Complex Analysis II

# Tag: mathematics

## 👓 Physicists Uncover Geometric ‘Theory Space’ | Quanta Magazine

*(Quanta Magazine)*

A decades-old method called the “bootstrap” is enabling new discoveries about the geometry underlying all quantum theories.

In the 1960s, the charismatic physicist Geoffrey Chew espoused a radical vision of the universe, and with it, a new way of doing physics. Theorists of the era were struggling to find order in an unruly zoo of newfound particles. They wanted to know which ones were the fundamental building blocks of nature and which were composites. But Chew, a professor at the University of California, Berkeley, argued against such a distinction. “Nature is as it is because this is the only possible nature consistent with itself,” he wrote at the time. He believed he could deduce nature’s laws solely from the demand that they be self-consistent. Continue reading “👓 Physicists Uncover Geometric ‘Theory Space’ | Quanta Magazine”

Syndicated copies to:## Chris Aldrich is reading “Clinton’s Substantial Popular-Vote Win” | New York Times

*(nytimes.com)*(3 hours 3 minutes 7 seconds)

She won by more than Gore in 2000, Nixon in 1968 or Kennedy in 1960, it seems. And therein lies a dilemma.

When are people going to come around and fix the electoral college? There’s lots of math to support different methods.

Syndicated copies to:## 🔖 H-theorem in quantum physics by G. B. Lesovik, et al.

*(Nature.com)*

### Abstract

Remarkable progress of quantum information theory (QIT) allowed to formulate mathematical theorems for conditions that data-transmitting or data-processing occurs with a non-negative entropy gain. However, relation of these results formulated in terms of entropy gain in quantum channels to temporal evolution of real physical systems is not thoroughly understood. Here we build on the mathematical formalism provided by QIT to formulate the quantum H-theorem in terms of physical observables. We discuss the manifestation of the second law of thermodynamics in quantum physics and uncover special situations where the second law can be violated. We further demonstrate that the typical evolution of energy-isolated quantum systems occurs with non-diminishing entropy. [1]

### Footnotes

*Scientific Reports*, vol. 6. Springer Nature, p. 32815, 12-Sep-2016 [Online]. Available: http://dx.doi.org/10.1038/srep32815

## Warren Weaver Bot!

*(Twitter)*

This is the signal for the second.

How can you * not *follow this twitter account?!

Now I’m waiting for a Shannon bot and a Weiner bot. Maybe a John McCarthy bot would be apropos too?!

Syndicated copies to:## NIMBioS Tutorial: Evolutionary Quantitative Genetics 2016

*(nimbios.org)*

This tutorial will review the basics of theory in the field of evolutionary quantitative genetics and its connections to evolution observed at various time scales. Quantitative genetics deals with the inheritance of measurements of traits that are affected by many genes. Quantitative genetic theory for natural populations was developed considerably in the period from 1970 to 1990 and up to the present, and it has been applied to a wide range of phenomena including the evolution of differences between the sexes, sexual preferences, life history traits, plasticity of traits, as well as the evolution of body size and other morphological measurements. Textbooks have not kept pace with these developments, and currently few universities offer courses in this subject aimed at evolutionary biologists. There is a need for evolutionary biologists to understand this field because of the ability to collect large amounts of data by computer, the development of statistical methods for changes of traits on evolutionary trees and for changes in a single species through time, and the realization that quantitative characters will not soon be fully explained by genomics. This tutorial aims to fill this need by reviewing basic aspects of theory and illustrating how that theory can be tested with data, both from single species and with multiple-species phylogenies. Participants will learn to use R, an open-source statistical programming language, to build and test evolutionary models. The intended participants for this tutorial are graduate students, postdocs, and junior faculty members in evolutionary biology.

## Disconnected, Fragmented, or United? A Trans-disciplinary Review of Network Science

*(Applied Network Science | SpringerLink)*

### Abstract

Syndicated copies to:During decades the study of networks has been divided between the efforts of social scientists and natural scientists, two groups of scholars who often do not see eye to eye. In this review I present an effort to mutually translate the work conducted by scholars from both of these academic fronts hoping to continue to unify what has become a diverging body of literature. I argue that social and natural scientists fail to see eye to eye because they have diverging academic goals. Social scientists focus on explaining how context specific social and economic mechanisms drive the structure of networks and on how networks shape social and economic outcomes. By contrast, natural scientists focus primarily on modeling network characteristics that are independent of context, since their focus is to identify universal characteristics of systems instead of context specific mechanisms. In the following pages I discuss the differences between both of these literatures by summarizing the parallel theories advanced to explain link formation and the applications used by scholars in each field to justify their approach to network science. I conclude by providing an outlook on how these literatures can be further unified.

## Weekly Recap: Interesting Articles 7/24-7/31 2016

Went on vacation or fell asleep at the internet wheel this week? Here’s some of the interesting stuff you missed.

## Science & Math

- Context Specific and Differential Gene Co-expression Networks via Bayesian Biclustering | PLOS Computational Biology
- The Competing Incentives of Academic Research in Mathematics
- [1607.08473] Quantum circuits and low-degree polynomials over F_2
- This Physics Pioneer Walked Away from it All | Nautilus
- Monumental proof to torment mathematicians for years to come: Conference on Shinichi Mochizuki’s work inspires cautious optimism. | Nature
- What Your Brain Looks Like When It Solves a Math Problem | New York Times
- Habits of Highly Mathematical People
- Why You Should Care About High-Dimensional Sphere Packing | Roots of Unity
- Initial steps toward reproducible research
- Bridging the Curation Gap between Research and Libraries – A Case Study
- Quantum steampunk: Quantum information applied to thermodynamics
- How Vector Space Mathematics Reveals the Hidden Sexism in Language
- How Sound Can Make Food Taste Better | Nautilus
- Top 10 algorithms of 20th century numerical analysis, from a talk by Alex Townsend
- UK vs. US: Who’s got the right way to teach math(s)? | Math with Bad Drawin
- Physics & Caffeine: Stop Motion Film Uses a Cup of Coffee to Explain Key Co
- The Water Kingdom: A Secret History of China by Philip Ball (review)
- The master of them all: Book review for”Leonhard Euler: Mathematical Genius in the Enlightenment” | The Economist
- Biologists Search for New Model Organisms: The bulk of biological research is centered on a handful of species. Are we missing a huge chunk of life’s secrets?
- One-sentence proof of Fermat’s theorem on sums of two squares | Fermat’s Library
- This protein designer aims to revolutionize medicines and materials
- Our last common ancestor inhaled hydrogen from underwater volcanoes
- Meet Luca, The Ancestor of All Living Things | New York Times
- *Disconnected, fragmented, or united? a trans-disciplinary review of network
- What’s Behind A Science vs. Philosophy Fight? | Big Think
- What is a “Neutral Network” Anyway? An Exploration and Rediscovery of the Aims of Net Neutrality in Theory and Practice
- The Brachistochrone Curve: The Problem of Quickest Descent | Fermat’s Library
- In what sense is Quantum Mechanics a theory of information? | Quora
- Major transitions in information technology | Philosophical Transactions of
- Human brain mapped in unprecedented detail: Nearly 100 previously unidentified brain areas revealed by examination of the cerebral cortex. | Nature
- Cell biologists should specialize, not hybridize: Dry cell biologists, who bridge computer science and cell biology, should have a pivotal role in driving effective team science, says Assaf Zaritsky | Nature
- Internet 3.0: How we take back control from the giants | New Scientist
- How a Guy From a Montana Trailer Park Overturned 150 Years of Biology | The Atlantic
- People can sense single photons | Nature News & Comment
- Defining synergy thermodynamically using quantitative measurements of entropy and free energy
- A Prime Case of Chaos | AMS.org
- Murray Gell-Mann (video interviews) – YouTube
- Mathematics & Chalk: A teary goodbye to Hagomoro | Jeremy Kun

## Publishing

- Want to Change Academic Publishing? Just Say No | Chronicle
- Textbooks Show Aging Signs: Curated Guides Are Next – 10+ Disruptive Factors Transforming the World of Education and Learning — Consequences, Opportunities, Tools
- Simon & Schuster, Penguin, Random House Don’t Want to Talk About Their Ebook Sales
- Amazon Sales Rank: Taming the Algorithm | Self-Publishing Author Advice
- What Authors Should Know About Advance Review Copies
- Ingram Launches Ingram Academic Services
- How a Publishing House Designs a Book Cover
- How Indie Bookstores Help Drive Book Discoverability
- How to Grow Your Email List
- 3 Ways Indie Publishers Sell Books | Digital Book World
- 10 Self-Publishing Trends to Watch
- Ingram Launches Academic Services for University Presses and Academic Publishers
- Indigo Goes Where Amazon, B&N, Goodreads, and a Dozen Publishers and Startus Have Dared to Tread
- How To Make An Ebook Feel More Like A Real Book
- Looking for open digital collections – Wynken de Worde

## Indieweb, Internet, Identity, Blogging, Social Media

- What is Open Source?
- Microformats with Tantek Çelik | tlks.io https://www.youtube.com/watch?v=kDQigkxyiqE
- My Text Editor is Absolutely Sublime | Devon Zuegel
- My zsh aliases | Devon Zuegel
- XOXO Festival
- Web Design in 4 minutes
- Custom Elements
- Design Principles
- Infographic: The Optimal Length for Every Social Media Update
- Notes For New (and Potential) Twitter Followers | Whatever
- How Blogs Work Today – Whatever
- My reply to: How Blogs Work Today | Whatever
- Unicode Character ‘ZERO WIDTH SPACE’ (U 200B)
- A Book Apart, Practical SVG
- Gillmor Gang Trumpathon
- The best news aggregation service – The Sweet Setup
- Social Startup Sprinklr Is Now Valued At $1.8 Billion After $105 Million Raise | Forbes
- Epeus’ epigone: Digital publics, Conversations and Twitter

## General

- The New Meaning of Success
- 7 Lessons from the Future of Content: Part One — Tools Are Cheap, Time Is Expensive
- 7 Lessons from the Future of Content: Part Two — Let’s Play Risk
- Aron Pilhofer Joining Temple University School of Media and Communication
- Secrets and agents: George Akerlof’s 1970 paper, “The Market for Lemons”, is a foundation stone of information economics. The first in our series on seminal economic ideas | The Economist
- John Oliver has the takedown of Donald Trump’s Republican convention
- Reference: New Interactive Map Of 100,000 Photos and Videos Reveal “Lost London in the Victorian Era”
- “better modifiers than “insane(ly)” (Grammar and Usage)
- A lesson in the errors of statistical thinking: Nate Silver on Trump
- Trump & Putin. Yes, It’s Really a Thing
- Charlie Parker Plays with Dizzy Gillespie in Only Footage Capturing the “Bird” in True Live Performance
- Let Me Remind You Fuckers Who I Am (Shit HRC Can’t Say/satire)

## Introduction to Complex Analysis | UCLA Extension

Dr. Michael Miller has announced his Autumn mathematics course, and it is…

## Introduction to Complex Analysis

## Course Description

Complex analysis is one of the most beautiful and useful disciplines of mathematics, with applications in engineering, physics, and astronomy, as well as other branches of mathematics. This introductory course reviews the basic algebra and geometry of complex numbers; develops the theory of complex differential and integral calculus; and concludes by discussing a number of elegant theorems, including many–the fundamental theorem of algebra is one example–that are consequences of Cauchy’s integral formula. Other topics include De Moivre’s theorem, Euler’s formula, Riemann surfaces, Cauchy-Riemann equations, harmonic functions, residues, and meromorphic functions. The course should appeal to those whose work involves the application of mathematics to engineering problems as well as individuals who are interested in how complex analysis helps explain the structure and behavior of the more familiar real number system and real-variable calculus.

## Prerequisites

Basic calculus or familiarity with differentiation and integration of real-valued functions.

## Details

MATH X 451.37 – 268651 Introduction to Complex Analysis

Fall 2016

Time 7:00PM to 10:00PM

Dates Tuesdays, Sep 20, 2016 to Dec 06, 2016

Contact Hours 33.00

Location: UCLA, Math Sciences Building

Standard credit (3.9 units) $453.00

Instructor: Michael Miller

Register Now at UCLA

For many who will register, this certainly won’t be their first course with Dr. Miller — yes, he’s that good! But for the newcomers, I’ve written some thoughts and tips to help them more easily and quickly settle in and adjust:

Dr. Michael Miller Math Class Hints and Tips | UCLA Extension

I often recommend people to join in Mike’s classes and more often hear the refrain: “I’ve been away from math too long”, or “I don’t have the prerequisites to even begin to think about taking that course.” For people in those categories, you’re in luck! If you’ve even had a soupcon of calculus, you’ll be able to keep up here. In fact, it was a similar class exactly a decade ago by Mike Miller that got me back into mathematics. (Happy 10th math anniversary to me!)

I look forward to seeing everyone in the Fall!

#### Update 9/1/16

### Textbook

Dr. Miller is back from summer vacation and emailed me this morning to say that he’s chosen the textbook for the class. We’ll be using *Complex Analysis with Applications* by Richard A. Silverman. [1]

(Note that there’s another introductory complex analysis textbook from Silverman that’s offered through Dover, so be sure to choose the correct one.)

As always in Dr. Miller’s classes, the text is just *recommended* (read: not required) and in-class notes are more than adequate. To quote him directly, “We will be using as a basic guide, but, as always, supplemented by additional material and alternate ways of looking at things.”

The bonus surprise of his email: He’s doing two quarters of Complex Analysis! So we’ll be doing both the Fall and Winter Quarters to really get some depth in the subject!

### Alternate textbooks

If you’re like me, you’ll probably take a look at some of the other common (and some more advanced) textbooks in the area. Since I’ve already compiled a list, I’ll share it:

#### Undergraduate

*Complex Analysis*by Joseph Bak and Donald J. Newman [2]*Complex Analysis*by Theodore Gamelin [3]*Complex Variables and Applications*by James Brown and Ruel Churchill [4]*Fundamentals of Complex Analysis with Applications to Engineering, Science, and Mathematics*by Edward Saff and Arthur D. Snider (Pearson, 2014, 3rd edition) [5]

#### More advanced

*Complex Analysis*by Lars Ahlfors [6]*Complex Analysis*by Serge Lang [7]*Functions of One Complex Variable*(Graduate Texts in Mathematics by John B. Conway (Springer, 1978) [8]*Complex Analysis*(Princeton Lectures in Analysis, No. 2) by Elias M. Stein and Rami Shakarchi (Princeton University Press, 2003) [9]

### References

*Complex Analysis with Applications*, 1st ed. Dover Publications, Inc., 2010, pp. 304–304 [Online]. Available: http://amzn.to/2c7KaQy

*Complex Analysis*, 3rd ed. Springer, 2010, pp. 328–328 [Online]. Available: http://amzn.to/2bLPW89

*Complex Analysis*. Springer, 2003, pp. 478–478 [Online]. Available: http://amzn.to/2bGNQct

*Complex Variables and Applications*, 8th ed. McGraw-Hill, 2008, pp. 468–468 [Online]. Available: http://amzn.to/2bLQWcu

*Fundamentals of Complex Analysis with Applications to Engineering, Science, and Mathematics*, 3rd ed. Pearson, 2003, pp. 563–563 [Online]. Available: http://amzn.to/2f3Nyj6

*Complex Analysis*, 3rd ed. McGraw-Hill, 1979, pp. 336–336 [Online]. Available: http://amzn.to/2bMXrxm

*Complex Analysis*, 4th ed. Springer, 2003, pp. 489–489 [Online]. Available: http://amzn.to/2c7OaR0

*Functions of One Complex Variable*, 2nd ed. Springer, 1978, pp. 330–330 [Online]. Available: http://amzn.to/2cggbF1

*Complex Analysis*. Princeton University Press, 2003, pp. 400–400 [Online]. Available: http://amzn.to/2bGOG9c

## Tom M. Apostol, 1923–2016

*(CalTech Division of Physics, Mathematics and Astronomy)*

Tom M. Apostol, professor of mathematics, emeritus at California Institute of Technology passed away on May 8, 2016. He was 92.

My proverbial mathematical great-grandfather passed away yesterday.

As many know, for over a decade, I’ve been studying a variety of areas of advanced abstract mathematics with Michael Miller. Mike Miller received his Ph.D. in 1974 (UCLA) under the supervision of Basil Gordon who in turn received his Ph.D. in 1956 (CalTech) under the supervision of Tom M. Apostol.

Incidentally going back directly three generations is Markov and before that Chebyshev and two generations before that Lobachevsky.

Sadly, I never got to have Tom as a teacher directly myself, though I did get to meet him several times in (what mathematicians might call) social situations. I did have the advantage of delving into his two volumes of Calculus as well as referring to his book on Analytic Number Theory. If it’s been a while since you’ve looked at calculus, I highly recommend an evening or two by the fire with a glass of wine while you revel in Calculus, Vol 1 or Calculus, Vol 2.

It’s useful to take a moment to remember our intellectual antecedents, so in honor of Tom’s passing, I recommend the bookmarked very short obituary (I’m sure more will follow), this obituary of Basil, and this issue of the Notices of the AMS celebrating Basil as well. I also came across a copy of *Fascinating Mathematical People* which has a great section on Tom and incidentally includes some rare younger photos of Sol Golomb who suddenly passed away last Sunday. (It’s obviously been a tough week for me and math in Southern California this week.)

## Devastating News: Sol Golomb has apparently passed away on Sunday

I was getting concerned that I hadn’t heard back from Sol for a while, particularly after emailing him late last week, and then I ran across this notice through ITSOC & the IEEE:

## Solomon W. Golomb (May 30, 1932 – May 1, 2016)

Shannon Award winner and long-time ITSOC member Solomon W. Golomb passed away on May 1, 2016.

Solomon W. Golomb was the Andrew Viterbi Chair in Electrical Engineering at the University of Southern California (USC) and was at USC since 1963, rising to the rank of University and Distinguished Professor. He was a member of the National Academies of Engineering and Science, and was awarded the National Medal of Science, the Shannon Award, the Hamming Medal, and numerous other accolades. As USC Dean Yiannis C. Yortsos wrote, “With unparalleled scholarly contributions and distinction to the field of engineering and mathematics, Sol’s impact has been extraordinary, transformative and impossible to measure. His academic and scholarly work on the theory of communications built the pillars upon which our modern technological life rests.”In addition to his many contributions to coding and information theory, Professor Golomb was one of the great innovators in recreational mathematics, contributing many articles to Scientific American and other publications. More recent Information Theory Society members may be most familiar with his mathematics puzzles that appeared in the Society Newsletter, which will publish a full remembrance later.

A quick search a moment later revealed this sad confirmation along with some great photos from an award Sol received just a week ago:

A sad day 4 @USC @USCViterbi @USCMingHsiehEE with the loss of beloved Sol Golomb. Was only last week we celebrated his Franklin medal.

— Yannis C. Yortsos (@DeanYortsos) May 2, 2016

With Andy Viterbi and Sol Golomb at the celebration of @TheFranklin @USCViterbi @USCMingHsiehEE pic.twitter.com/0iktSa9zf1

— Yannis C. Yortsos (@DeanYortsos) April 22, 2016

Sol Golomb receiving the @TheFranklin medal in Electrical Engineering @USCViterbi @USCMingHsiehEE pic.twitter.com/L3RFUGhsWs

— Yannis C. Yortsos (@DeanYortsos) April 21, 2016

As is common in academia, I’m sure it will take a few days for the news to drip out, but the world has certainly lost one of its greatest thinkers, and many of us have lost a dear friend, colleague, and mentor.

I’ll try touch base with his family and pass along what information *sniff* I can. I’ll post forthcoming obituaries as I see them, and will surely post some additional thoughts and reminiscences of my own in the coming days.

## What is Information? by Christoph Adami

*(arxiv.org)*

Information is a precise concept that can be defined mathematically, but its relationship to what we call "knowledge" is not always made clear. Furthermore, the concepts "entropy" and "information", while deeply related, are distinct and must be used with care, something that is not always achieved in the literature. In this elementary introduction, the concepts of entropy and information are laid out one by one, explained intuitively, but defined rigorously. I argue that a proper understanding of information in terms of prediction is key to a number of disciplines beyond engineering, such as physics and biology.

A proper understanding of information in terms of prediction is key to a number of disciplines beyond engineering, such as physics and biology.

Comments: 19 pages, 2 figures. To appear in Philosophical Transaction of the Royal Society A

Subjects: Adaptation and Self-Organizing Systems (nlin.AO); Information Theory (cs.IT); Biological Physics (physics.bio-ph); Quantitative Methods (q-bio.QM)

Cite as:arXiv:1601.06176 [nlin.AO] (or arXiv:1601.06176v1 [nlin.AO] for this version)

From: Christoph Adami

**[v1]** Fri, 22 Jan 2016 21:35:44 GMT (151kb,D) [.pdf]

Source: *Christoph Adami [1601.06176] What is Information? on arXiv*

## Quantum Biological Information Theory by Ivan B. Djordjevic | Springer

*(Springer, 2015)*

Springer recently announced the publication of the book *Quantum Biological Information Theory* by Ivan B. Djordjevic, in which I’m sure many readers here will have interest. I hope to have a review of it shortly after I’ve gotten a copy. Until then…

From the publisher’s website:

This book is a self-contained, tutorial-based introduction to quantum information theory and quantum biology. It serves as a single-source reference to the topic for researchers in bioengineering, communications engineering, electrical engineering, applied mathematics, biology, computer science, and physics. The book provides all the essential principles of the quantum biological information theory required to describe the quantum information transfer from DNA to proteins, the sources of genetic noise and genetic errors as well as their effects.

- Integrates quantum information and quantum biology concepts;
- Assumes only knowledge of basic concepts of vector algebra at undergraduate level;
- Provides a thorough introduction to basic concepts of quantum information processing, quantum information theory, and quantum biology;
- Includes in-depth discussion of the quantum biological channel modelling, quantum biological channel capacity calculation, quantum models of aging, quantum models of evolution, quantum models on tumor and cancer development, quantum modeling of bird navigation compass, quantum aspects of photosynthesis, quantum biological error correction.

Source: *Quantum Biological Information Theory | Ivan B. Djordjevic | Springer*

I’ll note that it looks like it also assumes some reasonable facility with quantum mechanics in addition to the material listed above.

Springer also has a downloadable copy of the preface and a relatively extensive table of contents for those looking for a preview. Dr. Djordjevic has been added to the ever growing list of researchers doing work at the intersection of information theory and biology.

Syndicated copies to:## Why math? JHU mathematician on teaching, theory, and the value of math in a modern world | Hub

*(The Hub)*

Great to see this interview with my friend and mathematician Richard Brown from Johns Hopkins Unviersity. Psst: He’s got an interesting little blog, or you can follow some of his work on Facebook and Twitter.

Click through for the full interview: Q+A with Richard Brown, director of undergraduate studies in Johns Hopkins University’s Department of Mathematics