Related papers: Asymptotically Optimal Representation of Palindrom…
The asymptotically optimal version of Rapidly-exploring Random Tree (RRT*) is often used to find optimal paths in a high-dimensional configuration space. The well-known issue of RRT* is its slow convergence towards the optimal solution. A…
Given a semiring with a preorder subject to certain conditions, the asymptotic spectrum, as introduced by Strassen (J. reine angew. Math. 1988), is a compact Hausdorff space together with a map from the semiring to the ring of continuous…
Lookup tables are a fundamental structure in many data processing and systems applications. Examples include tokenized text in NLP, quantized embedding collections in recommendation systems, integer sketches for streaming data, and…
Let $m\neq n$. An $m\times n\times p$ proper array is a three-dimensional array composed of directed cubes that obeys certain constraints. Because of these constraints, the $m\times n\times p$ proper arrays may be classified via a schema in…
A parameter estimation problem is considered, in which dispersed sensors transmit to the statistician partial information regarding their observations. The sensors observe the paths of continuous semimartingales, whose drifts are linear…
Palindromes are non-empty strings that read the same forward and backward. The problem of recognizing strings that can be represented as the concatenation of even-length palindromes, the concatenation of palindromes of length at least two,…
High-energy, large-scale particle colliders in nuclear and high-energy physics generate data at extraordinary rates, reaching up to $1$ terabyte and several petabytes per second, respectively. The development of real-time, high-throughput…
We present a semantic parser for Abstract Meaning Representations which learns to parse strings into tree representations of the compositional structure of an AMR graph. This allows us to use standard neural techniques for supertagging and…
Succinct data structures give space-efficient representations of large amounts of data without sacrificing performance. They rely one cleverly designed data representations and algorithms. We present here the formalization in Coq/SSReflect…
Over the last 20 years significant effort has been dedicated to the development of sampling-based motion planning algorithms such as the Rapidly-exploring Random Trees (RRT) and its asymptotically optimal version (e.g. RRT*). However,…
We study the classification performance of Kronecker-structured models in two asymptotic regimes and developed an algorithm for separable, fast and compact K-S dictionary learning for better classification and representation of…
We consider sparse array beamfomer design achieving maximum signal-to interference plus noise ratio (MaxSINR). Both array configuration and weights are attuned to the changing sensing environment. This is accomplished by simultaneously…
We present a data structure that can maintain a simple planar graph under edge contractions in linear total time. The data structure supports adjacency queries and provides access to neighbor lists in $O(1)$ time. Moreover, it can report…
Graph compression is a data analysis technique that consists in the replacement of parts of a graph by more general structural patterns in order to reduce its description length. It notably provides interesting exploration tools for the…
The architecture of the brain is too complex to be intuitively surveyable without the use of compressed representations that project its variation into a compact, navigable space. The task is especially challenging with high-dimensional…
This paper studies the question of how well a signal can be reprsented by a sparse linear combination of reference signals from an overcomplete dictionary. When the dictionary size is exponential in the dimension of signal, then the exact…
Given a set of vectors (the data) in a Hilbert space H, we prove the existence of an optimal collection of subspaces minimizing the sum of the square of the distances between each vector and its closest subspace in the collection. This…
We generalize to the case of compactified superstrings a construction given previously for critical superstrings of finite one loop amplitudes that are well-defined for all external momenta. The novel issues that arise for compactified…
Given a string $S$ of length $n$, the classic string indexing problem is to preprocess $S$ into a compact data structure that supports efficient subsequent pattern queries. In this paper we consider the basic variant where the pattern is…
We present a method to extract temporal hypergraphs from sequences of 2-dimensional functions obtained as solutions to Optimal Transport problems. We investigate optimality principles exhibited by these solutions from the point of view of…