Related papers: La Baguette Math\'emagique
Attempting to create a general framework for studying new results on transcendental numbers, this paper begins with a survey on transcendental numbers and transcendence, it then presents several properties of the transcendental numbers $e$…
Many problems in materials science and biology involve particles interacting with strong, short-ranged bonds, that can break and form on experimental timescales. Treating such bonds as constraints can significantly speed up sampling their…
In a general simulation of random walking (with the angle of motion picked uniformly), it can be seen that the probability of crossing a WiFi TX-RX link is directly proportional to the per-step distance and inversely proportional to the…
We propose the so-called jackknife empirical likelihood approach for the survey data of general unequal probability sampling designs, and analyze parameters defined according to U-statistics. We prove theoretically that jackknife…
The biological characteristics of human visual processing can be investigated through the study of optical illusions and their perception, giving rise to intuitions that may improve computer vision to match human performance. Geometric…
Let $\Omega \subset \mathbb{R}^2$ be a convex set. We study the problem of distributing a one-dimensional set $S$ with total length $L$ so that for any line $\ell$ in $\mathbb{R}^2$ the number of intersections $\#(\ell \cap S)$ is…
We consider fits to two or more datasets for which results from the sa me experiment share a common systematic uncertainty in addition to their individ ual statistical errors. This is important in extracting the maximum information from a…
In this paper we prove the "Tiling implies Spectral" part of Fuglede's paper for the case of three intervals. Then we prove the "Spectral implies Tiling" part of the conjecture for the case of three equal intervals as also when the…
We revisit empirical Bayes discrimination detection, focusing on uncertainty arising from both partial identification and sampling variability. While prior work has mostly focused on partial identification, we find that some empirical…
We use Stein's method to obtain bounds on the rate of convergence for a class of statistics in geometric probability obtained as a sum of contributions from Poisson points which are exponentially stabilizing, i.e. locally determined in a…
We consider the urn setting with two different objects, ``good'' and ``bad'', and analyze the number of draws without replacement until a good object is picked. Although the expected number of draws for this setting is a standard textbook…
Calculations and mechanistic explanations for the probabilistic movement of objects at the highly relevant cm length scales has been lacking and overlooked due to the complexity of current techniques. Predicting the final-configuration…
This paper is based on the study of random lozenge tilings of non-convex polygonal regions with interacting non-convexities (cuts) and the corresponding asymptotic kernel as in [3] and [4] (discrete tacnode kernel). Here this kernel is used…
In this paper we consider fractal percolation random Cantor sets $E$ on the plane constructed with non-homogeneous probabilities. We focus on the case when the probabilities are large enough to guarantee that the almost sure dimension of…
In the first part of this paper, we obtain symmetric formulae for the probabilities that a plane convex body hits exactly 1, 2, 3, 4, 5 or 6 triangles of a lattice of congruent triangles in the plane. Furthermore, a very simple formula for…
Current literature on posterior approximation for Bayesian inference offers many alternative methods. Does our chosen approximation scheme work well on the observed data? The best existing generic diagnostic tools treating this kind of…
A discrete-time stochastic process derived from a model of basketball is used to generalize any discrete distribution. The generalized distributions can have one or two more parameters than the parent distribution. Those derived from…
The geometry of unit $N$-dimensional $\ell_{p}$ balls has been intensively investigated in the past decades. A particular topic of interest has been the study of the asymptotics of their projections. Apart from their intrinsic interest,…
There seems to be an upper limit to predicting the outcome of matches in (semi-)professional sports. Recent work has proposed that this is due to chance and attempts have been made to simulate the distribution of win percentages to identify…
This paper develops a unified framework for partial identification and inference in stratified experiments with attrition, accommodating both equal and heterogeneous treatment shares across strata. For equal-share designs, we apply recent…