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#curvature — Public Fediverse posts

Live and recent posts from across the Fediverse tagged #curvature, aggregated by home.social.

  1. Now to sth completely different! After "why zebras don't have ulcers" was answered by Sapolsky, here is the next question: "how do zebras get their stripes" answered by a new maths research in @apsphysics :
    journals.aps.org/pre/abstract/
    Inspiring also for non-flat cosmologies... 😁

    #mathematics #applied_mathematics #diffusion #curvature #scicomm #InterdisciplinaryMathematics

  2. This is why #Engineers use #TransitionCurves in the form of #CornuSpirals or #Clothoids to connect from the straight segment onto a circular arc. It has the property that it starts with zero #curvature at the beginning and then the curvature increases linearly with distance travelled along the curve. At the appropriate curvature, it is connected to a circular arc with the same curvature.

    #MyWork #WxMaxima #CivilEngineering #HighwayEngineering #CCBYSA

  3. #Cosmology #SpaceTime #BigBang #Curvature

    Talking with my children about the time before the Big Bang. The best analogy we could come up with: Space-time is like the earth's surface, moving from the past to the future is like moving from north to south.
    Asking "what was before the Big Bang?" is like asking "what's north of the north pole?".

    Put differently: It all started with the Big Bang. Then things went south.

  4. Whenever I walk to/from home, I have to walk up/down an inclined street; I noticed that the asphalt floor has different curvatures depending on how near it is of a bend, and I try to find a less steep incline while walking.

    This got me inspiration for the few questions below. Any simple explanations, and related links, are welcome.

    Given a #differentiable surface within R^3, and two distinct points in it, there are infinitely many differentiable paths from one point to another, remaining on the surface. At each point of the #path, one can find the path's local #curvature. Then:

    - Find a path that minimizes the supreme of the curvature. In other words, find the "flattest" path.

    - Find a path that minimizes the variation of the curvature. In other words, find a path that "most resembles" a circle arc.

    Are these tasks always possible within the given conditions? Are any stronger conditions needed? Are there cases with an #analytic solution, or are they possible only with numerical approximations?

    #Analysis #DifferentialGeometry #Calculus #DifferentialEquations #NumericalMethods

  5. Whenever I walk to/from home, I have to walk up/down an inclined street; I noticed that the asphalt floor has different curvatures depending on how near it is of a bend, and I try to find a less steep incline while walking.

    This got me inspiration for the few questions below. Any simple explanations, and related links, are welcome.

    Given a #differentiable surface within R^3, and two distinct points in it, there are infinitely many differentiable paths from one point to another, remaining on the surface. At each point of the #path, one can find the path's local #curvature. Then:

    - Find a path that minimizes the supreme of the curvature. In other words, find the "flattest" path.

    - Find a path that minimizes the variation of the curvature. In other words, find a path that "most resembles" a circle arc.

    Are these tasks always possible within the given conditions? Are any stronger conditions needed? Are there cases with an #analytic solution, or are they possible only with numerical approximations?

    #Analysis #DifferentialGeometry #Calculus #DifferentialEquations #NumericalMethods

  6. Whenever I walk to/from home, I have to walk up/down an inclined street; I noticed that the asphalt floor has different curvatures depending on how near it is of a bend, and I try to find a less steep incline while walking.

    This got me inspiration for the few questions below. Any simple explanations, and related links, are welcome.

    Given a #differentiable surface within R^3, and two distinct points in it, there are infinitely many differentiable paths from one point to another, remaining on the surface. At each point of the #path, one can find the path's local #curvature. Then:

    - Find a path that minimizes the supreme of the curvature. In other words, find the "flattest" path.

    - Find a path that minimizes the variation of the curvature. In other words, find a path that "most resembles" a circle arc.

    Are these tasks always possible within the given conditions? Are any stronger conditions needed? Are there cases with an #analytic solution, or are they possible only with numerical approximations?

    #Analysis #DifferentialGeometry #Calculus #DifferentialEquations #NumericalMethods

  7. Whenever I walk to/from home, I have to walk up/down an inclined street; I noticed that the asphalt floor has different curvatures depending on how near it is of a bend, and I try to find a less steep incline while walking.

    This got me inspiration for the few questions below. Any simple explanations, and related links, are welcome.

    Given a #differentiable surface within R^3, and two distinct points in it, there are infinitely many differentiable paths from one point to another, remaining on the surface. At each point of the #path, one can find the path's local #curvature. Then:

    - Find a path that minimizes the supreme of the curvature. In other words, find the "flattest" path.

    - Find a path that minimizes the variation of the curvature. In other words, find a path that "most resembles" a circle arc.

    Are these tasks always possible within the given conditions? Are any stronger conditions needed? Are there cases with an #analytic solution, or are they possible only with numerical approximations?

    #Analysis #DifferentialGeometry #Calculus #DifferentialEquations #NumericalMethods

  8. Whenever I walk to/from home, I have to walk up/down an inclined street; I noticed that the asphalt floor has different curvatures depending on how near it is of a bend, and I try to find a less steep incline while walking.

    This got me inspiration for the few questions below. Any simple explanations, and related links, are welcome.

    Given a #differentiable surface within R^3, and two distinct points in it, there are infinitely many differentiable paths from one point to another, remaining on the surface. At each point of the #path, one can find the path's local #curvature. Then:

    - Find a path that minimizes the supreme of the curvature. In other words, find the "flattest" path.

    - Find a path that minimizes the variation of the curvature. In other words, find a path that "most resembles" a circle arc.

    Are these tasks always possible within the given conditions? Are any stronger conditions needed? Are there cases with an #analytic solution, or are they possible only with numerical approximations?

    #Analysis #DifferentialGeometry #Calculus #DifferentialEquations #NumericalMethods

  9. 'Large data limit of the MBO scheme for data clustering: convergence of the dynamics', by Tim Laux, Jona Lelmi.

    jmlr.org/papers/v24/22-1089.ht

    #viscosity #clustering #curvature

  10. Is the Universe finite?

    ++ Video is visually appealing, compact (28'). Tries to present the question of finiteness || infiniteness of Universe within the context of relativistic #cosmology. Intros to 2D #topology + #curvature are fair. Publicity for my group's research is nice :).

    - - The relation to *3D* topo+curv is absent; there are several bloopers in the narration.

    Overall a fair job. :)

    peertube.stream/w/o5v3JXJkUmaR (*subtitles* en+fr)

    @cartographer @stephenserjeant @ClaireLamman @cosmology

  11. What's an example of curvature in economics?

    Any elasticity, including our favourite "incentives".

    People switch to night shift for 25¢, showing that *any* differential creates "an" incentive.

    How much "force" is produced by a given pay differential? Considering a large range of differences means #curvature.

  12. Next week, the school of our thematic programme on #Geometry beyond #Riemann: #Curvature and #Rigidity is coming. 🤓 Hope everyone is registered who is into #Riemannian and #Lorentzian #conemanifolds, #Hilbert and #Finsler #metrics!

    Find out more about the schedule here. 📝
    esi.ac.at/events/e477/

    @univienna

    Click for the video here: twitter.com/ESIVienna/status/1

  13. An intriguing cover for this 2003 issue of Nature, featuring a dodecahedral space topology and this question:

    Is this the shape of the Universe?

    ☑️ The research paper: nature.com/articles/nature0194
    ☑️ A News & Views article: nature.com/articles/425566a
    ☑️ The full issue: nature.com/nature/volumes/425/

    #universe #cosmology #topology #curvature #cmb #wmap #bigbang #astronomy #astrophysics #astrodon #nature #cover #covers #naturecovers #space #science #research

  14. 'Implicit Bias of Gradient Descent for Mean Squared Error Regression with Two-Layer Wide Neural Networks', by Hui Jin, Guido Montufar.

    jmlr.org/papers/v24/21-0832.ht

    #gradient #curvature #laplacian

  15. ViViT: Curvature Access Through The Generalized Gauss-Newton’s Low-Rank Structure

    Felix Dangel, Lukas Tatzel, Philipp Hennig

    openreview.net/forum?id=DzJ7Jf

    #gradients #hessian #curvature

  16. Just one of the rats leaving the blue ship
    #introduction

    I'm #firstgen #academix and a synthetic chemist at #UZH #University in #Zurich. Soon we will move to the University of #Geneva #UniGe

    My group studies #curvature in #polyaromatic #pi systems and their #assembly into #supramolecular #materials. Will toot our latest work, amplify important voices, and anything in between.

    I am a #tea drinker and #tec #diver

    #chemiverse #chemtoots #chemtwitter #chemtweeps #chemistry #realtimechem

  17. Just one of the rats leaving the blue ship
    #introduction

    I'm #firstgen #academix and a synthetic chemist at #UZH #University in #Zurich. Soon we will move to the University of #Geneva #UniGe

    My group studies #curvature in #polyaromatic #pi systems and their #assembly into #supramolecular #materials. Will toot our latest work, amplify important voices, and anything in between.

    I am a #tea drinker and #tec #diver

    #chemiverse #chemtoots #chemtwitter #chemtweeps #chemistry #realtimechem

  18. Just one of the rats leaving the blue ship
    #introduction

    I'm #firstgen #academix and a synthetic chemist at #UZH #University in #Zurich. Soon we will move to the University of #Geneva #UniGe

    My group studies #curvature in #polyaromatic #pi systems and their #assembly into #supramolecular #materials. Will toot our latest work, amplify important voices, and anything in between.

    I am a #tea drinker and #tec #diver

    #chemiverse #chemtoots #chemtwitter #chemtweeps #chemistry #realtimechem