ترغب بنشر مسار تعليمي؟ اضغط هنا

الخوارزمية لتصنيف المضلعات الفانو الناعمة

An algorithm for the classification of smooth Fano polytopes

112   0   0.0 ( 0 )
 نشر من قبل Mikkel {\\O}bro
 تاريخ النشر 2007
  مجال البحث
والبحث باللغة English
 تأليف Mikkel {O}bro




اسأل ChatGPT حول البحث

We present an algorithm that produces the classification list of smooth Fano d-polytopes for any given d. The input of the algorithm is a single number, namely the positive integer d. The algorithm has been used to classify smooth Fano d-polytopes for d<=7. There are 7622 isomorphism classes of smooth Fano 6-polytopes and 72256 isomorphism classes of smooth Fano 7-polytopes.



قيم البحث

اقرأ أيضاً

This paper is concerned with the extreme points of the polytopes of stochastic tensors. By a tensor we mean a multi-dimensional array over the real number field. A line-stochastic tensor is a nonnegative tensor in which the sum of all entries on each line (i.e., one free index) is equal to 1; a plane-stochastic tensor is a nonnegative tensor in which the sum of all entries on each plane (i.e., two free indices) is equal to 1. In enumerating extreme points of the polytopes of line- and plane-stochastic tensors of order 3 and dimension $n$, we consider the approach by linear optimization and present new lower and upper bounds. We also study the coefficient matrices that define the polytopes.
We consider the problem of sampling from a density of the form $p(x) propto exp(-f(x)- g(x))$, where $f: mathbb{R}^d rightarrow mathbb{R}$ is a smooth and strongly convex function and $g: mathbb{R}^d rightarrow mathbb{R}$ is a convex and Lipschitz fu nction. We propose a new algorithm based on the Metropolis-Hastings framework, and prove that it mixes to within TV distance $varepsilon$ of the target density in at most $O(d log (d/varepsilon))$ iterations. This guarantee extends previous results on sampling from distributions with smooth log densities ($g = 0$) to the more general composite non-smooth case, with the same mixing time up to a multiple of the condition number. Our method is based on a novel proximal-based proposal distribution that can be efficiently computed for a large class of non-smooth functions $g$.
In the chapter Magic with a Matrix in emph{Hexaflexagons and Other Mathematical
Let $K subset R^d$ be a smooth convex set and let $P_la$ be a Poisson point process on $R^d$ of intensity $la$. The convex hull of $P_la cap K$ is a random convex polytope $K_la$. As $la to infty$, we show that the variance of the number of $k$-dimen sional faces of $K_la$, when properly scaled, converges to a scalar multiple of the affine surface area of $K$. Similar asymptotics hold for the variance of the number of $k$-dimensional faces for the convex hull of a binomial process in $K$.
Let $K$ be a convex body in $mathbb{R}^n$ and $f : partial K rightarrow mathbb{R}_+$ a continuous, strictly positive function with $intlimits_{partial K} f(x) d mu_{partial K}(x) = 1$. We give an upper bound for the approximation of $K$ in the symmet ric difference metric by an arbitrarily positioned polytope $P_f$ in $mathbb{R}^n$ having a fixed number of vertices. This generalizes a result by Ludwig, Schutt and Werner $[36]$. The polytope $P_f$ is obtained by a random construction via a probability measure with density $f$. In our result, the dependence on the number of vertices is optimal. With the optimal density $f$, the dependence on $K$ in our result is also optimal.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا