### Syndications of Interest

Christopher Olah's Blog

- Deep Learning, NLP, and Representations 2014-07-08In the last few years, deep neural networks have dominated pattern recognition. They blew the previous state of the art out of the water for many computer vision tasks. Voice recognition is also moving that way. But despite the results, we have to wonder… why do they work so well? This post reviews some extremely […]colah
- Fanfiction, Graphs, and PageRank 2014-07-07On a website called fanfiction.net, users write millions of stories about their favorite stories. They have diverse opinions about them. They love some stories, and hate others. The opinions are noisy, and it’s hard to see the big picture. With tools from mathematics and some helpful software, however, we can visualize the underlying structure. […]colah
- Neural Networks, Manifolds, and Topology 2014-04-09Recently, there’s been a great deal of excitement and interest in deep neural networks because they’ve achieved breakthrough results in areas such as computer vision. However, there remain a number of concerns about them. One is that it can be quite challenging to understand what a neural network is really doing. If one trains it well, it […]colah
- Visualizing Functions On Groups 2014-01-16Functions of the form or , where is a group, arise in lots of contexts. One very natural way this can happen is to have a probability distribution on a group, . The probability density of group elements is a function . Another way this can happen is if you have some function and has […]colah
- The Death of a Squirrel 2013-08-25(Trigger warning: descriptions of severe animal injury.) Today a squirrel was hit by a car a few feet away from me while I was walking down the side walk. Three of its legs kept twitching. I thought it had a broken leg. I came out of my stupor and went to grab it and pull […]colah
- Order Statistics 2013-08-16What is the distribution of the maximum of random variables? What started out a utilitarian question in my exploration of some generalized versions of the secretary problem turns out to be quite a deep topic. (Note that I have little background in probability and statistics. Please forgive (and inform me of, so I can fix!) […]colah
- Topology Notes 2013-06-14I’ve been talking about writing a topology textbook introductory notes on topology for years. Basically since I wrote my Rethinking Topology (or a Personal Topologodicy) post 2 years ago — it’s hard to believe it’s been that long! In any case, I finally started writing it. I’ve done a mild review of existing introductions to general topology (ie. I […]colah
- How My Neural Net Sees Blackboards (Part 2) 2013-06-09Previously, I discussed training a neural net to clean up images. I’m pleased to say that, using more sophisticated techniques, I’ve since achieved much better results. My latest approach is a four layer convolutional network. Sadly, the convolution throws away the sides of the images, so we get a black margin. In any case, compare […]colah
- I’m Sick and Tired of 3D Printed Guns 2013-05-29For the last few months, every time someone hears that I work with 3D printers they bring up 3D printed guns. I can’t say how many times it has happened in this month alone. And I’m getting really really tired of it. “They’re the killer app of 3D printers.” What a great pun. You don’t know […]colah
- How My Neural Net Sees Blackboards 2013-05-11For the last few weeks, I’ve been taking part in a small weekly neural net study group run by Michael Nielsen. It’s been really awesome! Neural nets are very very cool! They’re so cool, I had to use them somehow. Having been interested in mathematical handwriting recognition for a long time, I decided to train […]colah

Creative Commons

- Panel: A New Era of Open? COVID-19 and the Pursuit for Equitable Solutions 2021-02-25In response to the COVID-19 pandemic, Creative Commons published an article titled, “Now Is the Time for Open Access Policies—Here’s Why” in March 2020. A lot has changed since then and it’s important to assess the progress made and take a hard look at the dangers ahead. In this panel, we’ll examine the fields of […]Victoria Heath
- Open Minds: Celebrating Smithsonian Open Access With Effie Kapsalis 2021-02-24In two days, the Smithsonian will celebrate one year of Smithsonian Open Access. This initiative removed copyright restrictions from 2.8 million digital collection 2D and 3D images and nearly two centuries of data using Creative Commons’ public domain dedication tool (CC0). Launched just before many of us went into lockdown due to COVID-19, Smithsonian Open […]Victoria Heath
- Announcing Our New Podcast: “Open Minds … from Creative Commons” 2021-02-19Today we’re excited to launch a new podcast called Open Minds … from Creative Commons. It’s CC’s 20th anniversary this year. And to celebrate, we decided to launch this show, a series of conversations with people working on the issues we’re involved with and excited about. Expect Open Minds to feature folks from the worlds of […]Eric Steuer
- Save the Date for the 2021 CC Summit! 2021-02-16We’ve grown the CC Global Summit every year, with over 1300 participants and 200 presenters joining us in 2020 for discussion and debate, workshops and planning, talks and community building. After consulting with our community, we’re excited to build on the success of last year’s virtual event and host the second-ever virtual CC Global Summit […]Alison Pearce
- Meet CC South Africa, Our Next Feature for CC Network Fridays! 2021-02-12After introducing the CC Italy Chapter to you in July, the CC Netherlands Chapter in August, CC Bangladesh Chapter in September, CC Tanzania Chapter in October, and the CC India Chapter in November, the CC Mexico Chapter in December, and CC Argentina Chapter in January, we are now travelling to Africa to introduce the CC […]Julia Brungs
- Still Life: Art That Brings Comfort in Uncertain Times 2021-02-11There is a quiet, familiar beauty found in still life, a type of art that depicts primarily inanimate objects, like animals, food, or flowers. These comforting images offer a sense of certainty and simplicity in uncertain and complex times. This could explain why over six million Instagram users have fallen in love with still life […]Catherine Stihler
- Open Sharing Is Caring: A Valentine’s Day Challenge 2021-02-10February is the time to share virtual hugs, chocolates, and witty cards with family and friends for Valentine’s Day ♥️ (or “Friend’s Day” in Finland!) This Valentine’s Day, we want you to share something a little different: your creative work. In our Open Sharing is Caring challenge, we’re asking you to openly share an image, song, artwork, research paper, poem, GIF…whatever it […]Victoria Heath
- A Snapshot in Time: A Look at the Creative Commons Global Network 2021-02-10In 2017, the structure of the Creative Commons Global Network (CCGN) was finalized. After two years of implementing structural changes flowing from this, it felt timely to have a conversation with CCGN members. We wanted to gather feedback and carry out research on the perspectives of network members, at a specific point in time. What […]Anna Tumadóttir
- The Postal Worker, a Sea Shanty and the Public Domain 2021-02-03Until recently, I had never heard of the sea shanty “The Wellerman”. My sea shanty repertoire consisted of “What can you do with a drunken sailor” to sea-songs on the soundtrack of Master and Commander. However, Nathan Evans, a fellow Scot who hails, like me, from North Lanarkshire, has changed all of this. His rendition […]Catherine Stihler
- Say Hello to CC Belgium! 2021-01-29We are happy to introduce CC Belgium—the new CC Chapter in the heart of Europe. We have been running as an informal chapter for more than 10 years with different people as Chapter Leads. For several years, a team led by Severine Dussolier from CRID at the University of Namur, stewarded the translations of the […]Victoria Heath

Featured Blog Posts – Data Science Central

- The Beginner Guide for Creating a Multi-Vendor eCommerce Website 2021-02-26An online marketplace is a good idea to make your business successful and profitable. With this growing technology, the number of customers who make purchases online is increasing every year. Due to this, the eCommerce industry is ready to expand…Nikunj Shingala
- Give Your Business Users Simple Augmented Analytics 2021-02-26When you launch an analytics solution within your enterprise, you are probably concerned about getting your business users to adopt that solution. If you can’t engage the business user and achieve user adoption, your return on investment (ROI) will be poor! But, it is important to understand that the right augmented analytics solution can provide […]Kartik Patel
- Levels of Measurement (Nominal, Ordinal, Interval, Ratio) in Statistics 2021-02-26Image Source: Statistical Aid: A School of Statistics Definition In statistics, the statistical…Muhammad Touhidul Islam
- The Ethereum Virtual Machine (EVM) 2021-02-25Vitalik Buterin (https://vitalik.ca) conceptualized Ethereum (https://ethereum.org) in November, 2013. The core idea proposed was the development of a Turing-complete language that allows the development of arbitrary programs (smart contracts) for blockchain and…Monika Sangwan
- Increasing Adoption of Informatics will Promote Growth of Data Analytics Outsourcing Market 2021-02-25Data analytics tools empower associations to settle on better choices, increment effectiveness, decrease operational expenses, give modified contributions, and improve client administrations. Various organizations favor utilizing information investigation to examine huge measure of information through different quantitative and subjective strategies…Pragati Pa
- The Education Industrial Complex: The Hammer We Have 2021-02-24In a recent NY Times feature article, Noam Scheiber provided a pretty thorough picture of the mid-to-longer term economic challenges we’re facing and some of the alternative policies that the Biden administration may pursue to address them. The most important forces driving…Howard M Wiener
- DSC Weekly Digest 22 Feb 2021 2021-02-22 Kurt A Cagle
- How AI is Modernizing the Collections Process 2021-02-22Debt levels are rising and borrowers are increasingly unable to pay off the debts. The Covid-19 pandemic has not helped and there is a high risk of delinquency when it comes to types of credit, from business loans to mortgages. Traditional strategies are no longer enough to collect…Charlie Svensson
- Plug n' Play Predictive Analysis for Business User Data Prototyping 2021-02-22Whether your business is a small, single location brick and mortar enterprise or a large, multi-facility organization that spans the global market, you need access to sophisticated, easy-to-use business intelligence tools in order to compete in local, regional and global markets. When organizations undertake the process of researching and…Kartik Patel
- How to Modernize Enterprise Data and Analytics Platform (Part 1 of 4) 2021-02-22Data and Analytics Platform is a sub platform of the Enterprise Digital Business Technology Platform. It contains information management and analytical capabilities.…Alaa Mahjoub
- Benefits of Writing as a Hobby 2021-02-22Writing can be a tall order for anyone. Most people end up writing because they have no other option. However, if you treat it as a hobby, it takes away all the pressure. If your take writing is one of your hobbies, you will reap many benefits from it. Some of the benefits include: Be […]Yuly Olofsson
- 4 ways Cryptocurrency is Benefiting the Fintech Industry 2021-02-22In 2015, the World Economic Forum estimated the net worth of blockchain to be approximately US$ 20 billion. To ensure maximum security of…John Murphy
- Modernizing Data Dashboards. 2021-02-22Modernizing is critical to apply the latest technologies and practices to address areas where users are less than satisfied and data trust needs to be higher. In this article, learn about modernizing data visualization with dashboards and reports. Following…Technovert Solutions
- A Plethora of Machine Learning Articles: Part 1 2021-02-21Source: see here In Part 1 of this short series, I have included the most interesting articles that I wrote in the last few years. This part focuses on the business analytics / BI /…Vincent Granville
- The Bayesian vs frequentist approaches: Implications for machine learning – Part One 2021-02-21Background The arguments / discussions between the Bayesian vs frequentist approaches in statistics are long running. I am interested in how these approaches impact machine learning. Often, books on machine learning combine the two approaches, or in some cases, take only one approach. This does not help from a learning…ajit jaokar
- 1-Year Anniversary of the COVID Stock Market Crash 2021-02-21Those that encounter my blogs might notice two distinct types: 1) blogs that I formally prepare almost like an essay; and 2) those that are "unplugged" or informally prepared rather like a personal journal entry. The mystique of writing something where I don't exactly know the…Don Philip Faithful
- Why you need Data Quality Management for your business? 2021-02-19Data is the driving force of every organization in the modern world. As organizations continue to collect more and more data, the need to manage the quality of the data becomes more prominent each day. Data Quality Management can be defined as a set of practices undertaken by a data manager or a data organization […]Indhu
- Not Everything Needs to be “AI” 2021-02-19Rohit Prasad, head scientist for Alexa, recently published an article questioning whether the Turing Test is still a relevant benchmark for…Paul Barba
- Cloud Computing: Its Impact on the Financial Sector 2021-02-18Cloud computing may be a comparatively recent arrival on the scene. Nonetheless, it has managed to become quite the hit in the market. While it has found a plethora of specific applications across the broad spectrum of industries globally, it is this technology’s potential in the context of the financial sector that has been the […]Ryan Williamson
- Connecting RStudio To Amazon Redshift 2021-02-18In this document, we will discuss about the steps to be followed along with the necessary libraries and code chunks needed to establish the connectivity from R to S3 using aws roles and between R and Redshift using jdbc drivers. This steps will even work when the S3 and RStudio are in two different AWS […]Syed Abdul Sathar A

Planet Sage

- Sébastien Labbé: Tiling a polyomino with polyominoes in SageMath 2020-12-03Suppose that you 3D print many copies of the following 3D hexo-mino at home: sage: from sage.combinat.tiling import Polyomino, TilingSolver sage: p = Polyomino([(0,0,0), (0,1,0), (1,0,0), (2,0,0), (2,1,0), (2,1,1)], color='blue') sage: p.show3d() Launched html viewer for Graphics3d Object You would like to know if you can tile a larger polyomino or in particular a rectangular […]
- William Stein: DataDog: Don't make the same mistake I did -- a followup and thoughts about very unhappy customers 2020-04-13This is a followup to my previous blog post about DataDog billing. TL;DR:- I don't recommend DataDog,- dealing with unhappy customers is hard,- monitoring for data science nerds?Hacker News CommentsDataDog at Google Cloud SummitI was recently at the Seattle Google Cloud Summit and DataDog was well represented, with the biggest booth and top vendor billing […]
- Sébastien Labbé: Computer experiments for the Lyapunov exponent for MCF algorithms when dimension is larger than 3 2020-03-27In November 2015, I wanted to share intuitions I developped on the behavior of various distinct Multidimensional Continued Fractions algorithms obtained from various kind of experiments performed with them often involving combinatorics and digitial geometry but also including the computation of their first two Lyapunov exponents. As continued fractions are deeply related to the combinatorics […]

Yet Another Mathblog

- Quartic graphs with 12 vertices 2020-10-13This is a continuation of the post A table of small quartic graphs. As with that post, it’s modeled on the handy wikipedia page Table of simple cubic graphs. According to SageMath computations, there are 1544 connected, 4-regular graphs. Exactly 2 of these are symmetric (ie, arc transitive), also vertex-transitive and edge-transitive. Exactly 8 of these are […]wdjoyner
- A footnote to Robert H. Mountjoy 2020-08-27In an earlier post titled Mathematical romantic? I mentioned some papers I inherited of one of my mathematical hero’s Andre Weil with his signature. In fact, I was fortunate enough to go to dinner with him once in Princeton in the mid-to-late 1980s – a very gentle, charming person with a deep love of mathematics. […]wdjoyner
- The Riemann-Hurwitz formula for regular graphs 2020-08-21A little over 10 years ago, M. Baker and S. Norine (I’ve also seen this name spelled Norin) wrote a terrific paper on harmonic morphisms between simple, connected graphs (see “Harmonic morphisms and hyperelliptic graphs” – you can find a downloadable pdf on the internet of you google for it). Roughly speaking, a harmonic function […]wdjoyner
- The number-theoretic side of J. Barkley Rosser 2020-08-13By chance, I ran across a reference to a paper of J Barkey Rosser and it brought back fond memories of days long ago when I would browse the stacks in the math dept library at the University of Washington in Seattle. I remember finding papers describing number-theoretic computations of Rosser and Schoenfeld. I knew […]wdjoyner
- A table of small quartic graphs 2020-07-02This page is modeled after the handy wikipedia page Table of simple cubic graphs of “small” connected 3-regular graphs, where by small I mean at most 11 vertices. These graphs are obtained using the SageMath command graphs(n, [4]*n), where n = 5,6,7,… . 5 vertices: Let denote the vertex set. There is (up to isomorphism) […]wdjoyner
- Harmonic morphisms from cubic graphs of order 8 to a graph of order 4 2020-06-08There are five simple cubic graphs of order 8 (listed here) and there are 6 connected graphs of order 4 (listed here). But before we get started, I have a conjecture. Let be a simple graph on n1 vertices, a simple graph on n2 vertices, and assume there is a harmonic morphism . Call an […]wdjoyner
- Duursma zeta function of a graph 2020-05-28I’m going to start off with two big caveats: This is not Duursma‘s definition, it’s mine. I’m not convinced (yet?) that it’s a useful idea to examine such a zeta function. So that’s your warning – you may be wasting your time reading this! The Duursma zeta function of a linear block (error-correcting) code is […]wdjoyner
- Harmonic morphisms to D_3 – examples 2020-05-01This post expands on a previous post and gives more examples of harmonic morphisms to the tree . This graph is also called a star graph on 3+1=4 vertices, or the bipartite graph . We indicate a harmonic morphism by a vertex coloring. An example of a harmonic morphism can be described in the plot […]wdjoyner
- NCF Boolean functions 2020-04-20I recently learned about a new class of seemingly complicated, but in fact very simple functions which are called by several names, but perhaps most commonly as NCF Boolean functions (NCF is an abbreviation for “nested canalyzing function,” a term used by mathematical biologists). These functions were independently introduced by theoretical computer scientists in the […]wdjoyner
- Expected maximums and fun with Faulhaber’s formula 2020-03-28A recent Futility Closet post inspired this one. There, Greg Ross mentioned a 2020 paper by P Sullivan titled “Is the Last Banana Game Fair?” in Mathematics Teacher. (BTW, it’s behind a paywall and I haven’t seen that paper). Suppose Alice and Bob don’t want to share a banana. They each have a fair 6-sided […]wdjoyner

What's all this, then?

- Voting power (7): Quarreling voters 2021-01-23In all the previous discussions of voting power, we have assumed that all winning coalitions are equally likely. But in practice that is not necessarily the case. Two or more voters may be opposed on so many issues that they would never vote the same way on any issues: such a pair of voters may […]
- Voting power (6): Polynomial rings 2021-01-21As we have seen previously, it's possible to compute power indices by means of polynomial generating functions. We shall extend previous examples to include the Deegan-Packel index, in a way somewhat different to that of Alonso-Meijide et al (see previous post for reference). Again, suppose we consider the voting game \[ [30;28,16,5,4,3,3] \] What we'll […]
- Voting power (5): The Deegan-Packel and Holler power indices 2021-01-13We have explored the Banzhaf and Shapley-Shubik power indices, which both consider the ways in which any voter can be pivotal, or critical, or necessary, to a winning coalition. A more recent power index, which takes a different approach, was defined by Deegan and Packel in 1976, and considers only minimal winning coalitions. A winning […]
- Three-dimensional impossible CAD 2021-01-09Recently I friend and I wrote a semi-serious paper called "The geometry of impossible objects" to be delivered at a mathematics technology conference. The reviewer was not hugely complimentary, saying that there was nothing new in the paper. Well, maybe not, but we had fun pulling together some information about impossible shapes and how to […]
- Voting power (4): Speeding up the computation 2021-01-05Introduction and recapitulation Recall from previous posts that we have considered two power indices for computing the power of a voter in a weighted system; that is, the ability of a voter to influence the outcome of a vote. Such systems occur when the voting body is made up of a number of "blocs": these […]
- Voting power (3): The American swing states 2021-01-02As we all know, American Presidential elections are done with a two-stage process: first the public votes, and then the Electoral College votes. It is the Electoral College that actually votes for the President; but they vote (in their respective states) in accordance with the plurality determined by the public vote. This unusual system was […]
- Voting power (2): computation 2020-12-30Naive implementation of Banzhaf power indices As we saw in the previous post, computation of the power indices can become unwieldy as the number of voters increases. However, we can very simply write a program to compute the Banzhaf power indices simply by looping over all subsets of the weights: def banzhaf1(q,w): n = len(w) […]
- Voting power 2020-12-29After the 2020 American Presidential election, with the usual post-election analyses and (in this case) vast numbers of lawsuits, I started looking at the Electoral College, and trying to work out how it worked in terms of power. Although power is often conflated simply with the number of votes, that's not necessarily the case. We […]
- Electing a president 2020-11-06Every four years (barring death or some other catastrophe), the USA goes through the periodic madness of a presidential election. Wild behaviour, inaccuracies, mud-slinging from both sides have been central since George Washington's second term. And the entire business of voting is muddied by the Electoral College, the 538 members of which do the actual […]
- Enumerating the rationals 2020-01-17The rational numbers are well known to be countable, and one standard method of counting them is to put the positive rationals into an infinite matrix \(M=m_{ij}\), where \(m_{ij}=i/j\) so that you end up with something that looks like this: \[ \left[\begin{array}{ccccc} \frac{1}{1}&\frac{1}{2}&\frac{1}{3}&\frac{1}{4}&\dots\\[1ex] \frac{2}{1}&\frac{2}{2}&\frac{2}{3}&\frac{2}{4}&\dots\\[1ex] \frac{3}{1}&\frac{3}{2}&\frac{3}{3}&\frac{3}{4}&\dots\\[1ex] \frac{4}{1}&\frac{4}{2}&\frac{4}{3}&\frac{4}{4}&\dots\\[1ex] \vdots&\vdots&\vdots&\vdots&\ddots \end{array}\right] \] It is clear that not only […]
- Fitting the SIR model of disease to data in Julia 2020-01-14A few posts ago I showed how to do this in Python. Now it's Julia's turn. The data is the same: spread of influenza in a British boarding school with a population of 762. This was reported in the British Medical Journal on March 4, 1978, and you can read the original short article here. […]
- The Butera-Pernici algorithm (2) 2020-01-05The purpose of this post will be to see if we can implement the algorithm in Julia, and thus leverage Julia's very fast execution time. We are working with polynomials defined on nilpotent variables, which means that the degree of any generator in a polynomial term will be 0 or 1. Assume that our generators […]
- The Butera-Pernici algorithm (1) 2020-01-03Introduction We know that there is no general sub-exponential algorithm for computing the permanent of a square matrix. But we may very reasonably ask -- might there be a faster, possibly even polynomial-time algorithm, for some specific classes of matrices? For example, a sparse matrix will have most terms of the permanent zero -- can […]
- The size of the universe 2020-01-01As a first blog post for 2020, I'm dusting off one from my previous blog, which I've edited only slightly. I've been looking up at the sky at night recently, and thinking about the sizes of things. Now it's all very well to say something is for example a million kilometres away; that's just a […]
- Permanents and Ryser's algorithm 2019-12-21As I discussed in my last blog post, the permanent of an \(n\times n\) matrix \(M=m_{ij}\) is defined as \[ \text{per}(M)=\sum_{\sigma\in S_n}\prod_{i=1}^nm_{i,\sigma(i)} \] where the sum is taken over all permutations of the \(n\) numbers \(1,2,\ldots,n\). It differs from the better known determinant in having no sign changes. For example: \[ \text{per} \begin{bmatrix}a&b&c\\d&e&f\\g&h&i\end{bmatrix} =aei+afh+bfg+bdi+cdi+ceg. \] […]
- Speeds of Julia and Python 2019-12-18Introduction Python is of course one of the world's currently most popular languages, and there are plenty of statistics to show it. Of all languages in current use, Python is one of the oldest (in the very quick time-scale of programming languages) dating from 1990 - only C and its variants are older. However, it […]
- Poles of inaccessibility 2019-12-07Just recently there was a news item about a solo explorer being the first Australian to reach the Antarctic "Pole of Inaccessibility". Such a Pole is usually defined as that place on a continent that is furthest from the sea. The South Pole is about 1300km from the nearest open sea, and can be reached […]
- An interesting sum 2019-12-01I am not an analyst, so I find the sums of infinite series quite mysterious. For example, here are three. The first one is the value of \(\zeta(2)\), very well known, sometimes called the "Basel Problem" and first determined by (of course) Euler: \[ \sum_{n=1}^\infty\frac{1}{n^2}=\frac{\pi^2}{6}. \] Second, subtracting one from the denominator: \[ \sum_{n=2}^\infty\frac{1}{n^2-1}=\frac{3}{4} \] […]
- Runge's phenomenon in Geogebra 2019-09-14Runge's phenomenon says roughly that a polynomial through equally spaced points over an interval will wobble a lot near the ends. Runge demonstrated this by fitting polynomials through equally spaced point in the interval \([-1,1]\) on the function \[ \frac{1}{1+25x^2} \] and this function is now known as "Runge's function". It turns out that Geogebra […]
- Fitting the SIR model of disease to data in Python 2019-08-08Introduction and the problem The SIR model for spread of disease was first proposed in 1927 in a collection of three articles in the Proceedings of the Royal Society by Anderson Gray McKendrick and William Ogilvy Kermack; the resulting theory is known as Kermack–McKendrick theory; now considered a subclass of a more general theory known […]