Related papers: Pairs in Nested Steiner Quadruple Systems
Sharding has shown great potential to scale out blockchains. It divides nodes into smaller groups which allow for partial transaction processing, relaying and storage. Hence, instead of running one blockchain, we will run multiple…
The vision to develop quantum networks entails multi-user applications, which require the generation of long-distance multi-party entangled states. The current rapid experimental progress in building prototype-networks calls for new design…
We present results on the enumeration of crossings and nestings for matchings and set partitions. Using a bijection between partitions and vacillating tableaux, we show that if we fix the sets of minimal block elements and maximal block…
Two binary instrumental variables (IVs) are nested if individuals who comply under one binary IV also comply under the other. This situation often arises when the two IVs represent different intensities of encouragement or discouragement to…
Chen and Cheng [Ann. Statist. 34 (2006) 546--558] discussed the method of doubling for constructing two-level fractional factorial designs. They showed that for $9N/32\le n\le 5N/16$, all minimum aberration designs with $N$ runs and $n$…
Several methods for generating random Steiner triple systems (STSs) have been proposed in the literature, such as Stinson's hill-climbing algorithm and Cameron's algorithm, but these are not yet completely understood. Those algorithms, as…
This article aims to explain the Nested Benders algorithm for the solution of large-scale stochastic programming problems in a way that is intelligible to someone coming to it for the first time. In doing so it gives an explanation of…
In this paper, we introduce the concept of a nested family of torsion pairs and will prove that this concept is strongly related to the existence of stratifying systems. Specifically, every stratifying system induces a nested family of…
Heterogeneous bipartite quantum pure states, composed of two subsystems with a different number of levels, cannot have both reductions maximally mixed. In this work, we demonstrate existence of a wide range of highly entangled states of…
We propose a quantum repeater protocol and architecture that mitigates decoherence of the entangled states by optimizing the quantum memory buffer time. The protocol maximizes the rate of distillable entanglement in the average accessed…
Coded matrix multiplication is a technique to enable straggler-resistant multiplication of large matrices in distributed computing systems. In this paper, we first present a conceptual framework to represent the division of work amongst…
In the Stable Roommates problem, we seek a stable matching of the agents into pairs, in which no two agents have an incentive to deviate from their assignment. It is well known that a stable matching is unlikely to exist, but a stable…
Parity declustering allows faster reconstruction of a disk array when some disk fails. Moreover, it guarantees uniform reconstruction workload on all surviving disks. It has been shown that parity declustering for one-failure tolerant array…
A Ryser design $\mathcal{D}$ on $v$ points is a collection of $v$ proper subsets (called blocks) of a point-set with $v$ points such that every two blocks intersect each other in $\lambda$ points (and $\lambda < v$ is a fixed number) and…
In distributed matrix multiplication, a common scenario is to assign each worker a fraction of the multiplication task, by partitioning the input matrices into smaller submatrices. In particular, by dividing two input matrices into…
The continuously increasing amount of digital data generated by today's society asks for better storage solutions. This survey looks at a new generation of coding techniques designed specifically for the needs of distributed networked…
The design of many-core neuromorphic hardware is getting more and more complex as these systems are expected to execute large machine learning models. To deal with the design complexity, a predictable design flow is needed to guarantee…
A balanced incomplete block design is a set system in which all pairs of distinct elements occur with a constant frequency. By contrast, a Sarvate-Beam design induces an interval of distinct frequencies on pairs. In this paper, we settle…
We formulate the problem of finding the optimal entanglement swapping scheme in a quantum repeater chain as a Markov decision process and present its solution for different repeater's sizes. Based on this, we are able to demonstrate that…
Emerging optical and virtualization technologies enable the design of more flexible and demand-aware networked systems, in which resources can be optimized toward the actual workload they serve. For example, in a demand-aware datacenter…