Connect the dots: how many random points can a regular curve pass through?
نویسندگان
چکیده
منابع مشابه
Connect-The-Dots: How many random points can a regular curve pass through?
Suppose n points are scattered uniformly at random in the unit square [0, 1]. Question: How many of these points can possibly lie on some curve of length λ? Answer, proved here: OP (λ · √ n). We consider a general class of such questions; in each case, we are given a class Γ of curves in the square, and we ask: in a cloud of n uniform random points, how many can lie on some curve γ ∈ Γ? Classes...
متن کاملHow Many Random Points Can a Regular Curve Pass Through?
Suppose n points are scattered uniformly at random in the unit square [0, 1]. Question: How many of these points can possibly lie on some curves of length λ? Answer, proved here: OP (λ · √ n). We consider a general class of such questions; in each case, we are given a class Γ of curves in the square, and we ask: in a cloud of n uniform random points, how many can lie on some curve γ ∈ Γ? Classe...
متن کاملHow Many Rational Points Does a Random Curve Have?
A large part of modern arithmetic geometry is dedicated to or motivated by the study of rational points on varieties. For an elliptic curve over Q, the set of rational points forms a finitely generated abelian group. The ranks of these groups, when ranging over all elliptic curves, are conjectured to be evenly distributed between rank 0 and rank 1, with higher ranks being negligible. We will de...
متن کاملHow analysts cognitively "connect the dots"
As analysts attempt to make sense of a collection of documents, such as intelligence analysis reports, they need to “connect the dots” between pieces of information that may initially seem unrelated. We conducted a user study to analyze the cognitive process by which users connect pairs of documents and how they spatialize connections. Users created conceptual stories that connected the dots us...
متن کاملHow many rounds can Random Selection handle?∗
The construction of zero-knowledge proofs is greatly simplified if the protocol is only required be secure against the honest verifiers. Damg̊ard, Goldreich and Wigderson invented an technique, called Random Selection, to transform a public-coin honest verifier zero-knowledge protocol to a general zero-knowledge protocol [3]. However, it has been widely assumed that the technique itself only wor...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Advances in Applied Probability
سال: 2005
ISSN: 0001-8678,1475-6064
DOI: 10.1239/aap/1127483737