Related papers: Intersecting sets in probability spaces and Shelah…
The Szemer\'edi-Trotter theorem gives a bound on the maximum number of incidences between points and lines on the Euclidean plane. In particular it says that $n$ lines and $n$ points determine $O(n^{4/3})$ incidences. Let us suppose that an…
We consider shifts of a set $A\subseteq\mathbb{N}$ by elements from another set $B\subseteq\mathbb{N}$, and prove intersection properties according to the relative asymptotic size of $A$ and $B$. A consequence of our main theorem is the…
Given subvarieties $X, Y$ of a complex algebraic variety $S$ of complementary dimension, must they intersect? When $S$ is projective space, this is a consequence of the classical B\'ezout theorem, and an analogue for simple abelian…
With reference to a previous work, the problem of the experimental detection of non-causal synordination patterns between two series of physical events is examined. It is necessary that the patterns in question act in a reproducible, or at…
In the paper, we consider the problem of discovering sequential patterns from event-based spatio-temporal data. The problem is defined as follows: for a set of event types $F$ and for a dataset of events instances $D$ (where each instance…
We prove that a typical compact set does not contain any similar copy of a given pattern. We also prove that a typical compact set of $[0,1]^{d} (d\geq 2)$ intersects any $(d-1)$-dimensional plane in at most $d$ points. We study the…
For a finite poset $P$, we study the expected size of the intersection of two independent uniformly random antichains. Equivalently, we evaluate the sum of $|A\cap A'|$ over all ordered pairs of antichains. For general posets this statistic…
The detection of weak and rare effects in large amounts of data arises in a number of modern data analysis problems. Known results show that in this situation the potential of statistical inference is severely limited by the large-scale…
Consider the discrete cube $\{-1,1\}^N$ and a random collection of half spaces which includes each half space $H(x) := \{y \in \{-1,1\}^N: x \cdot y \geq \kappa \sqrt{N}\}$ for $x \in \{-1,1\}^N$ independently with probability $p$. Is the…
We study sequences of partitions of the unit interval into subintervals, starting from the trivial partition, in which each partition is obtained from the one before by splitting its subintervals in two, according to a given rule, and then…
The fundamental question considered in algorithms on strings is that of indexing, that is, preprocessing a given string for specific queries. By now we have a number of efficient solutions for this problem when the queries ask for an exact…
Let (X,\mu) be a measure space. For p, q\in (0,\infty] and arbitrary subsets P,Q of (0,\infty], we introduce and characterize some intersections of Lorentz spaces, denoted by ILp,Q(X,\mu), ILJ,q(X,\mu) and ILJ,Q(X,\mu).
This research creates a general class of "perturbation models" which are described by an underlying "null" model that accounts for most of the structure in data and a perturbation that accounts for possible small localized departures. The…
In this paper, we show that there is a close relation between consistency in a constraint network and set intersection. A proof schema is provided as a generic way to obtain consistency properties from properties on set intersection. This…
The natural habitat of most Bayesian methods is data represented by exchangeable sequences of observations, for which de Finetti's theorem provides the theoretical foundation. Dirichlet process clustering, Gaussian process regression, and…
The classic string indexing problem is to preprocess a string S into a compact data structure that supports efficient pattern matching queries. Typical queries include existential queries (decide if the pattern occurs in S), reporting…
The reason for recalling this old paper is the ongoing discussion on the attempts of circumventing certain assumptions leading to the Bell theorem (Hess-Philipp, Accardi). If I correctly understand the intentions of these Authors, the idea…
We introduce the following generalization of set intersection via characteristic vectors: for $n,q,s, t \ge 1$ a family $\mathcal{F}\subseteq \{0,1,\dots,q\}^n$ of vectors is said to be \emph{$s$-sum $t$-intersecting} if for any distinct…
Approach-level models were developed to accommodate the diversity of approaches within the same intersection. A random effect term, which indicates the intersection-specific effect, was incorporated into each crash type model to deal with…
Uniform probability distributions on $\ell_p$ balls and spheres have been studied extensively and are known to behave like product measures in high dimensions. In this note we consider the uniform distribution on the intersection of a…