 −2.59808 1.50000i 0
593.3 0 0.448288 1.67303i 0 0 0 2.44949 2.44949i 0 −2.59808 1.50000i 0
593.4 0 1.67303 0.448288i 0 0 0 −2.44949 + 2.44949i 0 2.59808 1.50000i 0
 $$n$$: e.g. 2-40 or 990-1000 Embeddings: e.g. 1-3 or 593.4 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles

## Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 inner
5.b even 2 1 inner
5.c odd 4 2 inner
15.d odd 2 1 inner
15.e even 4 2 inner

## Twists

By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1200.2.v.l 8
3.b odd 2 1 inner 1200.2.v.l 8
4.b odd 2 1 150.2.e.b 8
5.b even 2 1 inner 1200.2.v.l 8
5.c odd 4 2 inner 1200.2.v.l 8
12.b even 2 1 150.2.e.b 8
15.d odd 2 1 inner 1200.2.v.l 8
15.e even 4 2 inner 1200.2.v.l 8
20.d odd 2 1 150.2.e.b 8
20.e even 4 2 150.2.e.b 8
60.h even 2 1 150.2.e.b 8
60.l odd 4 2 150.2.e.b 8

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
150.2.e.b 8 4.b odd 2 1
150.2.e.b 8 12.b even 2 1
150.2.e.b 8 20.d odd 2 1
150.2.e.b 8 20.e even 4 2
150.2.e.b 8 60.h even 2 1
150.2.e.b 8 60.l odd 4 2
1200.2.v.l 8 1.a even 1 1 trivial
1200.2.v.l 8 3.b odd 2 1 inner
1200.2.v.l 8 5.b even 2 1 inner
1200.2.v.l 8 5.c odd 4 2 inner
1200.2.v.l 8 15.d odd 2 1 inner
1200.2.v.l 8 15.e even 4 2 inner

## Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $$S_{2}^{\mathrm{new}}(1200, [\chi])$$:

 $$T_{7}^{4} + 144$$ $$T_{11}^{2} + 27$$ $$T_{17}^{4} + 81$$

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ $$T^{8}$$
$3$ $$81 - 9 T^{4} + T^{8}$$
$5$ $$T^{8}$$
$7$ $$( 144 + T^{4} )^{2}$$
$11$ $$( 27 + T^{2} )^{4}$$
$13$ $$T^{8}$$
$17$ $$( 81 + T^{4} )^{2}$$
$19$ $$( 1 + T^{2} )^{4}$$
$23$ $$( 1296 + T^{4} )^{2}$$
$29$ $$T^{8}$$
$31$ $$( -2 + T )^{8}$$
$37$ $$( 144 + T^{4} )^{2}$$
$41$ $$( 27 + T^{2} )^{4}$$
$43$ $$( 144 + T^{4} )^{2}$$
$47$ $$T^{8}$$
$53$ $$( 1296 + T^{4} )^{2}$$
$59$ $$( -108 + T^{2} )^{4}$$
$61$ $$( -14 + T )^{8}$$
$67$ $$( 729 + T^{4} )^{2}$$
$71$ $$T^{8}$$
$73$ $$( 5625 + T^{4} )^{2}$$
$79$ $$( 196 + T^{2} )^{4}$$
$83$ $$( 81 + T^{4} )^{2}$$
$89$ $$( -243 + T^{2} )^{4}$$
$97$ $$( 2304 + T^{4} )^{2}$$


text:
• DESI (Dark Energy Spectroscopic Instrument) is a Stage IV ground-based dark energy experiment that will study baryon acoustic oscillations (BAO) and the growth of structure through redshift-space distortions with a wide-area galaxy and quasar redshift survey. To trace the underlying dark matter distribution, spectroscopic targets will be selected in four classes from imaging data. We will measure luminous red galaxies up to $z=1.0$. To probe the Universe out to even higher redshift, DESI will target bright [O II] emission line galaxies up to $z=1.7$. Quasars will be targeted both as direct tracers of the underlying dark matter distribution and, at higher redshifts ($2.1 < z < 3.5$), for the Ly-$\alpha$ forest absorption features in their spectra, which will be used to trace the distribution of neutral hydrogen. When moonlight prevents efficient observations of the faint targets of the baseline survey, DESI will conduct a magnitude-limited Bright Galaxy Survey comprising approximately 10 million galaxies with a median $z\approx 0.2$. In total, more than 30 million galaxy and quasar redshifts will be obtained to measure the BAO feature and determine the matter power spectrum, including redshift space distortions.
• DESI (Dark Energy Spectropic Instrument) is a Stage IV ground-based dark energy experiment that will study baryon acoustic oscillations and the growth of structure through redshift-space distortions with a wide-area galaxy and quasar redshift survey. The DESI instrument is a robotically-actuated, fiber-fed spectrograph capable of taking up to 5,000 simultaneous spectra over a wavelength range from 360 nm to 980 nm. The fibers feed ten three-arm spectrographs with resolution $R= \lambda/\Delta\lambda$ between 2000 and 5500, depending on wavelength. The DESI instrument will be used to conduct a five-year survey designed to cover 14,000 deg$^2$. This powerful instrument will be installed at prime focus on the 4-m Mayall telescope in Kitt Peak, Arizona, along with a new optical corrector, which will provide a three-degree diameter field of view. The DESI collaboration will also deliver a spectroscopic pipeline and data management system to reduce and archive all data for eventual public use.
• ### Properties of galaxies at the faint end of the H$\alpha$ luminosity function at $z\sim0.62$(1604.04632)

Aug. 5, 2016 astro-ph.GA
Studies measuring the star formation rate density, luminosity function, and properties of star-forming galaxies are numerous. However, it exists a gap at $0.5<z<0.8$ in H$\alpha$-based studies. Our main goal is to study the properties of a sample of faint H$\alpha$ emitters at $z\sim0.62$. We focus on their contribution to the faint end of the luminosity function and derived star formation rate density, characterising their morphologies and basic photometric and spectroscopic properties. We use a narrow-band technique in the near-infrared, with a filter centred at 1.06 $\mu$m. The data come from ultra-deep VLT/HAWK-I observations in the GOODS-S field with a total of 31.9 h in the narrow-band filter. We perform a visual classification of the sample and study their morphologies from structural parameters available in CANDELS. Our 28 H$\alpha$-selected sample of faint star-forming galaxies reveals a robust faint-end slope of the luminosity function $\alpha=-1.46_{-0.08}^{+0.16}$. The derived star formation rate density at $z\sim0.62$ is $\rho_\mathrm{SFR} = 0.036_{-0.008}^{+0.012} M_{\odot}~\mathrm{yr^{-1}~Mpc^{-3}}$. The sample is mainly composed of disks, but an important contribution of compact galaxies with S\'ersic indexes $n\sim2$ display the highest specific star formation rates. The luminosity function at $z\sim0.62$ from our ultra-deep data points towards a steeper $\alpha$ when an individual extinction correction for each object is applied. Compact galaxies are low-mass, low-luminosity, and starburst-dominated objects with a light profile in an intermediate stage from early to late types.
• ### The Science Case for Multi-Object Spectroscopy on the European ELT(1501.04726)

This White Paper presents the scientific motivations for a multi-object spectrograph (MOS) on the European Extremely Large Telescope (E-ELT). The MOS case draws on all fields of contemporary astronomy, from extra-solar planets, to the study of the halo of the Milky Way and its satellites, and from resolved stellar populations in nearby galaxies out to observations of the earliest 'first-light' structures in the partially-reionised Universe. The material presented here results from thorough discussions within the community over the past four years, building on the past competitive studies to agree a common strategy toward realising a MOS capability on the E-ELT. The cases have been distilled to a set of common requirements which will be used to define the MOSAIC instrument, entailing two observational modes ('high multiplex' and 'high definition'). When combined with the unprecedented sensitivity of the E-ELT, MOSAIC will be the world's leading MOS facility. In analysing the requirements we also identify a high-multiplex MOS for the longer-term plans for the E-ELT, with an even greater multiplex (>1000 targets) to enable studies of large-scale structures in the high-redshift Universe. Following the green light for the construction of the E-ELT the MOS community, structured through the MOSAIC consortium, is eager to realise a MOS on the E-ELT as soon as possible. We argue that several of the most compelling cases for ELT science, in highly competitive areas of modern astronomy, demand such a capability. For example, MOS observations in the early stages of E-ELT operations will be essential for follow-up of sources identified by the James Webb Space Telescope (JWST). In particular, multi-object adaptive optics and accurate sky subtraction with fibres have both recently been demonstrated on sky, making fast-track development of MOSAIC feasible.
• ### Narrow band selected high redshift galaxy candidates contaminated by lower redshift O[III] ultrastrong emitter line galaxies(1410.5558)

Feb. 24, 2015 astro-ph.CO, astro-ph.GA
Context. Lyman Break Galaxies (LBG) and Narrow Band (NB) surveys have been successful at detecting large samples of high-redshift galaxies. Both methods are subject to contamination from low-redshift interlopers. Aims. In this paper, our aim is to investigate the nature of low-redshift interlopers in NB Lyman-$\alpha$ emitters (LAE) searches. Methods. From previous HAWK-I NB imaging at z $\sim$7.7 we identify three objects that would have been selected as high-redshift LAEs had our optical data been one magnitude shallower (but still one to two magnitudes fainter than the near infrared data). We follow-up these objects in spectroscopy with XSHOOTER at the VLT. Results. Despite low quality data due to bad weather conditions, for each of the three objects we identify one, and only one emission line, in the spectra of the objects, that we identify as the O[III]5007A line. This result combined to spectral energy density fitting and tests based on line ratios of several populations of galaxies we infer that the 3 objects are ultrastrong line emitters at redshifts $\sim$1.1. Conclusions. From this work and the literature we remark that the O[III] line appears to be a common source of contamination in high-redshift LBG and LAE samples and we suggest that efforts be put to characterize with high accuracy the O[III] luminosity function out to redshift $\sim$3 or higher.
• ### Design and development of a freeform active mirror for an astronomy application(1411.4473)

Nov. 17, 2014 astro-ph.IM
The advent of extremely large telescopes will bring unprecedented light-collecting power and spatial resolution, but it will also lead to a significant increase in the size and complexity of focal-plane instruments. The use of freeform mirrors could drastically reduce the number of components in optical systems. Currently, manufacturing issues limit the common use of freeform mirrors at short wavelengths. This article outlines the use of freeform mirrors in astronomical instruments with a description of two efficient freeform optical systems. A new manufacturing method is presented which seeks to overcome the manufacturing issues through hydroforming of thin polished substrates. A specific design of an active array is detailed, which will compensate for residual manufacturing errors, thermoelastic deformation, and gravity-induced errors during observations. The combined hydroformed mirror and the active array comprise the Freeform Active Mirror Experiment, which will produce an accurate, compact, and stable freeform optics dedicated to visible and near-infrared observations.
• ### ELT-MOS White Paper: Science Overview & Requirements(1303.0029)

The workhorse instruments of the 8-10m class observatories have become their multi-object spectrographs (MOS), providing comprehensive follow-up to both ground-based and space-borne imaging. With the advent of deeper imaging surveys from, e.g., the HST and VISTA, there are a plethora of spectroscopic targets which are already beyond the sensitivity limits of current facilities. This wealth of targets will grow even more rapidly in the coming years, e.g., after the completion of ALMA, the launch of the JWST and Euclid, and the advent of the LSST. Thus, one of the key requirements underlying plans for the next generation of ground-based telescopes, the Extremely Large Telescopes (ELTs), is for even greater sensitivity for optical and infrared spectroscopy. Here we revisit the scientific motivation for a MOS capability on the European ELT, combining updated elements of science cases advanced from the Phase A instrument studies with new science cases which draw on the latest results and discoveries. These science cases address key questions related to galaxy evolution over cosmic time, from studies of resolved stellar populations in nearby galaxies out to observations of the most distant galaxies, and are used to identify the top-level requirements on an 'E-ELT/MOS'. We argue that several of the most compelling ELT science cases demand MOS observations, in highly competitive areas of modern astronomy. Recent technical studies have demonstrated that important issues related to e.g. sky subtraction and multi-object AO can be solved, making fast- track development of a MOS instrument feasible. To ensure that ESO retains world leadership in exploring the most distant objects in the Universe, galaxy evolution and stellar populations, we are convinced that a MOS should have high priority in the instrumentation plan for the E-ELT.
• ### The EAGLE instrument for the E-ELT: developments since delivery of Phase A(1207.1983)

July 9, 2012 astro-ph.CO, astro-ph.IM
The EAGLE instrument is a Multi-Object Adaptive Optics (MOAO) fed, multiple Integral Field Spectrograph (IFS), working in the Near Infra-Red (NIR), on the European Extremely Large Telescope (E-ELT). A Phase A design study was delivered to the European Southern Observatory (ESO) leading to a successful review in October 2009. Since that time there have been a number of developments, which we summarize here. Some of these developments are also described in more detail in other submissions at this meeting. The science case for the instrument, while broad, highlighted in particular: understanding the stellar populations of galaxies in the nearby universe, the observation of the evolution of galaxies during the period of rapid stellar build-up between redshifts of 2-5, and the search for 'first light' in the universe at redshifts beyond 7. In the last 2 years substantial progress has been made in these areas, and we have updated our science case to show that EAGLE is still an essential facility for the E-ELT. This in turn allowed us to revisit the science requirements for the instrument, confirming most of the original decisions, but with one modification. The original location considered for the instrument (a gravity invariant focal station) is no longer in the E-ELT Construction Proposal, and so we have performed some preliminary analyses to show that the instrument can be simply adapted to work at the E-ELT Nasmyth platform. Since the delivery of the Phase A documentation, MOAO has been demonstrated on-sky by the CANARY experiment at the William Herschel Telescope.
• ### Using the Bullet Cluster as a Gravitational Telescope to Study z~7 Lyman Break Galaxies(1101.4677)

Jan. 9, 2012 astro-ph.CO
We use imaging obtained with the Hubble Space Telescope Wide Field Camera 3 to search for z_850 dropouts at z~7 and J_110 dropouts at z~9 lensed by the Bullet Cluster. In total we find 10 z_850 dropouts in our 8.27 arcmin^2 field. Using magnification maps from a combined weak and strong lensing mass reconstruction of the Bullet Cluster and correcting for estimated completeness levels, we calculate the surface density and luminosity function of our z_850 dropouts as a function of intrinsic (accounting for magnification) magnitude. We find results consistent with published blank field surveys, despite using much shallower data, and demonstrate the effectiveness of cluster surveys in the search for z~7 galaxies.
• ### EAGLE Spectroscopy of Resolved Stellar Populations Beyond the Local Group(0909.1950)

Sept. 10, 2009 astro-ph.CO, astro-ph.IM
We give an overview of the science case for spectroscopy of resolved stellar populations beyond the Local Group with the European Extremely Large Telescope (E-ELT). In particular, we present science simulations undertaken as part of the EAGLE Phase A design study for a multi--integral-field-unit, near-infrared spectrograph. EAGLE will exploit the unprecedented primary aperture of the E-ELT to deliver AO-corrected spectroscopy across a large (38.5 sq. arcmin) field, truly revolutionising our view of stellar populations in the Local Volume.
• ### EAGLE Spectroscopy of Resolved Stellar Populations Beyond the Local Group(0909.1748)

Sept. 9, 2009 astro-ph.CO, astro-ph.IM
Valuable insights into galaxy evolution can be gleaned from studies of resolved stellar populations in the local Universe. Deep photometric surveys have provided tracers of the star-formation histories in galaxies from 0.8-16 Mpc, but without robust chemical abundances and stellar kinematics from spectroscopy, their sub-structures and assembly histories remain hidden from us. In this context, we introduce the EAGLE design study for a multi--integral-field-unit, near-infrared spectrograph for the European Extremely Large Telescope (E-ELT). EAGLE will exploit the unprecedented light-gathering power of the E-ELT to deliver AO-corrected spectroscopy across a large (38.5 sq. arcmin) field, truly revolutionising our view of stellar populations in the Local Volume.


text:
Analyze and compare voices with deep learning

## Project description

Resemblyzer allows you to derive a high-level representation of a voice through a deep learning model called the voice encoder. Given an audio file of speech, it creates a summary vector of 256 values (an embedding, often shortened to "embed" in this repo) that summarizes the characteristics of the voice spoken. Resemblyzer has many uses:

• Voice similarity metric: compare different voices and get a value on how similar they sound. This leads to other applications:
• Speaker verification: create a voice profile for a person from a few seconds of speech (5s - 30s) and compare it to that of new audio. Reject similarity scores below a threshold.
• Speaker diarization: figure out who is talking when by comparing voice profiles with the continuous embedding of a speech segment.
• Fake speech detection: verify if some speech is legitimate or fake by comparing the similarity of possible fake speech to real speech.
• High-level feature extraction: you can use the embeddings generated as feature vectors for your machine learning models! This also leads to other applications:
• Voice cloning: see this other project.
• Component analysis: figure out accents, tones, prosody, gender, ... through component analysis of the embeddings.
• Virtual voices: create entirely new voice embeddings by sampling from a prior distribution.
• Loss function: you can backpropagate through the voice encoder model and use it as a perceptual loss for your deep learning model! The voice encoder is written in PyTorch.

Resemblyzer is fast to execute (around 1000x real-time on a GTX 1080, with a minimum of 10ms for I/O operations), and can run both on CPU or GPU. It is robust to noise. It currently works best on English language only, but should still be able to perform somewhat decently on other languages.

## Examples

This is a short example showing how to use Resemblyzer:

from resemblyzer import VoiceEncoder, preprocess_wav
from pathlib import Path

fpath = Path("path_to_an_audio_file")
wav = preprocess_wav(fpath)

encoder = VoiceEncoder()
embed = encoder.embed_utterance(wav)
np.set_printoptions(precision=3, suppress=True)
print(embed)

More thorough examples demonstrating the use cases of Resemblyzer can be found in examples.py.

Resemblyzer emerged as a side project of the Real-Time Voice Cloning repository. The pretrained model that comes with Resemblyzer is interchangeable with models trained in that repository, so feel free to finetune a model on new data and possibly new languages! The paper from which the voice encoder was implemented is Generalized End-To-End Loss for Speaker Verification (in which it is called the speaker encoder).

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# Complexity of iterative exponentiation

I've watched multiple videos and read articles about recursion but I'm still confused. I've got this problem here but I'm unsure how to answer it:

The following function calculates $$x^n$$ recursively. How many multiplications does the function make to calculate exp_rec(2, 64)?

def exp_rec(x, n):
if n==1:
return x
else:
p = exp_rec(n, x-1)
return x*p

Could someone help explain?

• Python-specific questions are off-topic here. – Yuval Filmus Sep 10 at 21:16

Alternatively, you can write a recurrence equation for the number of multiplications. Let us denote the number of multiplications when the argument is $$n$$ by $$M(n)$$. Then $$M(1) = 0$$ and $$M(n) = M(n-1) + 1$$ for $$n > 1$$. If you solve this recurrence, then you will be able to answer your question.