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Recent Questions - Mathematics Stack Exchange most recent 30 from math.stackexchange.com

  • Drawing Iterated Function Systems
    by Kcurse on September 24, 2020 at 4:38 am

    I am a little confused as to how to draw IFSs. I have seen an example of the Koch curve but I don't understand how to draw from equations. If it could be explained to me how each part of the equation contributes to the drawing that would be fantastic. Note that I mean drawing by hand and not coding.

  • Derivation - Number of images formed by 2 Mirrors =$\frac{360}{\theta} -1 $
    by Mayank on September 24, 2020 at 4:36 am

    Derive :Number of images formed by two plane mirrors inclined at an angle of $\theta$ is given by $$\frac{360}{\theta} -1 $$What I think : Inclined mirror forms images in circle and one image lies in one sectors. No of images = Number of sectors=$\frac{360}{\theta}$ And 1 is subtracted from $\frac{360}{\theta}$ because a sector is occupied by the object. I think this is not a proper derivation. How to prove that Inclined mirror forms images in circle? I saw a answer but I didn't understand it. How to derive it formally?

  • A complex polynomial $\mathbb R^2 \rightarrow \mathbb R^2$ is surjective.
    by Jorge Fernández-Hidalgo on September 24, 2020 at 4:34 am

    Consider a non-constant polynomial in $\mathbb C$ and consider the map from $\mathbb R^2$ to $\mathbb R^2$ that it encodes. Is it possible to show it is a surjective function? We know it is one because of the fundamental theorem of algebra. But would we be able to prove it without knowing it is a polynomial? As a particular example we can consider the polynomial $x^3-2x^2-4$ and see it encodes the map $f(x,y) = (x^3 + 2 x^2 - 3 x y^2 - 2 (y^2 + 2), y (3 x^2 + 4 x - y^2))$ Is there some sort of theory that encompasses this phenomenon and can be used to say functions of this kind are surjective (without knowing a-priori the expression is of this kind)? Like maybe some sort of invariant that can be calculated for the expression or something.

  • Integrating factor for $xdx +(x-y^2)dy=0.$
    by 123N on September 24, 2020 at 4:32 am

    How to find integrating factor for $xdx+(x-y^2)dy=0.$ Here $M=x$ and $N=x-y^2$. This equation is not exact. Clearly not seperable, homogeneous or linear(either in terms of $\frac{dy}{dx}$ or in terms of $\frac{dx}{dy}$). This is not even Bernoulli's equation. Also $\frac{1}{M}\left[\frac{\partial N}{\partial x}-\frac{\partial M}{\partial y}\right]=\frac 1 x,$ a function $x$, but since the rule requires this expression to be a function of $y$, this one is not applicable too.

  • How to solve scenario using permutations
    by ranveer_12 on September 24, 2020 at 4:31 am

    Xtreme clothing company making snowboarding pants in five colors and sizes of smal,medium,large,and extra-large.The number of different color-size variations of snowboarding pants this company makes is? my work: so since their are five choice we have 5 spaces and we have 4 choices of sizes,we have 4 spaces equation=5!/4!=5 the answer=5


Bad Science Ben Goldacre's Bad Science column from the Guardian and more...

  • Evidence to House of Commons Sci Tech Select Committee on Research Integrity
    by Ben Goldacre on December 5, 2017 at 11:42 am

    Sorry not to be in regular blogging mode at the moment. Here’s a video of our evidence session to parliament, where they are running an inquiry into research integrity. I think clinical trials are the best possible way to approach this issue. Lots of things in “research integrity” are hard to capture in hard logical

  • How do the world’s biggest drug companies compare, in their transparency commitments?
    by Ben Goldacre on July 27, 2017 at 6:33 am

    Here’s a paper, and associated website, that we launch today: we have assessed, and then ranked, all the biggest drug companies in the world, to compare their public commitments on trials transparency. Regular readers will be familiar with this ongoing battle. In medicine we use the results of clinical trials to make informed treatments about

  • Meaningful Transparency Commitments: the WHO Joint Statement from Trial Funders
    by Ben Goldacre on July 26, 2017 at 4:17 pm

    By now I hope you all know about the ongoing global scandal of clinical trial results being left unpublished, and of course our AllTrials campaign. Doctors, researchers, and patients cannot make truly informed choices about which treatments work best if they don’t have access to all the trial results. Earlier this year, I helped out

  • How many epidemiologists does it take to change a lightbulb?
    by Ben Goldacre on February 1, 2017 at 12:49 pm

    Robin Ince just asked if I know any epidemiologist lightbulb jokes. I wrote this for him. How many epidemiologists does it take to change a lightbulb? We’ve found 12,000 switches hidden around the house. Some of them turn this lightbulb on, some of them don’t; some of them only work sometimes; and some of them

  • “Transparency, Beyond Publication Bias”. A video of my super-speedy talk at IJE.
    by Ben Goldacre on October 11, 2016 at 8:01 am

    People often talk about “trials transparency” as if this means “all trials must be published in an academic journal”. In reality, true transparency goes much further than this. We need Clinical Study Reports, and individual patient data, of course. But we also need the consent forms, so we can see what patients were told. We need


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  • Is BERT Always the Better Cheaper Faster Answer in NLP? Apparently Not.
    by William Vorhies on September 21, 2020 at 9:28 pm

    Summary: Since BERT NLP models were first introduced by Google in 2018 they have become the go-to choice.  New evidence however shows that LSTM models may widely outperform BERT meaning you may need to evaluate both approaches for your NLP project. Over the last year or two, if you needed to bring in an NLP…

  • Weekly Digest, September 21
    by Vincent Granville on September 21, 2020 at 12:30 am

    Monday newsletter published by Data Science Central. Previous editions can be found here. The contribution flagged with a + is our selection for the picture of the week. To subscribe, follow this link. Announcement…

  • Risk Avoidance Spectrum and Character Types
    by Don Philip Faithful on September 20, 2020 at 8:08 pm

    Ever since I started following stocks again, I have been preoccupied with developing a "game plan" to help prevent me from making emotional investment decisions.  Plans can be improved.  What I have come up with so far is a stress avoidance model to study how different character types might perform in relation to the market.  Since quite a number of investors are actually algorithms - and many trades are algorithmically triggered - the concept of stress needs…

  • The illusion of choice
    by Diego Lopez Yse on September 19, 2020 at 11:00 pm

    Do you think your actions are the result of your own free choices? What if those actions are the inevitable…

  • Algorithms of Social Manipulation
    by Diego Lopez Yse on September 19, 2020 at 10:52 pm

    Do you know how your apps work? Are you aware of what tech companies are doing in the back with your data?…


  • Book: Evaluating Machine Learning Models
    by Emmanuelle Rieuf on March 14, 2017 at 6:12 pm

    Data science today is a lot like the Wild West: there’s endless opportunity and excitement, but also a lot of chaos and confusion. If you’re new to data science and applied machine learning, evaluating a machine-learning model can seem pretty overwhelming. Now you have help. With this O’Reilly report, machine-learning expert Alice Zheng takes you through the model…

  • Book: Python For Dummies
    by Emmanuelle Rieuf on August 25, 2016 at 10:50 pm

    Python is one of the most powerful, easy-to-read programming languages around, but it does have its limitations. This general purpose, high-level language that can be extended and embedded is a smart option for many programming problems, but a poor solution to others. Python For Dummies is the quick-and-easy guide to getting…

  • Book: Python Machine Learning Blueprints
    by Emmanuelle Rieuf on August 24, 2016 at 8:16 pm

    Key FeaturesPut machine learning principles into practice to solve real-world problems Get to grips with Python's impressive range of Machine Learning libraries and frameworks From retrieving data from APIs to cleaning and visualization, become more confident at tackling every stage of the data pipelineBook…

  • Book: Data Science Essentials in Python
    by Emmanuelle Rieuf on August 23, 2016 at 6:10 pm

    Go from messy, unstructured artifacts stored in SQL and NoSQL databases to a neat, well-organized dataset with this quick reference for the busy data scientist. Understand text mining, machine learning, and network analysis; process numeric data with the NumPy and Pandas modules; describe and analyze data using statistical and…

  • Book: Statistics for Non-Statisticians
    by Emmanuelle Rieuf on August 23, 2016 at 1:08 am

    Aimed at practitioners The presentation is as non-mathematical as possible Includes many examples of the use of statistical functions in spreadsheets Employs a realistic sample survey as an exemplar throughout the book Fills a gap in the existing literature on…

  • Book: Systems Analytics: Adaptive Machine Learning workbook
    by Emmanuelle Rieuf on August 10, 2016 at 5:45 pm

    SYSTEMS Analytics title refers to a new development effort in the field of Machine Learning grounded firmly in Systems Theory; the subtitle, “ADAPTIVE Machine Learning”, captures the link to the current state of the art. My intention in writing this book is to bring mathematically trained graduates in engineering, physics, mathematics and…

  • Book: Superforecasting: The Art and Science of Prediction
    by Emmanuelle Rieuf on August 3, 2016 at 11:11 pm

    To be published on September 13, 2016; you can pre-order here ($17.) By Philip Tetlock and Dan Gardner. 352 Pages.Everyone would benefit from seeing further into the future, whether buying stocks, crafting…

  • Book: Efficient R Programming
    by Emmanuelle Rieuf on July 1, 2016 at 5:37 am

    This is the online version of the O’Reilly book: Efficient R programming. To build the book:Install the latest version of R If you are using RStudio, make sure that’s up-to-date as wellInstall the book dependencies.…

  • Python Machine Learning
    by Emmanuelle Rieuf on June 28, 2016 at 7:01 pm

    Unlock deeper insights into Machine Leaning with this vital guide to cutting-edge predictive analyticsAbout This BookLeverage Python's most powerful open-source libraries for deep learning, data wrangling, and data visualization Learn effective strategies and best practices to improve and optimize machine learning systems…

  • Book: Effective Data Visualization: The Right Chart for the Right Data
    by Emmanuelle Rieuf on June 28, 2016 at 6:38 pm

    Written by sought-after speaker, designer, and researcher Stephanie D. H. Evergreen, Effective Data Visualizationshows readers how to create Excel charts and graphs that best communicate data findings. This comprehensive how-to guide functions as a set of blueprints—supported by research and the author’s extensive experience with clients in industries all over the world—for conveying data in an impactful way. Delivered in Evergreen’s humorous and approachable style, the book covers the…