The second mode called Structure, represent protein as ‘residue gas,’ where every amino acid is represented as a triangle, build from the N-Cα-C atoms that are displaced and rotated in space (affine matrices), and further refined with geometry-aware attention operation termed ‘invariant ...
44.J_rg Brüdern, Harmonic analysis of arithmetic functions__(University of G_tti 57:47 45.Sergei Konyagin A construction of A. Schinzel - many numbers in a short inter 01:01:46 46.Gal Binyamini Point counting for foliations in Diophantine geometry (NTWS 046 59:31 47.Will Sawin...
Another related analogy between Euclidean and Minkowskian geometry is the decomposition of a timelike 4-vector into components relative to a Minkowski coordinate system, e.g. for particle 4-momentum where is a unit 3-vector parallel to 3-velocity, , , and . This is the Minkowskian equivalent...
Understand what an azimuth is by learning its definition. Explore the uses of azimuth calculation and discover how azimuth is calculated for different purposes. What is an Azimuth? A coordinate system is a set of measurements that can be used to identify locations in space. While rectangular ...
it is all polynomials vanishing at the origin modulo those,vanishing to degree higher than one. Taylor's theorem shows this makes sense also for smooth functions. Then to globalize this concept, consider the injection of X into XxX as the diagonal, where X is some manifold, or affine space...
If there are some unwanted linear dependencies in the frequencies, we can do some linear algebra to eliminate one of the frequencies (using some geometry of numbers to keep the quantitative bounds under control) and continue the iteration. If instead the approximation is too inaccurate, then the...
Conjecture 3 (Strong Kakeya conjecture) Let be a two-dimensional family of lines in that meet , and assume the Wolff axiom that no (affine) plane contains more than a one-dimensional family of lines in . Let be the union of the restriction of every line in . Then . Actually, to mak...
In algebraic geometry, we can use the concept of an affine space as a model for understanding the world around us. An affine space is a set of points that are related by rational functions. This means that these points are connected to one another in terms of distance or angle....
What does a smooth embedding mean?Functions in MathA function in mathematics is defined as the relation between two sets, these sets have corresponding values where every element or value for one of the set is associated to the elements or values to the remaining set....
Toric Orbits in the Affine Sieve - Alex Kontorovich 58:50 Uniformity in the dynamical Bogomolov conjecture - Myrto Mavraki 49:45 Systems of points with Coulomb interactions – Sylvia Serfaty – ICM2018 01:07:14 Enno Lenzmann Turbulence in completely integrable PDEs The Calogero-Moser deriva...