Related papers: The intersection of algorithmically random closed …
Delorme suggested that the set of all complete intersection numerical semigroups can be computed recursively. We have implemented this algorithm, and particularized it to several subfamilies of this class of numerical semigroups: free and…
Random code-trees with necks were introduced recently to generalise the notion of $V$-variable and random homogeneous sets. While it is known that the Hausdorff and packing dimensions coincide irrespective of overlaps, their exact Hausdorff…
Current discrete randomness and information conservation inequalities are over total recursive functions, i.e. restricted to deterministic processing. This restriction implies that an algorithm can break algorithmic randomness conservation…
This is a survey of constructive and computable measure theory with an emphasis on the close connections with algorithmic randomness. We give a brief history of constructive measure theory from Brouwer to the present, emphasizing how…
The wide availability of biological data at the genome-scale and across multiple variables has resulted in statistical questions regarding the enrichment or depletion of the number of discrete objects (e.g. genes) identified in individual…
Geometrical measurements of biological objects form the basis of many quantitative analyses. Hausdorff measures such as the volume and the area of objects are simple and popular descriptors of individual objects, however, for most…
Bernoulli convolutions are certain measures on the unit interval depending on a parameter $\beta$ between 1 and 2. In spite of their simple definition, they are not yet well understood. We study their two-dimensional density which exists by…
In this paper, we investigate the Hausdorff dimension of naturally occurring sets of inhomogeneous well-approximable points with a sequence of real invertible matrices $\mathcal{A}=(A_n)_{n\in\mathbb{N}}$. Specifically, for a given point…
Geometric embeddings have recently received attention for their natural ability to represent transitive asymmetric relations via containment. Box embeddings, where objects are represented by n-dimensional hyperrectangles, are a particularly…
Random intersection graphs containing an underlying community structure are a popular choice for modelling real-world networks. Given the group memberships, the classical random intersection graph is obtained by connecting individuals when…
We introduce and study an infinite random triangulation of the unit disk that arises as the limit of several recursive models. This triangulation is generated by throwing chords uniformly at random in the unit disk and keeping only those…
Random embeddings project high-dimensional spaces to low-dimensional ones; they are careful constructions which allow the approximate preservation of key properties, such as the pair-wise distances between points. Often in the field of…
Oriented closed curves on an orientable surface with boundary are described up to continuous deformation by reduced cyclic words in the generators of the fundamental group and their inverses. By self-intersection number one means the…
We consider the problem of decomposing a higher-order tensor with binary entries. Such data problems arise frequently in applications such as neuroimaging, recommendation system, topic modeling, and sensor network localization. We propose a…
This paper deals with the problem of detecting non-isotropic high-dimensional geometric structure in random graphs. Namely, we study a model of a random geometric graph in which vertices correspond to points generated randomly and…
We study concentration inequalities for structured weighted sums of random data, including (i) tensor inner products and (ii) sequential matrix sums. We are interested in tail bounds and concentration inequalities for those structured…
We consider multiple and set-indexed sums of random vectors taking values in Euclidean space of growing dimension. It is shown that, when viewed as finite metric spaces, the sets of values of such sums converge in probability. The limit is…
Let At denote the set of infinite sequences of effective dimension t. We determine both how close and how far an infinite sequence of dimension s can be from one of dimension t, measured using the Besicovitch pseudometric. We also identify…
A previous paper (hep-lat/9311011) proposed a new kind of random walk on a spherically-symmetric lattice in arbitrary noninteger dimension $D$. Such a lattice avoids the problems associated with a hypercubic lattice in noninteger dimension.…
We study the set of irregular points for topologically mixing subshifts of finite type. It is well known that despite the irregular set having zero measure for every invariant measure, it has full topological entropy and full Hausdorff…