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# Mutual fund separation theorem - Wikipedia, the free encyclopedia

In portfolio theory, a mutual fund separation theorem, mutual fund theorem, or separation theorem is a theorem stating that, under certain conditions, any investor's optimal portfolio can be constructed by holding each of certain mutual funds in appropriate ratios, where the number of mutual funds is smaller than the number of individual assets in the portfolio. Here a mutual fund refers to any specified benchmark portfolio of the available assets. There are two advantages of having a mutual fund theorem. First, if the relevant conditions are met, it may be easier (or lower in transactions costs) for an investor to purchase a smaller number of mutual funds than to purchase a larger number of assets individually. Second, from a theoretical and empirical standpoint, if it can be assumed that the relevant conditions are indeed satisfied, then implications for the functioning of asset markets can be derived and tested.

Portfolios can be analyzed in a mean-variance framework, with every investor holding the portfolio with the lowest possible return variance consistent with that investor's chosen level of expected return (called a mean-variance efficient portfolio), if the returns on the assets are jointly elliptically distributed, including the special case in which they are jointly normally distributed.[1][2] Under mean-variance analysis, it can be shown[3] that every variance-minimizing portfolio given a particular expected return (that is, every efficient portfolio) can be formed as a combination of any two efficient portfolios. If the investor's optimal portfolio has an expected return that is between the expected returns on two efficient benchmark portfolios, then that investor's portfolio can be characterized as consisting of positive quantities of the two benchmark portfolios.

To see two-fund separation in a context in which no risk-free asset is available, using matrix algebra, let $\sigma^2$ be the variance of the portfolio return, let $\mu$ be the level of expected return on the portfolio that portfolio return variance is to be minimized contingent upon, let $r$ be the vector of expected returns on the available assets, let $X$ be the vector of amounts to be placed in the available assets, let $W$ be the amount of wealth that is to be allocated in the portfolio, and let $1$ be a vector of ones. Then the problem of minimizing the portfolio return variance subject to a given level of expected portfolio return can be stated as

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# Wikipedia & Learning Support 1

Collection of Important and Useful Articles.
 Rescooped by Nuno Edgar Fernandes from Papers

## Cooperation, competition and the emergence of criticality in communities of adaptive systems

The hypothesis that living systems can benefit from operating at the vicinity of critical points has gained momentum in recent years. Criticality may confer an optimal balance between too ordered and exceedingly noisy states. Here we present a model, based on information theory and statistical mechanics, illustrating how and why a community of agents aimed at understanding and communicating with each other converges to a globally coherent state in which all individuals are close to an internal critical state, i.e. at the borderline between order and disorder. We study—both analytically and computationally—the circumstances under which criticality is the best possible outcome of the dynamical process, confirming the convergence to critical points under very generic conditions. Finally, we analyze the effect of cooperation (agents trying to enhance not only their fitness, but also that of other individuals) and competition (agents trying to improve their own fitness and to diminish those of competitors) within our setting. The conclusion is that, while competition fosters criticality, cooperation hinders it and can lead to more ordered or more disordered consensual outcomes.

Via Samir, Complexity Digest
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 Rescooped by Nuno Edgar Fernandes from Computational Tinkering

## The Blockchain for Education: An Introduction :: Audrey Watters

Is blockchain poised to be “the next big thing” in education?
This has become a question I hear with increasing frequency about a technology that, up until quite recently, was primarily associated with the cryptocurrency Bitcoin. The subtext to the question, I suppose: do educators need to pay attention to the blockchain? What, if anything, should they know about it?

"Admittedly, I haven’t bothered to learn much about blockchain or Bitcoin either, despite the last few years of zealous headlines in various tech publications. I haven’t included either in any of the “Top Ed-Tech Trends” series I’ve written. And frankly, I’m still not convinced there’s a “there” there. But with the news this year that Sony plans to launch a testing platform powered by blockchain, with some current and former Mozilla employees exploring the blockchain and badges, and with a big promotional splash at SXSWedu about blockchain’s potential to help us rethinking learning (as “earning” no less), I realized it was time to do some research (for myself) in the hopes of writing a clear explanation (for others too) of what blockchain is – one that isn’t too technical but that doesn’t simply wave away important questions by resorting to buzzwords and jargon – that blockchain is “the most important IT invention of our age,” for example.

"This is the early result of that research. It’s meant to serve as an introductory guide for those in education who are interested in learning a bit more about the blockchain and its potential applications in ed-tech."

Via Jim Lerman, Bonnie Bracey Sutton, Susan Einhorn
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 Rescooped by Nuno Edgar Fernandes from Learning with MOOCs

## Price is right for the next generation of digital courses - FT.com

When massive open online courses emerged four years ago the thing that really caught the public imagination is that they were free. Thousands of people enrolled on courses provided by academic institutions on third-party Mooc platforms such as

Via Peter Mellow
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 Rescooped by Nuno Edgar Fernandes from Learning with MOOCs

## Price is right for the next generation of digital courses - FT.com

When massive open online courses emerged four years ago the thing that really caught the public imagination is that they were free. Thousands of people enrolled on courses provided by academic institutions on third-party Mooc platforms such as

Via Peter Mellow
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 Rescooped by Nuno Edgar Fernandes from Computational Tinkering

## Machine Learning And Human Bias: An Uneasy Pair

“We’re watching you.” This was the warning that the Chicago Police Department gave to more than 400 people on its “Heat List.”

The list, an attempt to identify the people most likely to commit violent crime in the city, was created with a predictive algorithm that focused on factors including, per the Chicago Tribune, “his or her acquaintances and their arrest histories – and whether any of those associates have been shot in the past.”

Algorithms like this obviously raise some uncomfortable questions. Who is on this list and why? Does it take race, gender, education and other personal factors into account? When the prison population of America is overwhelmingly Black and Latino males, would an algorithm based on relationships disproportionately target young men of color?

Transparency in the inputs to such algorithms and how their outputs are used is likely to be an important component of such efforts. Ethical considerations like these have recently been recognized as important problems by the academic community: new courses are being created and meetings like FAT-ML are providing venues for papers and discussions on the topic.

Via Susan Einhorn
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 Rescooped by Nuno Edgar Fernandes from COMPUTATIONAL THINKING and CYBERLEARNING

## 21st Century Literacy | School of Interactive Computing

Paul Herring's curator insight,

“I believe that computing is a new kind of literacy that is critical for all professions in the 21st century,” says Guzdial. “If I'm right, doing computing education well is as important as doing mathematics or physics education well and needs a similar level and kind of support.”

 Rescooped by Nuno Edgar Fernandes from COMPUTATIONAL THINKING and CYBERLEARNING

## Learn this beginner-friendly coding language that's used by sites like Google and Dropbox

Python is the programming language of choice at Google, Dropbox and Pinterest. It's also very beginner-friendly if you're considering switching careers.

Via Bonnie Bracey Sutton
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 Rescooped by Nuno Edgar Fernandes from Educational Technology News

## Producing High Quality eLearning Videos: The Ultimate Guide

How To Produce eLearning Videos: What eLearning Professionals Should Know. Check The Ultimate Guide For Producing High Quality eLearning Videos.

Via EDTECH@UTRGV

Great advice, if you can afford it. Write a script, keep it short and record in a quiet location away from phones and distractions. There are some tips everyone can follow without too much cost.

Edgar Mata's curator insight,

Cómo producir vídeos para elearning.

Dustin Fowler's curator insight,

Here's a guide for creating educational videos.  While these are great, I find that you need a blend between great quality and quick production.

 Rescooped by Nuno Edgar Fernandes from Educational Technology News

## Push Learning: How Smart Notifications Will Change Education

"Learner profiles will soon drive "push learning" that will queue playlists of learning experiences to help learners skill up."

Via EDTECH@UTRGV
Scott Holcomb's curator insight,

John Dargan's curator insight,

May not be useful. Just setting up Scoop.it

 Rescooped by Nuno Edgar Fernandes from EdTech Evolution - Mapping the Intersection of tech, innovation, and instruction

## How to Transform Teaching with Tablets

When you look at the very best work happening in iPad classrooms, you'll see students creating media, showcasing their understanding, collaborating with peers, and communicating with broad audiences. The pockets of excellence are ever-present and inspiring. On the whole, however, tablets are most often used to reproduce existing practices—to distribute resources and enable students to take notes.

Past generations of school leaders might have been forgiven for permitting these patterns of technology adoption, but today we have the benefit of history to look back on. We know that without a change in our technology integration strategies, there's no reason to expect that a new device will magically create new teaching practices in schools.

To make the most of the investment in tablet computers, school leaders need to do three things. First, they need to work with their communities to articulate a clear vision for how new technology will improve instruction. Second, they need to help educators imagine how new technologies can support those visions. Finally, they need to support teachers and students on a developmental journey that will take them from using tablets for consumption to using them for curation, creation, and connection."

Via John Evans, Mel Riddile, Dean J. Fusto
Ajo Monzó's curator insight,

Very interesting, thanks!

Mershon Viscusie's curator insight,

How will learning be different?

How will students improve as learners? As scholars? As citizens?

What will they be able to do 3 or 4 years after the ipad adoption that they can’t do now?

What does awesome look like?

How does an ipad align with a vision of  meaningful and purposeful learning?

 Rescooped by Nuno Edgar Fernandes from EdTech Evolution - Mapping the Intersection of tech, innovation, and instruction

## 100 Practical Ed Tech Tips Videos

On a cold winter night four or five months ago I started to organize the screencast videos that I've made over the years. I called the list Practical Ed Tech Tips.

Via Dean J. Fusto
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 Rescooped by Nuno Edgar Fernandes from COMPUTATIONAL THINKING and CYBERLEARNING

## Computational Thinking Breaks a Logjam | BU Tod...

Marty Walsh had a problem. Boston’s mayor wanted to address pay disparities between men and women, publicizing, as a first step, the average gap in different Boston industries.

Via Bonnie Bracey Sutton
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 Rescooped by Nuno Edgar Fernandes from 21st Century Learning and Teaching

## Technology Integration in Education #1: Twitter

I am writing a series of blog posts related to the integration of technology in the classroom. Each blog post will include practical examples of how to use a specific tool and integrate it into you...

We are living in revolutionary times. It is urgent that we think of education, children and teaching differently from the past. The classroom needs to be a place of innovation where students are able to connect with others, feel empowered and curious and have a say in their learning. Technology provides us with tools to expand our minds and extend our reach (Sir Ken Robinson, 2014).

Via Gust MEES
Gust MEES's curator insight,

The classroom needs to be a place of innovation where students are able to connect with others, feel empowered and curious and have a say in their learning. Technology provides us with tools to expand our minds and extend our reach (Sir Ken Robinson, 2014).

Marisol Pamela Hernández Orellana's curator insight,

Mientras nosotros los docentes (cosa que personalmente no comparto!) estamos pensando que las redes sociales y la tecnología distraen al estudiante....ellos las utilizan y se forman!!! ....de modo que quién se esta quedando atrás???

Nicole Sprainger's curator insight,

Another Ken Robinson "gem!"

 Rescooped by Nuno Edgar Fernandes from Learning*Education*Technology

## How computational thinking has changed professional sports

Billy Beane

Computational thinking is a really valuable approach or our students to
problem solve and introduce them to the world of coding, algorithms and
computer science.  It is often difficult to find examples of real world
computational thinking that engages students.

Recently I watched the film 'Moneyball' which upon reflection was a great
example of computational thinking in action in which all four elements
(decomposing, pattern recognition, abstraction and algorithmic
design.) were used to achieve a positive outcome.  I hope you find story
useful in better understanding computational thinking and also translating

Billy Beane was an average baseball player  shipped around America’s Major
League competition in the eighties until he realised he could not achieve
the heights he dreamed of, and the teams hiring him realised Billy Beane
was not going to take them to the ‘Promised Land.’

Post playing career Billy was hired by the Oakland A’s as their general
manager to try and bring them a championship.  Five years into the role
Billy came to the realisation that he was trying to win an unfair game.
And it was all because the MLB does not have a salary cap for purchasing
players.

This was highlighted in 2001 when the New York Yankees faced the Oakland
A’s in a regular season game which drew no major significance except for
this...

Team Salary Cap Comparison

Team Payroll Comparison

New York Yankee’s: $144 million Oakland A’s:$39 million

Beane conceded his Oakland A’s were little more than a talent incubator for
wealthier teams to poach and decided in 2002 things must change or else his
career as General Manager would yield the same results as his career as a
player.

essentially disbanded the Oakland A’s scouting and development group and
entrusted it to Paul De Podesta who was a Harvard Economics Graduate
driven challenges.  He was a great computational thinker.

De Podesta’s mantra was that the Oakland A’s would no longer invest in
Podesta as to the statistics and data he believed made an indisputable
difference to the win loss column they began statistically to break down
every player in Baseball to a single  piece of data  identifying  what
impact they had upon winning based upon their salary.

De Podesta identified superstars who were phenomenally overpaid, and
nobodies who were absolute steals based upon their measly salaries.

De Podesta

De Podesta  and Beane exemplified all four elements of Computational
thinking during this process.

* De Podesta decomposed their current situation, the elements of
success in baseball every player in MLB to a series of statistical
value.

* Beane identified statistical patterns, sequences and structures that
occurred in winning baseball teams.

* They abstracted opinion and discounted irrelevant data which that is
unproven in influencing wins and losses in baseball.

* De Podesta created an algorithm for success based upon statistical
data and salary which reinvented the Oakland A’s team and still fit
well within their salary limit.

Oakland started the season poorly under a cloud of criticism from all
corners of the baseball world.  Outwardly it appeared as if Oakland traded
or dumped their most treasured players and replaced them with trash.

Amidst early mounting losses and criticism both Beane and De Podesta
believed they had done their research and stood by their formula for
success.

To cut a long story short the Oakland A’s started to become the team which
Beane and Depodesta envisioned even though they were in the eyes of many
nothing more than a washed up, rag tag B league team.

They went on the longest winning streak in professional baseball in a
century (20 games) and finished atop their division with a win loss record
of 103-59.  This was exceptional when considering they had a losing record
over the first third of the season.

They did not win the championship in 2002 but the Boston Redsox adopted
Beane and DePodesta’s “moneyball”  approach in 2003 and won the ultimate
prize in 2004.

Beane was offered the highest paying contract in sports amangement in 2003
by the Boston Redsox which he turned down. He is still the GM of the
Oakland Athletics.

DePodesta has moved around multiple U.S sporting teams and even leagues to
share his Computational Thinking  approach to winning and losing which is
valued by nearly every major professional sport as an essential element for
accountability and success.

Via Skip Zalneraitis
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 Rescooped by Nuno Edgar Fernandes from STEM Education

## Computer science is the key to America’s skills crisis

The United States faces a global competitiveness crisis that, if not addressed, will put our nation at a strategic disadvantage for decades to come. In just a..

Via Ted Feller
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 Rescooped by Nuno Edgar Fernandes from Learning with MOOCs

The marketing spiel exudes confidence: “Get the job you want in 2016!” But the connection between massive open online courses (Moocs) and future employment is not so clear. Over the past five years, Moocs have become an educational ecosystem

Via Peter Mellow
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 Rescooped by Nuno Edgar Fernandes from Computational Tinkering

## Creativity via Big Data: from big data to computational thinking to creative problem-solving (innovation)

Einstein published his ideas and became a pivotal element in shifting the way we think about physics - from the Newtonian model to the Quantum - in turn this changed the way we think about the world and allowed us to develop new ways of engaging with the world.

We are at a similar juncture.  The development of computational technologies allows us to think about astronomical volumes of data and to make meaning of that data.

The mindshift that occurs is that “the machine is our friend”.  The computer, like all machines, extends our capabilities.  As a consequence the types of thinking now required in industry are those that get away from thinking like a computer and shift towards creative engagement with possibilities.  Logical thinking is still necessary but it starts to be driven by imagination.

Computational thinking and data science change the way we think about defining and solving problems.

Via Kim Flintoff, Susan Einhorn
Kim Flintoff's curator insight,

Presented today at the Financial, Administrative and Professional Services Training Council Industry Currency Day.

 Rescooped by Nuno Edgar Fernandes from Computational Tinkering

## Is learning computer science linked to improved learning in other subjects?

Many passionate computer science educators believe computational thinking, problem solving, persistence and analysis learned in computer science helps students do better in other courses, especially math.

There’s a clear correlation

According to College Board data, students who take the AP Computer Science exam earn higher AP Calculus and Statistics scores relative to peers who previously performed at a similar level in math.

..

Via Susan Einhorn
Chris Carter's curator insight,

The evidence is building ...

Mark E. Deschaine, PhD's curator insight,

The evidence is building ...

 Rescooped by Nuno Edgar Fernandes from CxAnnouncements

## Postdoctoral position in complex systems (Econophysics)

Are you fascinated by interdisciplinary work? — Are you into data analysis and model building? If yes, you might be interested in this position. In the last decades Econophysics emerged as a new, interdisciplinary field. Our group has longstanding expertise. We develop models for various issues in the economy, particularly in the financial markets. We apply the same standards as in traditional physics and base our models as much as possible on the empirical information.

University of Duisburg-Essen

http://www.theo.physik.uni-due.de/tp/ags/guhr_dir/positions.php?lang=en

Via Complexity Digest
A. J. Alvarez-Socorro's curator insight,

Becas / Scholarships / Fellowships

 Rescooped by Nuno Edgar Fernandes from COMPUTATIONAL THINKING and CYBERLEARNING

## A Programming Languages Alphabet Book Could Spark an Interest in Coding

You have no idea what your kids will grow up to be while they’re still toddlers, but that doesn’t mean you can’t gently nudge them towards one vocation or another.

Via Bonnie Bracey Sutton
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 Rescooped by Nuno Edgar Fernandes from Educational Technology News

## Students Learn to Write by Teaching This Robot

A new robot-powered app exemplifies learning through teaching.

Via EDTECH@UTRGV
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 Rescooped by Nuno Edgar Fernandes from EdTech Evolution - Mapping the Intersection of tech, innovation, and instruction

## 200 Free Educational Documentaries for Teachers

April 28, 2015Looking for some interesting free documentaries to use in your class or probably use for your own professional and intellectual growth? This list from Open Culture has you covered. It...

Via Dean J. Fusto
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 Rescooped by Nuno Edgar Fernandes from EdTech Evolution - Mapping the Intersection of tech, innovation, and instruction

## Great Educational Web Tools for Making Virtual Field Trips

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 Rescooped by Nuno Edgar Fernandes from Educational technology , Erate, Broadband and Connectivity

## Computational Thinking Breaks a Logjam | BU Today | Boston University

Marty Walsh had a problem. Boston’s mayor wanted to address pay disparities between men and women, publicizing, as a first step, the average gap in different Boston industries. Normally, calculating that gap would require taking the actual pay gap at each company in an industry, adding them up, and then dividing by the number of companies to reach an average. But companies’ payrolls are proprietary, because their disclosure could be a boon to competitors, a black eye for the firms, and ammo for disgruntled employees who could sue over pay inequities.

Enter Bestavros, a College of Arts and Sciences computer science professor, who proposed an ingeniously simple algorithm from computer science that will allow the city to calculate those industry pay averages, by gender, from a total of 60 participating employers, without any daylight shining on an individual company’s proprietary information.

Via Susan Einhorn, Bonnie Bracey Sutton
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 Rescooped by Nuno Edgar Fernandes from Educational News and Web Tools

## The Stages Of Education Technology

The Stages Of Education Technology

Via Dan Kirsch
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