Related papers: Representation Gap of the Motzkin Monoid
A property of sparse representations in relation to their capacity for information storage is discussed. It is shown that this feature can be used for an application that we term Encrypted Image Folding. The proposed procedure is realizable…
This paper proposes a group membership verification protocol preventing the curious but honest server from reconstructing the enrolled signatures and inferring the identity of querying clients. The protocol quantizes the signatures into…
The Topological Representation Theorem for (oriented) matroids states that every (oriented) matroid can be realized as the intersection lattice of an arrangement of codimension one homotopy spheres on a homotopy sphere. In this paper, we…
Tensor network decomposition, originated from quantum physics to model entangled many-particle quantum systems, turns out to be a promising mathematical technique to efficiently represent and process big data in parsimonious manner. In this…
Many proofs in discrete mathematics and theoretical computer science are based on the probabilistic method. To prove the existence of a good object, we pick a random object and show that it is bad with low probability. This method is…
We show that the algebra of the coloured rook monoid $R_n^{(r)}$, {\em i.e.} the monoid of $n \times n$ matrices with at most one non-zero entry (an $r$-th root of unity) in each column and row, is the algebra of a finite groupoid, thus is…
The prominent success of neural networks, mainly in computer vision tasks, is increasingly shadowed by their sensitivity to small, barely perceivable adversarial perturbations in image input. In this work, we aim at explaining this…
Learning with graphs has attracted significant attention recently. Existing representation learning methods on graphs have achieved state-of-the-art performance on various graph-related tasks such as node classification, link prediction,…
Given a collection S of subsets of some set U, and M a subset of U, the set cover problem is to find the smallest subcollection C of S such that M is a subset of the union of the sets in C. While the general problem is NP-hard to solve,…
Backward reachability analysis is essential to synthesizing controllers that ensure the correctness of closed-loop systems. This paper is concerned with developing scalable algorithms that under-approximate the backward reachable sets, for…
Statistical analysis of a graph often starts with embedding, the process of representing its nodes as points in space. How to choose the embedding dimension is a nuanced decision in practice, but in theory a notion of true dimension is…
P vs NP problem is the most important unresolved problem in the field of computational complexity. Its impact has penetrated into all aspects of algorithm design, especially in the field of cryptography. The security of cryptographic…
In machine learning, graph embedding algorithms seek low-dimensional representations of the input network data, thereby allowing for downstream tasks on compressed encodings. Recently, within the framework of network renormalization,…
In this paper we consider a Metzner-Kapturowski-like decoding algorithm for high-order interleaved sum-rank-metric codes, offering a novel perspective on the decoding process through the concept of an error code. The error code, defined as…
Given a zigzag filtration, we want to find its barcode representatives, i.e., a compatible choice of bases for the homology groups that diagonalize the linear maps in the zigzag. To achieve this, we convert the input zigzag to a levelset…
Density based representations of atomic environments that are invariant under Euclidean symmetries have become a widely used tool in the machine learning of interatomic potentials, broader data-driven atomistic modelling and the…
The analysis of the decoding failure rate of the bit-flipping algorithm has received increasing attention. For a binary linear code we consider the minimum number of rows in a parity-check matrix such that the bit-flipping algorithm is able…
Network or graph structures are ubiquitous in the study of complex systems. Often, we are interested in complexity trends of these system as it evolves under some dynamic. An example might be looking at the complexity of a food web as…
Ellipsoids are a common representation for reachability analysis, because they can be transformed efficiently under affine maps, and allow conservative approximation of Minkowski sums, which let one incorporate uncertainty and linearization…
The enormous amount of data to be represented using large graphs exceeds in some cases the resources of a conventional computer. Edges in particular can take up a considerable amount of memory as compared to the number of nodes. However,…