### Syndications of Interest

Ars Mathematica

- Nine Chapters on the Semigroup Art 2015-02-28While Googling something or other, I came across Nine Chapters on the Semigroup Art, which is a leisurely introduction to the theory of semigroups. (While the document is labelled “lecture notes”, the typography is quite beautiful.)Walt
- What Did Grothendieck Do? 2015-01-01Happy New Year! The publicity in the wake of Grothendieck’s death has left a certain number of non-mathematicians with the question of what it was exactly that he did. I wrote an answer elsewhere that people seemed to find informative, … Continue reading →Walt
- Learning about Stochastic Processes the Almost Sure Way 2014-11-09George Lowther at Almost Sure has written a terrific series of posts explaining stochastic processes and the stochastic calculus. Stochastic calculus is widely used in physics and finance, so there are many informal introductions that get across the main ideas … Continue reading →Walt
- Arguesian Lattices 2014-09-23As is well-known, the lattice of submodules of a module is modular. What I did not know is that the converse is not true, and that lattices of submodules must satisfy a stronger property, the arguesian law. The Arguesian law … Continue reading →Walt
- K2, not the mountain 2014-03-20Chandan Singh Dalawat has a nice survey article about K2. It just gives the highlights of the theory, without proofs, so it’s closer to a teaser trailer than it is to full-length movie. But sometimes you just want a teaser … Continue reading →Walt
- Cayley Bacharach Theorem through History 2014-02-10I came across this terrific article that describes a sequence of results beginning with Pappas’ theorem through the Cayley-Bacharach theorem to modern formulations in terms of the Gorenstein (!) condition. The connection between classical topics in algebraic geometry and modern … Continue reading →Walt
- Nonassociative Algebras 2013-12-30I periodically feel like I should learn more about nonassociative algebra. (I’ve studied Lie algebras, and technically Lie algebras are non-associative, but they’re pretty atypical of nonassociative algebras.) There’s a mysterious circle of “exceptional” examples that are all related — … Continue reading →Walt
- Determinacy 2013-11-30One of my ambitions in life is to understand projective determinacy. Fortunately, Tim Gowers has written a series of posts to explain Martin’s proof that Borel sets are determined. The main source of interest in determinacy is that results suggest … Continue reading →Walt
- A Generalized Fermat Equation 2013-08-31I came across a number theory paper Twists of X(7) and Primitive Solutions of x2 + y3 = z7 that I find completely fascinating. I find it fascinating because a) the question is so easy, b) the answer is so … Continue reading →Walt
- Linear Bestiary of Francois Pottier 2013-07-09Ugh, I suck at this blogging thing. I periodically get ambitious, and make big plans. That doesn’t actually lead to any completed posts, just many long half-finished posts, and hundreds of open tabs in Firefox. I think I’ll start with … Continue reading →Walt

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

- Creative Commons 2019 Annual Report 2020-11-05I am very pleased to share Creative Commons’ 2019 Annual Report. This report offers an overview of the important work CC did last year across the many domains and subject areas we work in. (Look for CC’s 2020 annual report to be released in early 2021, where we will have lots to share about this […]Catherine Stihler
- The Linked Commons 2.0: What’s New? 2020-11-04This is part of a series of posts introducing the projects built by open source contributors mentored by Creative Commons during Google Summer of Code (GSoC) 2020 and Outreachy. Subham Sahu was one of those contributors and we are grateful for his work on this project. The CC Catalog data visualization—the Linked Commons 2.0—is a […]Victoria Heath
- Important Updates to the Creative Commons Catalog 2020-11-02This is part of a series of posts introducing the projects built by open source contributors mentored by Creative Commons during Google Summer of Code (GSoC) 2020 and Outreachy. K. S. Srinidhi Krishna and Charini Nanayakkara were two of those contributors and we are grateful for their work on this project. The Creative Commons (CC) […]Kriti Godey
- Say Hello to Our New CC Open Source Website! 2020-11-02This is part of a series of posts introducing the projects built by open source contributors mentored by Creative Commons during Google Summer of Code (GSoC) 2020 and Outreachy. This post was written by Dhruvi Butti, a 2020 Outreachy intern and a 3rd-year undergrad at IIIT Surat. “Celebrate endings—for they precede new beginnings.” – Jonathan […]Kriti Godey
- You Can Now Sponsor CC’s Open Source Work on GitHub! 2020-10-27Creative Commons is now accepting sponsorship via GitHub Sponsors! CC’s small engineering team builds essential open-source infrastructure for CC-licensed and public domain content. Our tools make it easier for anyone to: release original content under an open license. find and responsibly reuse openly licensed and public domain content. connect to the larger ecosystem of openly […]Kriti Godey
- Making the CC Global Network Work Better for You 2020-10-21This post is written by Ethan Senack, a member of Creative Commons USA and the Global Network Council Executive Committee. Just over a year ago, the Executive Committee of the CC Global Network Council (GNC) launched an open process to collect feedback from all members on the network structure, with the purpose of understanding what […]Victoria Heath
- Facing 2020 at the CC Global Summit: A Look at This Year’s Keynotes 2020-10-15Let’s take a moment and step out of the heavy fog that is 2020 and try to look back at the last few months with a new perspective. Through the challenges and uncertainties, we believe there have been opportunities for personal reflection, social solidarity, and care. Of course, we recognize this is not true for […]Claudio Ruiz
- Internationalizing the Open COVID Pledge: Translations and Outreach 2020-10-14“United Nations Headquarters” by United Nations Photo is licensed under CC BY-NC-ND 2.0 As an important part of our stewardship of the Open COVID Pledge, we are pleased to announce that the Pledge is now available in all six of the official languages of the United Nations: Arabic, Chinese, English, French, Russian, and Spanish. This […]Diane Peters
- Meet CC Tanzania, Our Next Feature for CC Network Fridays! 2020-10-09After introducing the CC Italy Chapter to you in July, the CC Netherlands Chapter in August and CC Bangladesh Chapter in September, we are now travelling to Africa to introduce the CC Tanzania Chapter! The Creative Commons Global Network (CCGN) consists of 45 CC Country Chapters spread across the globe. They’re the home for a […]Julia Brungs
- Implementing the Marrakesh Treaty in Latin America: A Look at the Experiences of Four CC Community Members 2020-09-30Four years ago today, the Marrakesh Treaty entered into force. The Treaty is truly special in the international copyright law universe: it has a clear humanitarian and social development dimension and it’s the first international treaty that focuses on the beneficiaries of limitations and exceptions, rather than on the rights of creators or holders of […]Brigitte Vézina

Featured Blog Posts – Data Science Central

- Three steps for conquering the last mile of analytics 2020-11-09Becoming insights-driven is now the ultimate prize of digital transformation, and many organizations are making significant progress toward this goal. However, putting insights into action – the “last mile” of analytics – is still a challenge for many organizations. With continued investments in data, analytics and AI, as well as the broader availability of machine-learning […]Courtney Peters
- Public Cloud: The Indispensable Component for Businesses 2020-11-09Every public Cloud has some essential features like- a scalable architecture, offering a pay-per-consumption model, instant reach to the masses and diversified component options. Usually, the migration-driven journey often depicts a standard architectural structure. Cloud can transform a basic prototype into reality, automate key processes and enhance customer experiences through real-time engagements containing in-depth insights. […]Rishabh Sinha
- Recent Java enhancements for numeric calculations 2020-11-07In the past, slow evaluation of mathematical functions and large memory footprint were the most significant drawbacks of Java compared to C++/C for numeric computations and scientific data analysis. However, recent enhancements in the Java Virtual Machine (JVM) enabled faster and better numerical computing due to several enhancements in evaluating trigonometric functions. In this article […]jwork.ORG
- Multi-stage heterogeneous ensemble meta-learning with hands-off demo 2020-11-07In this blog, I will introduce a R package for Heterogeneous Ensemble Learning (Classification, Regression) that is fully automated. It significantly lowers the barrier for the practitioners to apply heterogeneous ensemble learning techniques in an amateur fashion to their everyday predictive problems.…Ajay Arunachalam
- DSC Friday News, 6 Nov 2020 2020-11-07The DSC News is published by Data Science Central, and highlights new content from our Weekly Digest. Previous editions can be found here. The contribution flagged with a + is our selection for the…Kurt Cagle
- A taxonomy of explainable (XAI) AI models 2020-11-06I am reading a very interesting paper called Principles and Practice of Explainable Machine Learning by Vaishak Belle (University of Edinburgh & Alan Turing Institute) and Ioannis Papantonis (University of Edinburgh) which presents a taxonomy of explainable AI (XAI). XAI is a complex subject…ajit jaokar
- Solving a few AI problems with Python: Part 1 2020-11-06In this blog we shall discuss about a few problems in artificial intelligence and their python implementations. The problems discussed here appeared as programming assignments in the edX course CS50’s Introduction to Artificial Intelligence with Python…Sandipan Dey
- Fueling Digital Transformation with Service Design 2020-11-04One of the industry’s great debates (bigger than regular Cap’n Crunch versus Cap’n Crunch with Crunchberries) is “What is Digital Transformation?” Here’s my take: Digital Transformation is the fundamental reinvention of an organization’s business model by synergizing advanced analytics (composable, reusable analytic…Bill Schmarzo
- How do I select SVM kernels? 2020-11-04This article was written by Sebastian Raschka. Given an arbitrary dataset, you typically don't know which kernel may work best. I recommend starting with the simplest hypothesis space first -- given that you don't know much about your data -- and work your way up towards the more complex hypothesis spaces. So, the linear kernel […]Andrea Manero-Bastin
- AI and Employee experience| How does it positively go together? 2020-11-04Do you know 62% of workforce believe that AI will carry a favourable impact on their jobs? And 67% say it is necessary to develop the skills for working in coordination with intelligent machines. As per the research studies, AI will be the driving force behind cultural and economic shifts that will make the workforce […]Sukumar Jena
- Mistakes that most of the analysts do in their analytics 2020-11-04In the field of data science or analytical sciences, any solution can be potential to solve any problem. But, to derive such prospective solutions, the following are the top common mistakes in their practice. Unable to apply common sense and subject matter expertise for providing solutions to any given problem using analytical tools and…Vijay Kumar
- Java: What Makes it the Top Choice for Data Science 2020-11-03Data science uses algorithms, tools, and technologies to identify patterns in data and eventually glean valuable insights from the raw data. Simply put, it allows us to make sense of all that abundance of data that we seem to have all around us. We don’t have to tell you why data science has quickly gained […]Ryan Williamson
- Weekly Digest, Tuesday, 3 November 2020 2020-11-03From The Editor's Desk This version of the DSC Weekly Digest is running a bit late, in part because the editor (me), as a data junkie, has been a bit preoccupied watching the always engaging and occasionally horrifying sport known as the US Election. This is when all of us become data scientists - running […]Kurt Cagle
- AI Generated Avatars Becoming Digital Influencers 2020-11-03As the recent rise in Covid-19 threatens once again to shutter advertising agencies, film studios, and similar media "factories" globally, a quiet, desperate shift is taking place in the creation of new media, brought about by increasingly sophisticated AI capabilities. A new spate of actors and models are making their way to people's screens, such […]Kurt Cagle
- Data Science Movies Recommendation System 2020-11-02Nearly everybody wants to invest their recreation energy to watch motion pictures with their loved ones. We as a whole have a similar encounter when we sit on our lounge chair to pick a film that we will watch and go through the following two hours yet can't discover one following 20 minutes. It is […]Sriram K
- 4 Powerful Use Cases for Data Science in Finance 2020-11-02Data-driven solutions play a fundamental role in enhancing the services and profit margins of modern businesses in the finance…Olha Zhydik
- Digital Transformation in the age of COVID-19 2020-11-02COVID-19, by limiting us to our homes and bringing the global economy to a standstill has proved that the world healthcare ecosystem is not prepared for a pandemic. However, what it did teach us is that as consumers we are prepared to adopt the digital era in all life facets. This new found pro digital […]Bhupinder Kour
- Career Scope in Machine Learning in 2021 2020-11-02As you must be aware, there are a lot of applications that are a by-product of Machine learning techniques. Machine learning is one of the hottest skills in today’s market. In fact, as per one of the recent LinkedIn surveys, there are over 7k machine learning jobs available. Additionally, there is a tremendous growth rate […]Lokesh
- A Process to minimize the gap between research and its applications 2020-10-31Human history is numerous pieces of evidence, doctrine, theologies through logic, and by extensive research in every field exists in the universe. There is a huge gap between research and its practical application. Studies should conduct with enormous responsibility with extreme efforts, but which has a very minimal effect on real-world problems. The majority of […]Vijay Kumar
- Thursday News, October 29 2020-10-29Here is our selection of featured articles and technical resources posted since Monday: Announcements Fully online MS in Data Science at CUNY DSC Articles How Kids Channel Their Internal Data Scientist to Become Candy Optimization…Vincent Granville

Planet Sage

- 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 […]
- William Stein: Should I Resign from My Full Professor Job to Work Fulltime on Cocalc? 2019-05-09Nearly 3 years ago, I gave a talk at a Harvard mathematics conference announcing that “I am leaving academia to build a company”. What I really did is go on unpaid leave for three years from my tenured Full Professor position. No further extensions of that leave is possible, so I finally have to decide whether or not to […]

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?

- 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 number, […]
- 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 […]
- Mapping voting gains between elections 2019-07-20So this goes back quite some time to the recent Australian Federal election on May 18. In my own electorate (known formally as a “Division”) of Cooper, the Greens, who until recently had been showing signs of winning the seat, were pretty well trounced by Labor. Some background asides First, “Labor” as in “Australian Labor […]
- Educational disciplines: size against market growth 2019-06-14Here is an interactive version of this diagram: [!APF Figure 4](/APF_figure_4.png) (click on the image to show a larger version.)
- Tschirnhausen's solution of the cubic 2019-05-04A general cubic polynomial has the form \[ ax^3+bx^2+cx+d \] but a general cubic equation can have the form \[ x^3+ax^2+bx+c=0. \] We can always divide through by the coefficient of \(x^3\) (assuming it to be non-zero) to obtain a monic equation; that is, with leading coefficient of 1. We can now remove the \(x^2\) […]
- Tschirnhausen transformations and the quartic 2019-05-04Here we show how a Tschirnhausen transformation can be used to solve a quartic equation. The steps are: Ensure the quartic is missing the cubic term, and its initial coefficient is 1. We can do this by first dividing by the initial coefficient to obtain an equation \[ x^4+b_3x^3+b_2x^2+b_1x+b_0=0 \] and then replace the variable […]
- Colonial massacres, 1794 to 1928 2019-01-27The date January 26 is one of immense current debate in Australia. Officially it’s the date of Australia Day, which supposedly celebrates the founding of Australia. To Aboriginal peoples it is a day of deep mourning and sadness, as the date commemorates over two centuries of oppression, bloodshed, and dispossession. To them and their many […]
- Vote counting in the Australian Senate 2019-01-21Recently we have seen senators behaving in ways that seem stupid, or contrary to accepted public opinion. And then people will start jumping up and down and complaining that such a senator only got a tiny number of first preference votes. One commentator said that one senator, with 19 first preference votes, “couldn’t muster more […]
- Concert review: Lixsania and the Labyrinth 2018-11-09This evening I saw the Australia Brandenburg Orchestra with guest soloist Lixsania Fernandez, a virtuoso player of the viola da gamba, from Cuba. (Although she studied, and now lives, in Spain.) Lixsania is quite amazing: tall, statuesque, quite absurdly beautiful, and plays with a technique that encompasses the wildest of baroque extravagances as well as […]
- Linear programming in Python (2) 2018-10-29Here’s an example of a transportation problem, with information given as a table: This is an example of a balanced, non-degenerate transportation problem. It is balanced since the sum of supplies equals the sum of demands, and it is non-degenerate as there is no proper subset of supplies whose sum is equal to that of […]