Johnny Logic

The Sounds of Sorting

John L. Taylor — Wed, 01 Sep 2010 19:48:43 +0000

This video provides a pretty intuitive visualization and audibilization of different sorting algorithms (insert sort, bubble sort, selection sort, merge sort, gnome sort). Even without explaining the algorithms with pseudo-code, or the like, I daresay one can get a decent sense of how they work from this:

Bookmarks for May 27th through July 28th

John L. Taylor — Wed, 28 Jul 2010 18:00:42 +0000

These are my links for May 27th through July 28th:

Statistical Modeling: The Two Cultures – There are two cultures in the use of statistical modeling to reach conclusions from data. One assumes that the data are generated by a given stochastic data model. The other uses algorithmic models and treats the data mechanism as unknown. The statistical community has been committed to the almost exclusive use of data models. This commitment

has led to irrelevant theory, questionable conclusions, and has kept statisticians from working on a large range of interesting current problems. Algorithmic modeling, both in theory and practice, has developed rapidly in fields outside statistics. It can be used both on large complex data sets and as a more accurate and informative alternative to data modeling on smaller data sets. If our goal as a field is to use data to solve problems, then we need to move away from exclusive dependence on data models and adopt a more diverse set of tools.
Brief history of data visualization – Data visualization is a pretty literal term that means, quite simply, the visual representation of quantitative data. In this course we’ll learn common techniques for visualizing data, as well as some strategies for managing information digitally. But first, a brief history.
S. Thompson. Motif-index of folk-literature – a classification of narrative elements in folktales, ballads, myths, fables, mediaeval romances, exempla, fabliaux, jest-books, and local legends.
What is data science? – O’Reilly Radar – We’ve all heard it: according to Hal Varian, statistics is the next sexy job. Five years ago, in What is Web 2.0, Tim O’Reilly said that “data is the next Intel Inside.” But what does that statement mean? Why do we suddenly care about statistics and about data?

In this post, I examine the many sides of data science — the technologies, the companies and the unique skill sets.
[1005.0437] A Unifying View of Multiple Kernel Learning – Recent research on multiple kernel learning has lead to a number of approaches for combining kernels in regularized risk minimization. The proposed approaches include different formulations of objectives and varying regularization strategies. In this paper we present a unifying general optimization criterion for multiple kernel learning and show how existing formulations are subsumed as special cases. We also derive the criterion’s dual representation, which is suitable for general smooth optimization algorithms. Finally, we evaluate multiple kernel learning in this framework analytically using a Rademacher complexity bound on the generalization error and empirically in a set of experiments.

Food on the Inside

John L. Taylor — Mon, 19 Jul 2010 05:33:49 +0000

Beautiful MRI imagery of food, from Inside Insides:

Love and Tensor Algebra

John L. Taylor — Sat, 10 Jul 2010 05:41:52 +0000

from “The Cyberiad” by Stanislaw Lem:

Come, let us hasten to a higher plane,
Where dyads tread the fairy fields of Venn,
Their indices bedecked from one to n,
Commingled in an endless Markov chain!

Come, every frustum longs to be a cone,
And every vector dreams of matrices.
Hark to the gentle gradient of the breeze:
It whispers of a more ergodic zone.

In Riemann, Hilbert or in Banach space
Let superscripts and subscripts go their ways.
Our asymptotes no longer out of phase,
We shall encounter, counting, face to face.

I’ll grant thee random access to my heart,
Thou’lt tell me all the constants of thy love;
And so we two shall all love’s lemmas prove,
And in our bound partition never part.

For what did Cauchy know, or Christoffel,
Or Fourier, or any Boole or Euler,
Wielding their compasses, their pens and rulers,
Of thy supernal sinusoidal spell?

Cancel me not–for what then shall remain?
Abscissas, some mantissas, modules, modes,
A root or two, a torus and a node:
The inverse of my verse, a null domain.

Ellipse of bliss, converge, O lips divine!
The product of our scalars is defined!
Cyberiad draws nigh, and the skew mind
Cuts capers like a happy haversine.

I see the eigenvalue in thine eye,
I hear the tender tensor in thy sigh.
Bernoulli would have been content to die,
Had he but known such a2 cos 2 phi!

17th Poet Laureate Announced

John L. Taylor — Fri, 02 Jul 2010 16:45:34 +0000

We have a new poet laureate, W.S. Merwin. Here is one of his:

Separation

Your absence has gone through me
Like thread through a needle.
Everything I do is stitched with its color.

and another:

Rain Light

All day the stars watch from long ago
my mother said I am going now
when you are alone you will be all right
whether or not you know you will know
look at the old house in the dawn rain
all the flowers are forms of water
the sun reminds them through a white cloud
touches the patchwork spread on the hill
the washed colors of the afterlife
that lived there long before you were born
see how they wake without a question
even though the whole world is burning

Lovely.

Persistence of Homology

John L. Taylor — Thu, 24 Jun 2010 00:32:59 +0000

I recently started reading Topology for Computing by Afra J. Zomorodian, and before it launched into its admirably lucid explanation of topology, group theory and the like, it featured a clever illustration by the author:

Bookmarks for May 27th from 02:21 to 09:21

John L. Taylor — Thu, 27 May 2010 18:01:20 +0000

These are my links for May 27th from 02:21 to 09:21:

Introduction to Graphical Modelling – The aim of this chapter is twofold. In the first part we will provide a brief overview of the mathematical and statistical foundations of graphical models, along with their fundamental properties, estimation and basic inference procedures. In particular we will develop Markov networks (also known as Markov random fields) and Bayesian networks, which comprise most past and current literature on graphical models. In the second part we will review some applications of graphical models in systems biology.
[1005.0437] A Unifying View of Multiple Kernel Learning – Recent research on multiple kernel learning has lead to a number of approaches for combining kernels in regularized risk minimization. The proposed approaches include different formulations of objectives and varying regularization strategies. In this paper we present a unifying general optimization criterion for multiple kernel learning and show how existing formulations are subsumed as special cases. We also derive the criterion's dual representation, which is suitable for general smooth optimization algorithms. Finally, we evaluate multiple kernel learning in this framework analytically using a Rademacher complexity bound on the generalization error and empirically in a set of experiments.
Introduction to Graphical Modelling – The aim of this chapter is twofold. In the first part we will provide a brief overview of the mathematical and statistical foundations of graphical models, along with their fundamental properties, estimation and basic inference procedures. In particular we will develop Markov networks (also known as Markov random fields) and Bayesian networks, which comprise most past and current literature on graphical models. In the second part we will review some applications of graphical models in systems biology.
Project Euler – Project Euler is a series of challenging mathematical/computer programming problems that will require more than just mathematical insights to solve. Although mathematics will help you arrive at elegant and efficient methods, the use of a computer and programming skills will be required to solve most problems.

Bookmarks for May 4th through May 14th

John L. Taylor — Sat, 15 May 2010 00:04:24 +0000

These are my links for May 4th through May 14th:

[1005.1320] The myth of equidistribution for high-dimensional simulation – A pseudo-random number generator (RNG) might be used to generate w-bit random samples in d dimensions if the number of state bits is at least dw. Some RNGs perform better than others and the concept of equidistribution has been introduced in the literature in order to rank different RNGs. We define what it means for a RNG to be (d,w)-equidistributed, and then argue that (d,w)-equidistribution is not necessarily a desirable property.
[1005.1327] Statistical Model Checking : An Overview – Quantitative properties of stochastic systems are usually specified in logics that allow one to compare the measure of executions satisfying certain temporal properties with thresholds. The model checking problem for stochastic systems with respect to such logics is typically solved by a numerical approach that iteratively computes (or approximates) the exact measure of paths satisfying relevant subformulas; the algorithms themselves depend on the class of systems being analyzed as well as the logic used for specifying the properties. Another approach to solve the model checking problem is to \emph{simulate} the system for finitely many runs, and use \emph{hypothesis testing} to infer whether the samples provide a \emph{statistical} evidence for the satisfaction or violation of the specification. In this short paper, we survey the statistical approach, and outline its main advantages in terms of efficiency, uniformity, and simplicity.
Untangling the Quantum Entanglement Behind Photosynthesis: Berkeley scientists shine new light on green plant secrets « Berkeley Lab News Center – The future of clean green solar power may well hinge on scientists being able to unravel the mysteries of photosynthesis, the process by which green plants convert sunlight into electrochemical energy. To this end, researchers with the U.S. Department of Energy (DOE)’s Lawrence Berkeley National Laboratory (Berkeley Lab) and the University of California (UC), Berkeley have recorded the first observation and characterization of a critical physical phenomenon behind photosynthesis known as quantum entanglement.

Bookmarks for April 26th through April 30th

John L. Taylor — Fri, 30 Apr 2010 20:00:39 +0000

These are my links for April 26th through April 30th:

DoCIS: Documents in Computer and Library & Information Science – DoCIS is a service of the rclis digital library. rclis is dedicated to promoting free access to data about documents in computing and library and information science.DoCIS provides an integrated browsing/searching interface to rclis data. To start browsing our collection, please look at the list of journals and conference proceedings that we cover.
See our service principles and our internal documentation for details.
Mathematical Problems by David Hilbert – The supply of problems in mathematics is inexhaustible, and as soon as one problem is solved numerous others come forth in its place. Permit me in the following, tentatively as it were, to mention particular definite problems, drawn from various branches of mathematics, from the discussion of which an advancement of science may be expected.
Let us look at the principles of analysis and geometry. The most suggestive and notable achievements of the last century in this field are, as it seems to me, the arithmetical formulation of the concept of the continuum in the works of Cauchy, Bolzano and Cantor, and the discovery of non-euclidean geometry by Gauss, Bolyai, and Lobachevsky. I therefore first direct your attention to some problems belonging to these fields.
Institute of Mathematical Statistics Lecture Notes – Monograph Series – Free collection of mathematical statistics monographs.
MathFiction – Of the many works of fiction that are published, very few involve mathematics or mathematicians. However, people who like mathematics (or are mathematicians ourselves) may especially enjoy reading those few that do. Moreover, as I argue in an article in the AMS Notices, mathematicians should be interested in these works of “mathematical fiction” even if we do not enjoy them because they both affect and reflect the non-mathematician’s view of this subject.

A Turing Machine, IRLish

John L. Taylor — Mon, 26 Apr 2010 16:13:07 +0000

A functioning Turing machine! OK, it doesn’t have an indefinitely extensible tape, but you get the idea.