Related papers: Collision-resistant hash-shuffles on the reals
We present new algorithms to perform fast probabilistic collision queries between convex as well as non-convex objects. Our approach is applicable to general shapes, where one or more objects are represented using Gaussian probability…
Recent advances in random linear systems on finite fields have paved the way for the construction of constant-time data structures representing static functions and minimal perfect hash functions using less space with respect to existing…
In this paper we investigate invertibility of graphs with a unique perfect matching, i.e. graphs having a unique 1-factor. We recall the new notion of the so-called negatively invertible graphs investigated by the authors in the recent…
We herein propose a new robust estimation method based on random projections that is adaptive and, automatically produces a robust estimate, while enabling easy computations for high or infinite dimensional data. Under some restricted…
A cohesive power of a structure is an effective analog of the classical ultrapower of a structure. We start with a computable structure, and consider its countable ultrapower over a cohesive set of natural numbers. A cohesive set is an…
This paper establishes the equivalence between robust safety and the existence of a barrier function certificate for differential inclusions. More precisely, for a robustly-safe differential inclusion, a barrier function is constructed as…
The definition of conservative-irreversible functions is extended to smooth manifolds. The local representation of these functions is studied and reveals that not each conservative-irreversible function is given by the weighted product of…
We develop a new approach to recurrence and the existence of non-constant harmonic functions on infinite weighted graphs. The approach is based on the capacity of subsets of metric boundaries with respect to intrinsic metrics. The main tool…
We characterize some major algorithmic randomness notions via differentiability of effective functions. (1) As the main result we show that a real number z in [0,1] is computably random if and only if each nondecreasing computable function…
We prove existence and uniqueness of the solution of a one-dimensional rough differential equation driven by a step-2 rough path and reflected at zero. In order to deal with the lack of control of the reflection measure the proof uses some…
We consider continuous functions f : [0,1] \to R that cut the real axis at every point of a measurable set of positive measure and we construct examples where f fails to have bounded variation, and at the opposite end, where f admits…
Hash tables are ubiquitous, and the choice of hash function, which maps a key to a bucket, is key to their performance. We argue that the predominant approach of fixing the hash function for the lifetime of the hash table is suboptimal and…
Let $n$ be a positive integer and $f$ a differentiable function from a convex subset $C$ of the Euclidean space $\mathbb{R}^n$ to a smooth manifold. We define an invariant of $f$ via counting certain threshold functions associated to $f$.…
A fundamental property of choice functions is stability, which, loosely speaking, prescribes that choice sets are invariant under adding and removing unchosen alternatives. We provide several structural insights that improve our…
We define new families of Tillich-Z\'emor hash functions, using higher dimensional special linear groups over finite fields as platforms. The Cayley graphs of these groups combine fast mixing properties and high girth, which together give…
Transportation maps between probability measures are critical objects in numerous areas of mathematics and applications such as PDE, fluid mechanics, geometry, machine learning, computer science, and economics. Given a pair of source and…
The property that a one to one function from the natural numbers to itself preserves the density of sub-sets is shown to be equivalent to a condition on the covering of intervals in the range of the function by images of intervals in the…
This work establishes a solution to the problem of assessing the capacity of multi-object assemblies to withstand external forces without becoming unstable. Our physically-grounded approach handles arbitrary structures made from rigid…
In this note, we study the easy certificate classes introduced by Hemaspaandra, Rothe, and Wechsung, with regard to the question of whether or not surjective one-way functions exist. This is an important open question in cryptology. We show…
For a random walk killed at leaving a cone we suggest two new constructions of a positive harmonic function. These constructions allow one to remove a quite strong extendability assumption, which has been imposed in our previous paper…