This book considers a relatively new metric in complex systems, transfer entropy, derived from a series of measurements, usually a time series. After a qualitative introduction and a chapter that explains the key ideas from statistics required to understand the text, the authors then present information theory and transfer entropy in depth. A key feature of the approach is the authors' work to show the relationship between information flow and complexity. The later chapters demonstrate information transfer in canonical systems, and applications, for example in neuroscience and in finance.
The book will be of value to advanced undergraduate and graduate students and researchers in the areas of computer science, neuroscience, physics, and engineering.
ISBN: 978-3-319-43221-2 (Print), 978-3-319-43222-9 (Online)
Want to read; h/t to Joseph Lizier.
Continue reading “🔖 An Introduction to Transfer Entropy: Information Flow in Complex Systems”
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The legendary editor who founded the Washington Monthly and pioneered explanatory journalism trains his keen, principled eye on the changes that have reshaped American politics and civic life beginning with the New Deal.
“We Do Our Part” was the slogan of Franklin Delano Roosevelt’s National Recovery Administration—and it captured the can-do spirit that allowed America to survive the Great Depression and win World War II. Although the intervening decades have seen their share of progress as well, in some ways we have regressed as a nation. Over the course of a sixty-year career as a Washington, D.C., journalist, historian, and challenger of conventional wisdom, Charles Peters has witnessed these drastic changes firsthand. This stirring book explains how we can consolidate the gains we have made while recapturing the generous spirit we have lost.
In a volume spanning the decades, Peters compares the flood of talented, original thinkers who flowed into the nation’s capital to join FDR’s administration with the tide of self-serving government staffers who left to exploit their opportunities on Wall Street and as lobbyists from the 1970s to today. During the same period, the economic divide between rich and poor grew, as we shifted from a culture of generosity to one of personal aggrandizement. With the wisdom of a prophet, Peters connects these two trends by showing how this money-fueled elitism has diminished our trust in one another and our nation—and changed Washington for the worse.
While Peters condemns the crass buckraking that afflicts our capital, and the rampant consumerism that fuels our greed, he refuses to see America’s downward drift as permanent. By reminding us of our vanished civic ideal, We Do Our Part also points the way forward. Peter argues that if we want to revive the ethos of the New Deal era—a time when government attracted the brightest and the most dedicated, and when our laws reflected a spirit of humility and community—we need only demand it of ourselves and our elected officials.
With a new administration in Washington, the time is ripe for a reassessment of our national priorities. We Do Our Part offers a vital road map of where we have been and where we are going, drawn from the invaluable perspective of a man who has seen America’s better days and still believes in the promise that lies ahead.
h/t to reference in PBS Newshour.
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In the early 1840s the American West, though claimed by the United States, was considered by many white Americans to be untamed, wild, and possibly rife with unknown wealth. This was a West that existed largely in the American imagination.
In fact, the area west of the Missouri was home to complex Native societies, was divided into political structures, and was intimately known, if not formally mapped.
These two competing Wests - that imagined by many Americans and that inhabited by Souix, Pawnee, Snake and Nez Pierce tribes - were mapped both geographically and textually by John C. Frémont between 1842 and 1843. Frémont set out from St. Louis in the summer of 1842, and began to chronicle his journey west, in the wake of "emigrants" who were moving to the Oregon Territory - a route known as the "Oregon Trail." Frémont's first expedition covered the land between the Missouri River and the Rocky Mountains during the summer and fall of 1842. In the summer of 1843 he set out to write an account of the second half of the Oregon Trail, from the Rocky Mountains to the Columbia River in Oregon.
The maps contained here are drawn from the Library of Congress's collection "Topographical map of the road from Missouri to Oregon, commencing at the mouth of the Kansas in the Missouri River and ending at the mouth of the Walla-Wallah in the Columbia." They were created using Frémont's journal, and cover his first and second expeditions. I have annotated the maps with accounts of the resting places, flora, fauna, and people Frémont's and his party encountered on their journey west.
You’ve played the game Oregon Trail via DOS (as a child), online, or via app but have you traced the actual trail taken by John C. Frémont between 1842 and 1843? Now you can with this daily interactive map with journal.
Thanks Anelise Shrout!
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Some personal thoughts and opinions on what ``good quality mathematics'' is, and whether one should try to define this term rigorously. As a case study, the story of Szemer\'edi's theorem is presented.
This looks like a cool little paper.
Some thoughts after reading
And indeed it was. The opening has lovely long (though possibly incomplete) list of aspects of good mathematics toward which mathematicians should strive. The second section contains an interesting example which looks at the history of a theorem and it’s effect on several different areas. To me most of the value is in thinking about the first several pages. I highly recommend this to all young budding mathematicians.
In particular, as a society, we need to be careful of early students in elementary and high school as well as college as the pedagogy of mathematics at these lower levels tends to weed out potential mathematicians of many of these stripes. Students often get discouraged from pursuing mathematics because it’s “too hard” often because they don’t have the right resources or support. These students, may in fact be those who add to the well-roundedness of the subject which help to push it forward.
I believe that this diverse and multifaceted nature of “good mathematics” is very healthy for mathematics as a whole, as it it allows us to pursue many different approaches to the subject, and exploit many different types of mathematical talent, towards our common goal of greater mathematical progress and understanding. While each one of the above attributes is generally accepted to be a desirable trait to have in mathematics, it can become detrimental to a field to pursue only one or two of them at the expense of all the others.
As I look at his list of scenarios, it also reminds me of how areas within the humanities can become quickly stymied. The trouble in some of those areas of study is that they’re not as rigorously underpinned, as systematic, or as brutally clear as mathematics can be, so the fact that they’ve become stuck may not be noticed until a dreadfully much later date. These facts also make it much easier and clearer in some of these fields to notice the true stars.
As a reminder for later, I’ll include these scenarios about research fields:
- A field which becomes increasingly ornate and baroque, in which individual
results are generalised and refined for their own sake, but the subject as a
whole drifts aimlessly without any definite direction or sense of progress;
- A field which becomes filled with many astounding conjectures, but with no
hope of rigorous progress on any of them;
- A field which now consists primarily of using ad hoc methods to solve a collection
of unrelated problems, which have no unifying theme, connections, or purpose;
- A field which has become overly dry and theoretical, continually recasting and
unifying previous results in increasingly technical formal frameworks, but not
generating any exciting new breakthroughs as a consequence; or
- A field which reveres classical results, and continually presents shorter, simpler,
and more elegant proofs of these results, but which does not generate any truly
original and new results beyond the classical literature.
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