Related papers: A recursive construction for simple $t$-designs us…
Matrices are built and designed by applying procedures from lower order matrices. Matrix tensor products, direct sums or multiplication of matrices are such procedures and a matrix built from these is said to be a {\em separable} matrix. A…
In recent years, the creation of block-structured dictionary has attracted a lot of interest. Learning such dictionaries involve two step process: block formation and dictionary update. Both these steps are important in producing an…
Random sequential adsorption algorithm is a popular tool for modelling structure of monolayers built in irreversible adsorption experiments. However, this algorithm becomes very inefficient when the density of molecules in a layer rises.…
For a fixed root of a quiver, it is a very hard problem to construct all or even only one indecomposable representation with this root as dimension vector. We investigate two methods which can be used for this purpose. In both cases we get…
Reversibility is a key issue in the interface between computation and physics, and of growing importance as miniaturization progresses towards its physical limits. Most foundational work on reversible computing to date has focussed on…
It is commonly agreed that the success of future proof assistants will rely on their ability to incorporate computations within deduction in order to mimic the mathematician when replacing the proof of a proposition P by the proof of an…
Row-column designs play an important role in applications where two orthogonal sources of error need to be controlled for by blocking. Field or greenhouse experiments, in which experimental units are arranged as a rectangular array of…
The dimension of a block design is the maximum positive integer $d$ such that any $d$ of its points are contained in a proper subdesign. Pairwise balanced designs PBD$(v,K)$ have dimension at least two as long as not all points are on the…
In this article, three types of joins are introduced for subspaces of a vector space. Decompositions of the Gra{\ss}mannian into joins are discussed. This framework admits a generalization of large set recursion methods for block designs to…
We propose a computational design tool to enable casual end-users to easily design, fabricate, and assemble flat-pack furniture with guaranteed manufacturability. Using our system, users select parameterized components from a library and…
An RNA molecule is structured on several layers. The primary and most obvious structure is its sequence of bases, i.e. a word over the alphabet {A,C,G,U}. The higher structure is a set of one-to-one base-pairings resulting in a…
MDS matrices allow to build optimal linear diffusion layers in block ciphers. However, MDS matrices cannot be sparse and usually have a large description, inducing costly software/hardware implementations. Recursive MDS matrices allow to…
In this paper, six constructions of difference families are presented. These constructions make use of difference sets, almost difference sets and disjoint difference families, and give new point of views of relationships among these…
Self-assembly materials are traditionally designed so that molecular or meso-scale components form a single kind of large structure. Here, we propose a scheme to create "multifarious assembly mixtures", which self-assemble many different…
Truss optimization is a rich research field receiving renewed interest in limiting the carbon emissions of construction. However, a persistent challenge has been to construct highly optimized and often complex designs. This contribution…
A new class of exact-repair regenerating codes is constructed by combining two layers of erasure correction codes together with combinatorial block designs, e.g., Steiner systems, balanced incomplete block designs and t-designs. The…
The design of embedded systems, that are ubiquitously used in mobile devices and cars, is becoming continuously more complex such that efficient system-level design methods are becoming crucial. My research aims at developing systems that…
In this paper we study a certain generalization of combinatorial designs related to almost difference sets, namely the $t$-adesign, which was coined by Cunsheng Ding in 2015. It is clear that $2$-adesigns are a kind of partially balanced…
Within the framework of finite element systems, we show how spaces of differential forms may be constructed, in such a way that they are equipped with commuting interpolators and contain prescribed functions, and are minimal under these…
A class of random discrete distributions $P$ is introduced by means of a recursive splitting of unity. Assuming supercritical branching, we show that for partitions induced by sampling from such $P$ a power growth of the number of blocks is…