Related papers: Locating Patterns in the De Bruijn Torus
The graph of overlapping permutations is a directed graph that is an analogue to the De Bruijn graph. It consists of vertices that are permutations of length $n$ and edges that are permutations of length $n+1$ in which an edge $a_1\cdots…
A unibike curve is a track that can be made by either a bicycle or a unicycle. More precisely, the end of a unit tangent vector at any point on a unibike curve lies on the curve (so the bike's front wheel always lies on the track made by…
The de Bruijn graph $G_K$ of a set of strings $S$ is a key data structure in genome assembly that represents overlaps between all the $K$-length substrings of $S$. Construction and navigation of the graph is a space and time bottleneck in…
A binary matrix can be scanned by moving a fixed rectangular window (submatrix) across it, rather like examining it closely under a microscope. With each viewing, a convenient measurement is the number of 1s visible in the window, which…
Grid maps are widely used in robotics to represent obstacles in the environment and differentiating dynamic objects from static infrastructure is essential for many practical applications. In this work, we present a methods that uses a deep…
The DEtection TRansformer (DETR) algorithm has received considerable attention in the research community and is gradually emerging as a mainstream approach for object detection and other perception tasks. However, the current field lacks a…
Bayesian Networks (BNs) have become increasingly popular over the last few decades as a tool for reasoning under uncertainty in fields as diverse as medicine, biology, epidemiology, economics and the social sciences. This is especially true…
Recent decades have seen the discovery of numerous complex materials. At the root of the complexity underlying many of these materials lies a large number of possible contending atomic- and larger-scale configurations and the intricate…
In this work we present a general and versatile algorithmic framework for exhaustively generating a large variety of different combinatorial objects, based on encoding them as permutations. This approach provides a unified view on many…
One of the strategies to detect the pose and shape of unknown objects is their geometric modeling, consisting on fitting known geometric entities. Classical geometric modeling fits simple shapes such as spheres or cylinders, but often those…
In this article, we show how to transform a colored de Bruijn graph (dBG) into a practical index for processing massive sets of sequencing reads. Similar to previous works, we encode an instance of a colored dBG of the set using BOSS and a…
Occupancy grids encode for hot spots on a map that is represented by a two dimensional grid of disjoint cells. The problem is to recursively update the probability that each cell in the grid is occupied, based on a sequence of sensor…
A lot of attention has been paid to the investigation of the algebraic properties of linear codes. In most cases, this investigation involves the determination of required code automorphisms, which are useful for decoders, such as the…
A universal cycle is a cyclic sequence in which each object of a combinatorial family appears exactly once as a contiguous window. While such cycles are well understood for many discrete structures and linear subspaces, the case of affine…
We propose a family of gradient reconstruction schemes based on the solution of over-determined systems by orthogonal or oblique projections. In the case of orthogonal projections, we retrieve familiar weighted least-squares gradients, but…
Two dimensional matrices with binary (0/1) entries are a common data structure in many research fields. Examples include ecology, economics, mathematics, physics, psychometrics and others. Because the columns and rows of these matrices…
A number of applications of Steiner triple systems (e.g. disk erasure codes) exist that require a special ordering of its blocks. Universal cycles, introduced by Chung, Diaconis, and Graham in 1992, and Gray codes are examples of listing…
The Consecutive Ones Property is an important notion for binary matrices, both from a theoretical and applied point of view. Tucker gave in 1972 a characterization of matrices that do not satisfy the Consecutive Ones Property in terms of…
A new efficient algorithm is presented for finding all simple cycles that satisfy a length constraint in a directed graph. When the number of vertices is non-trivial, most cycle-finding problems are of practical interest for sparse graphs…
Clustering is an important topic in algorithms, and has a number of applications in machine learning, computer vision, statistics, and several other research disciplines. Traditional objectives of graph clustering are to find clusters with…