🔖 A de Bruijn identity for discrete random variables by Oliver Johnson, Saikat Guha

Bookmarked A de Bruijn identity for discrete random variables by Oliver Johnson, Saikat Guha (arxiv.org)
We discuss properties of the "beamsplitter addition" operation, which provides a non-standard scaled convolution of random variables supported on the non-negative integers. We give a simple expression for the action of beamsplitter addition using generating functions. We use this to give a self-contained and purely classical proof of a heat equation and de Bruijn identity, satisfied when one of the variables is geometric.

👓 Artificial Intelligence suddenly got a whole lot more interesting | Ilyas Khan via Pulse | LinkedIn

Read Artificial Intelligence suddenly got a whole lot more interesting by Ilyas Kahn

Just over a year ago a senior Google engineer (Greg Corrado) explained why quantum computers, in the opinion of his research team did not lend themselves to Deep Learning techniques such as convolutional neural networks or even recurrent neural networks.

As a matter of fact, Corrado’s comments were specifically based on Google’s experience with the D-Wave machine, but as happens so often in the fast evolving Quantum Computing industry, the nuance that the then architecture and capacity of D-Wave’s quantum annealing methodology did not (and still does not) lend itself to Deep Learning or Deep Learning Neural Network (“DNN”) techniques was quickly lost in the headline. The most quoted part of Corrado’s comments became a sentence that further reinforced the view that Corrado (and thus Google) were negative about Deep Learning and Quantum Computing per-se and quickly became conflated to be true of all quantum machines and not just D-Wave :

“The number of parameters a quantum computer can hold, and the number of operations it can hold, are very small” (full article here).

The headline for the article that contained the above quote was “Quantum Computers aren’t perfect for Deep Learning“, that simply serves to highlight the less than accurate inference, and I have now lost count of the number of times that someone has misquoted Corrado or attributed his quote to Google’s subsidiary Deep Mind, as another way of pointing out limitations in quantum computing when it comes either to Machine Learning (“ML”) more broadly or Deep Learning more specifically.

Ironically, just a few months earlier than Corrado’s talk, a paper written by a trio of Microsoft researchers led by the formidable Nathan Wiebe (the paper was co-authored by his colleagues Ashish Kapoor and Krysta Svore) that represented a major dive into quantum algorithms for deep learning that would be advantageous over classical deep learning algorithms was quietly published on arXiv. The paper got a great deal less publicity than Corrado’s comments, and in fact even as I write this article more than 18 months after the paper’s v2 publication date, it has only been cited a handful of times (copy of most recent updated paper here)

Before we move on, let me deal with one obvious inconsistency between Corrado’s comments and the Wiebe/Kapoor/Svore (“WKS”) paper and acknowledge that we are not comparing “apples with apples”. Corrado was speaking specifically about the actual application of Deep Learning in the context of a real machine – the D-Wave machine, whilst WKS are theoretical quantum information scientists and their “efficient” algorithms need a machine before they can be applied. However, that is also my main point in the article. Corrado was speaking only about D-Wave, and Corrado is in fact a member of the Quantum Artificial Intelligence team, so it would be a major contradiction if Corrado (or Google more broadly) felt that Quantum Computing and AI were incompatible !

I am not here speaking only about the semantics of the name of Corrado’s team. The current home page, as of Nov 27th 2016, for Google’s Quantum AI Unit (based out in Venice Beach, LA) has the following statement (link to the full page here):

“Quantum Computing merges two great scientific revolutions of the 20th century: computer science and quantum physics. Quantum physics is the theoretical basis of the transistor, the laser, and other technologies which enabled the computing revolution. But on the algorithmic level today’s computing machinery still operates on “classical” Boolean logic. Quantum computing is the design of hardware and software that replaces Boolean logic by quantum law at the algorithmic level. For certain computations such as optimization, sampling, search or quantum simulation this promises dramatic speedups. Soon we hope to falsify the strong Church-Turing thesis: we will perform computations which current computers cannot replicate. We are particularly interested in applying quantum computing to artificial intelligence and machine learning. This is because many tasks in these areas rely on solving hard optimization problems or performing efficient sampling”

There is a lot to digest in that quote – including the tantalising statement about the strong “Church-Turing Thesis” (“CTT”). Coincidentally this is a very rich area of debate and research that if even trivially followed in this article would take up far more space than is available. For those interested in the foundational aspects of CTT you could do worse than invest a little time listening to the incomparable Scott Aaronson who spoke over summer on this topic (link here). And just a last word on CTT whilst we are on the subject, few, if anyone, will speculate right now that quantum computers will actually threaten the original Church-Turing Thesis and in the talk referenced above, Scott does a great job in outlining just why that is the case. Ironically the title of his talk is “Quantum Supremacy” and the quote that I have taken from Google’s website is directly taken from the team led by Hartmut Neven who has stated very publicly that Google will achieve that standard (ie Quantum Supremacy) in 2017.

Coming back to Artificial Intelligence and quantum computing, we should remember that even as recently as 14 to 18 months ago, most people would have been cautious about forecasting the advent of even small scale quantum computing. It is easy to forget, especially in the heady days since mid 2016, but none of Google, IBM or Microsoft had unveiled their advances, and as I wrote last week (here), things have clearly moved on very significantly in a relatively short space of time. Not only do we have an open “arms” race between the West and China to build a large scale quantum machine, but we have a serious clash of some of the most important technology innovators in recent times. Amazingly, scattered in the mix are a small handful of start-ups who are also building machines. Above all however, the main takeaway from all this activity from my point of view is that I don’t think it should be surprising that converting “black-box”neural network outputs into probability distributions will become the focus for anyone approaching DNN from a quantum physics and quantum computing background.

It is this significant advance that means that for the very same reason that Google/IBM/Microsoft talk openly about their plans to build a machine (and in the case of Google an acknowledgement that they have actually now built a quantum computer of their own) means that one of the earliest applications likely to be tested on even proto-type quantum computers will be some aspect of Machine Learning. Corrado was right to confirm that in the opinion of the Google team working at the time, the D-Wave machine was not usable for AI or ML purposes. It was not his fault that his comments were mis-reported. It is worth noting that one of the people most credibly seen as the “grandfather” of AI and Machine Learning, Geoffrey Hinton is part of the same team at Google that has adopted the Quantum Supremacy objective. There are clearly amazing teams assembled elsewhere, but where quantum computing meets Artificial Intelligence, then its hard to beat the sheer intellectual fire power of Google’s AI team.

Outside of Google, a nice and fairly simple way of seeing how the immediate boundary between the theory of quantum machine learning and its application on “real” machines has been eroded can be seen by looking at two versions of exactly the same talk by one of the sector’s early cheer leaders, Seth Lloyd. Here is a link to a talk that Lloyd gave through Google Tech Talks in early 2014, and here is a link to exactly the same talk except that it was delivered a couple of months ago. Not surprisingly Lloyd, as a theorist, brings a similar approach to the subject as WKS, but in the second of the two presentations, he also discusses one of his more recent pre-occupations in analysing large data sets using algebraic topological methods that can be manipulated by a quantum computer.

For those of you who might not be familiar with Lloyd I have included a link below to the most recent form of his talk on a quantum algorithm for large data sets represented by topological analysis.

One of the most interesting aspects that is illuminated by Lloyds position on quantum speed up using quantum algorithms for classical machine learning operations is his use of the example of the “Principal Component Analysis” algorithm (“PCA”). PCA is one of the most common machine learning techniques in classical computing, and Lloyd (and others) have been studying quantum computing versions for at least the past 3 to 4 years.

Finding a use case for a working quantum algorithm that can be implemented in a real use case such as one of the literally hundreds of applications for PCA is likely to be one of the earliest ways that quantum computers with even a limited number of qubits could be employed. Lloyd has already shown how a quantum algorithm can be proven to exhibit “speed up” when looking just at the number of steps taken in classifying the problem. I personally do not doubt that a suitable protocol will emerge as soon as people start applying themselves to a genuine quantum processor.

At Cambridge Quantum Computing, my colleagues in the quantum algorithm team have been working on the subject from a different perspective in both ML and DNN. The most immediate application using existing classical hardware has been from the guys that created ARROW> , where they have looked to build gradually from traditional ML through to DNN techniques for detecting and then classifying anomalies in “pure” times series (initially represented by stock prices). In the recent few weeks we have started advancing from ML to DNN, but the exciting thing is that the team has always looked at ARROW> in a way that lends itself to being potentially upgraded with possible quantum components that in turn can be run on early release smaller scale quantum processor. Using a team of quantum physicists to approach AI problems so they can ultimately be worked off a quantum computer clearly has some advantages.

There are, of course, a great many areas other than the seemingly trivial sphere of finding anomalies in share prices where AI will be applied. In my opinion the best recently published overview of the whole AI space (an incorporating the phase transition to quantum computing) is the Fortune Article (here) that appeared at the end of September and not surprisingly the focus on medical and genome related AI applications for “big” data driven deep learning applications figure highly in that part of the article that focuses on the current state of affairs.

I do not know exactly how far we are away from the first headlines about quantum processors being used to help generate efficiency in at least some aspects of DNN. My personal guess is that deep learning dropout protocols that help mitigate the over-fitting problem will be the first area where quantum computing “upgrades” are employed and I suspect very strongly that any machine that is being put through its paces at IBM or Google or Microsoft is already being designed with this sort of application in mind. Regardless of whether we are years away or months away from that first headline, the center of gravity in AI will have moved because of Quantum Computing.

Source: Artificial Intelligence suddenly got a whole lot more interesting | Ilyas Khan, KSG | Pulse | LinkedIn

🔖 A Physical Basis for the Second Law of Thermodynamics: Quantum Nonunitarity

Bookmarked A Physical Basis for the Second Law of Thermodynamics: Quantum Nonunitarity (arxiv.org)
It is argued that if the non-unitary measurement transition, as codified by Von Neumann, is a real physical process, then the "probability assumption" needed to derive the Second Law of Thermodynamics naturally enters at that point. The existence of a real, indeterministic physical process underlying the measurement transition would therefore provide an ontological basis for Boltzmann's Stosszahlansatz and thereby explain the unidirectional increase of entropy against a backdrop of otherwise time-reversible laws. It is noted that the Transactional Interpretation (TI) of quantum mechanics provides such a physical account of the non-unitary measurement transition, and TI is brought to bear in finding a physically complete, non-ad hoc grounding for the Second Law.
Download .pdf copy

🔖 H-theorem in quantum physics by G. B. Lesovik, et al.

Bookmarked H-theorem in quantum physics (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

[1]
G. B. Lesovik, A. V. Lebedev, I. A. Sadovskyy, M. V. Suslov, and V. M. Vinokur, “H-theorem in quantum physics,” Scientific Reports, vol. 6. Springer Nature, p. 32815, 12-Sep-2016 [Online]. Available: http://dx.doi.org/10.1038/srep32815

Tangled Up in Spacetime

Bookmarked Tangled Up in Spacetime by Clara MoskowitzClara Moskowitz (Scientific American)
Hundreds of researchers in a collaborative project called "It from Qubit" say space and time may spring up from the quantum entanglement of tiny bits of information.

🔖 Free download of Quantum Theory, Groups and Representations: An Introduction by Peter Woit

Bookmarked Final Draft of Quantum Theory, Groups and Representations: An Introduction by Peter Woit (Not Even Wrong | math.columbia.edu)
Peter Woit has just made the final draft (dated 10/25/16) of his new textbook Quantum Theory, Groups and Representations: An Introduction freely available for download from his website. It covers quantum theory with a heavy emphasis on groups and representation theory and “contains significant amounts of material not well-explained elsewhere.” He expects to finish up the diagrams and publish it next year some time, potentially through Springer.

I finally have finished a draft version of the book that I’ve been working on for the past four years or so. This version will remain freely available on my website here. The plan is to get professional illustrations done and have the book published by Springer, presumably appearing in print sometime next year. By now it’s too late for any significant changes, but comments, especially corrections and typos, are welcome.

At this point I’m very happy with how the book has turned out, since I think it provides a valuable point of view on the relation between quantum mechanics and mathematics, and contains significant amounts of material not well-explained elsewhere.

Peter Woit (), theoretical physicist, mathematician, professor Department of Mathematics, Columbia University
in Final Draft Version | Not Even Wrong

 

🔖 Quantum Information Science II

Bookmarked Quantum Information Science II (edX)
Learn about quantum computation and quantum information in this advanced graduate level course from MIT.

About this course

Already know something about quantum mechanics, quantum bits and quantum logic gates, but want to design new quantum algorithms, and explore multi-party quantum protocols? This is the course for you!

In this advanced graduate physics course on quantum computation and quantum information, we will cover:

  • The formalism of quantum errors (density matrices, operator sum representations)
  • Quantum error correction codes (stabilizers, graph states)
  • Fault-tolerant quantum computation (normalizers, Clifford group operations, the Gottesman-Knill Theorem)
  • Models of quantum computation (teleportation, cluster, measurement-based)
  • Quantum Fourier transform-based algorithms (factoring, simulation)
  • Quantum communication (noiseless and noisy coding)
  • Quantum protocols (games, communication complexity)

Research problem ideas are presented along the journey.

What you’ll learn

  • Formalisms for describing errors in quantum states and systems
  • Quantum error correction theory
  • Fault-tolerant quantum procedure constructions
  • Models of quantum computation beyond gates
  • Structures of exponentially-fast quantum algorithms
  • Multi-party quantum communication protocols

Meet the instructor

bio for Isaac ChuangIsaac Chuang Professor of Electrical Engineering and Computer Science, and Professor of Physics MIT

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

Publishing

Indieweb, Internet, Identity, Blogging, Social Media

General

My Review Copy of The Big Picture by Sean Carroll

I’m already a major chunk of the way through the book, having had an early ebook version of the text prior to publication. This is the published first edition with all the diagrams which I wanted to have prior to finishing my full review, which is forthcoming.

One thing I will mention is that it’s got quite a bit more philosophy in it than most popular science books with such a physics bent. Those who aren’t already up to speed on the math and science of modern physics can certainly benefit from the book (like most popular science books of its stripe, it doesn’t have any equations — hairy or otherwise), and it’s certain to help many toward becoming members of both of C.P. Snow’s two cultures. It might not be the best place for mathematicians and physicists to start moving toward the humanities with the included philosophy as the philosophy is very light and spotty in places and the explanations of the portions they’re already aware of may put them out a bit.

I’m most interested to see how he views complexity and thinking in the final portion of the text.

More detail to come…

Matter, energy… knowledge: How to harness physics’ demonic power | New Scientist

Bookmarked Matter, energy… knowledge: How to harness physics' demonic power (New Scientist)
Running a brain-twisting thought experiment for real shows that information is a physical thing – so can we now harness the most elusive entity in the cosmos?
This is a nice little overview article of some of the history of thermodynamics relating to information in physics and includes some recent physics advances as well. There are a few references to applications in biology at the micro level as well.

References

Forthcoming ITBio-related book from Sean Carroll: “The Big Picture: On the Origins of Life, Meaning, and the Universe Itself”

In catching up on blogs/reading from the holidays, I’ve noticed that physicist Sean Carroll has a forthcoming book entitled The Big Picture: On the Origins of Life, Meaning, and the Universe Itself (Dutton, May 10, 2016) that will be of interest to many of our readers. One can already pre-order the book via Amazon.

Prior to the holidays Sean wrote a blogpost that contains a full overview table of contents, which will give everyone a stronger idea of its contents. For convenience I’ll excerpt it below.

I’ll post a review as soon as a copy arrives, but it looks like a strong new entry in the category of popular science books on information theory, biology and complexity as well as potentially the areas of evolution, the origin of life, and physics in general.

As a side bonus, for those reading this today (1/15/16), I’ll note that Carroll’s 12 part lecture series from The Great Courses The Higgs Boson and Beyond (The Learning Company, February 2015) is 80% off.

The Big Picture

 

THE BIG PICTURE: ON THE ORIGINS OF LIFE, MEANING, AND THE UNIVERSE ITSELF

0. Prologue

* Part One: Cosmos

  • 1. The Fundamental Nature of Reality
  • 2. Poetic Naturalism
  • 3. The World Moves By Itself
  • 4. What Determines What Will Happen Next?
  • 5. Reasons Why
  • 6. Our Universe
  • 7. Time’s Arrow
  • 8. Memories and Causes

* Part Two: Understanding

  • 9. Learning About the World
  • 10. Updating Our Knowledge
  • 11. Is It Okay to Doubt Everything?
  • 12. Reality Emerges
  • 13. What Exists, and What Is Illusion?
  • 14. Planets of Belief
  • 15. Accepting Uncertainty
  • 16. What Can We Know About the Universe Without Looking at It?
  • 17. Who Am I?
  • 18. Abducting God

* Part Three: Essence

  • 19. How Much We Know
  • 20. The Quantum Realm
  • 21. Interpreting Quantum Mechanics
  • 22. The Core Theory
  • 23. The Stuff of Which We Are Made
  • 24. The Effective Theory of the Everyday World
  • 25. Why Does the Universe Exist?
  • 26. Body and Soul
  • 27. Death Is the End

* Part Four: Complexity

  • 28. The Universe in a Cup of Coffee
  • 29. Light and Life
  • 30. Funneling Energy
  • 31. Spontaneous Organization
  • 32. The Origin and Purpose of Life
  • 33. Evolution’s Bootstraps
  • 34. Searching Through the Landscape
  • 35. Emergent Purpose
  • 36. Are We the Point?

* Part Five: Thinking

  • 37. Crawling Into Consciousness
  • 38. The Babbling Brain
  • 39. What Thinks?
  • 40. The Hard Problem
  • 41. Zombies and Stories
  • 42. Are Photons Conscious?
  • 43. What Acts on What?
  • 44. Freedom to Choose

* Part Six: Caring

  • 45. Three Billion Heartbeats
  • 46. What Is and What Ought to Be
  • 47. Rules and Consequences
  • 48. Constructing Goodness
  • 49. Listening to the World
  • 50. Existential Therapy
  • Appendix: The Equation Underlying You and Me
  • Acknowledgments
  • Further Reading
  • References
  • Index

Source: Sean Carroll | The Big Picture: Table of Contents

Quantum Biological Information Theory by Ivan B. Djordjevic | Springer

Bookmarked Quantum Biological Information Theory (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

9783319228150I’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.

The Information Universe Conference

Yesterday, via a notification from Lanyard, I came across a notice for the upcoming conference “The Information Universe” which hits several of the sweet spots for areas involving information theory, physics, the origin of life, complexity, computer science, and microbiology. It is scheduled to occur from October 7-9, 2015 at the Infoversum Theater in Groningen, The Netherlands.

I’ll let their site speak for itself below, but they already have an interesting line up of speakers including:

Keynote speakers

  • Erik Verlinde, Professor Theoretical Physics, University of Amsterdam, Netherlands
  • Alex Szalay, Alumni Centennial Professor of Astronomy, The Johns Hopkins University, USA
  • Gerard ‘t Hooft, Professor Theoretical Physics, University of Utrecht, Netherlands
  • Gregory Chaitin, Professor Mathematics and Computer Science, Federal University of Rio de Janeiro, Brasil
  • Charley Lineweaver, Professor Astronomy and Astrophysics, Australian National University, Australia
  • Lude Franke, Professor System Genetics, University Medical Center Groningen, Netherlands
Infoversum Theater, The Netherlands
Infoversum Theater, The Netherlands

Conference synopsis from their homepage:

The main ambition of this conference is to explore the question “What is the role of information in the physics of our Universe?”. This intellectual pursuit may have a key role in improving our understanding of the Universe at a time when we “build technology to acquire and manage Big Data”, “discover highly organized information systems in nature” and “attempt to solve outstanding issues on the role of information in physics”. The conference intends to address the “in vivo” (role of information in nature) and “in vitro” (theory and models) aspects of the Information Universe.

The discussions about the role of information will include the views and thoughts of several disciplines: astronomy, physics, computer science, mathematics, life sciences, quantum computing, and neuroscience. Different scientific communities hold various and sometimes distinct formulations of the role of information in the Universe indicating we still lack understanding of its intrinsic nature. During this conference we will try to identify the right questions, which may lead us towards an answer.

  • Is the universe one big information processing machine?
  • Is there a deeper layer in quantum mechanics?
  • Is the universe a hologram?
  • Is there a deeper physical description of the world based on information?
  • How close/far are we from solving the black hole information paradox?
  • What is the role of information in highly organized complex life systems?
  • The Big Data Universe and the Universe : are our numerical simulations and Big Data repositories (in vitro) different from real natural system (in vivo)?
  • Is this the road to understanding dark matter, dark energy?

The conference will be held in the new 260 seats planetarium theatre in Groningen, which provides an inspiring immersive 3D full dome display, e.g. numerical simulations of the formation of our Universe, and anything else our presenters wish to bring in. The digital planetarium setting will be used to visualize the theme with modern media.

The Information Universe Website

Additional details about the conference including the participants, program, venue, and registration can also be found at their website.

String Theory, Black Holes, and Information

Four decades ago, Stephen Hawking posed the black hole information paradox about black holes and quantum theory. It still challenges the imaginations of theoretical physicists today. Yesterday, Amanda Peet (University of Toronto) presented the a lecture entitled “String Theory Legos for Black Holes” yesterday at the Perimeter Institute for Theoretical Physics. A quick overview/teaser trailer for the lecture follows along with some additional information and the video of the lecture itself.

The “Information Paradox” with Amanda Peet (teaser trailer)

“Black holes are the ‘thought experiment’ par excellence, where the big three of physics – quantum mechanics, general relativity and thermodynamics – meet and fight it out, dragging in brash newcomers such as information theory and strings for support. Though a unification of gravity and quantum field theory still evades string theorists, many of the mathematical tools and ideas they have developed find applications elsewhere.

One of the most promising approaches to resolving the “information paradox” (the notion that nothing, not even information itself, survives beyond a black hole’s point-of-no-return event horizon) is string theory, a part of modern physics that has wiggled its way into the popular consciousness.

On May 6, 2015, Dr. Amanda Peet, a physicist at the University of Toronto, will describe how the string toolbox allows study of the extreme physics of black holes in new and fruitful ways. Dr. Peet will unpack that toolbox to reveal the versatility of strings and (mem)branes, and will explore the intriguing notion that the world may be a hologram.

Amanda Peet Amanda Peet is an Associate Professor of Physics at the University of Toronto. She grew up in the South Pacific island nation of Aotearoa/New Zealand, and earned a B.Sc.(Hons) from the University of Canterbury in NZ and a Ph.D. from Stanford University in the USA. Her awards include a Radcliffe Fellowship from Harvard and an Alfred P. Sloan Foundation Research Fellowship. She was one of the string theorists interviewed in the three-part NOVA PBS TV documentary “Elegant Universe”.

Web site: http://ap.io/home/.

Dr. Amanda Peet’s Lecture “String Theory Legos for Black Holes”