A tripling construction for overlarge sets of KTS

AbstractAn overlarge set of KTS(v), denoted by OLKTS(v), is a collection {(X∖{x},Bx):x∈X}, where X is a (v+1)-set, each (X∖{x},Bx) is a KTS(v) and {Bx:x∈X} forms a partition of all triples on X. In this paper, we give a tripling construction for overlarge sets of KTS. Our main result is that: If there exists an OLKTS(v) with a special property, then there exists an OLKTS(3v). It is obtained that there exists an OLKTS(3m(2u+1)) for u=22n−1−1 or u=qn, where prime power q≡7 (mod 12) and m≥0,n≥1

Efficient Two-Stage Group Testing Algorithms for Genetic Screening

Efficient two-stage group testing algorithms that are particularly suited for rapid and less-expensive DNA library screening and other large scale biological group testing efforts are investigated in this paper. The main focus is on novel combinatorial constructions in order to minimize the number of individual tests at the second stage of a two-stage disjunctive testing procedure. Building on recent work by Levenshtein (2003) and Tonchev (2008), several new infinite classes of such combinatorial designs are presented.Comment: 14 pages; to appear in "Algorithmica". Part of this work has been presented at the ICALP 2011 Group Testing Workshop; arXiv:1106.368

Selected Papers in Combinatorics - a Volume Dedicated to R.G. Stanton

Professor Stanton has had a very illustrious career. His contributions to mathematics are varied and numerous. He has not only contributed to the mathematical literature as a prominent researcher but has fostered mathematics through his teaching and guidance of young people, his organizational skills and his publishing expertise. The following briefly addresses some of the areas where Ralph Stanton has made major contributions

Entanglement-assisted quantum low-density parity-check codes

This paper develops a general method for constructing entanglement-assisted quantum low-density parity-check (LDPC) codes, which is based on combinatorial design theory. Explicit constructions are given for entanglement-assisted quantum error-correcting codes (EAQECCs) with many desirable properties. These properties include the requirement of only one initial entanglement bit, high error correction performance, high rates, and low decoding complexity. The proposed method produces infinitely many new codes with a wide variety of parameters and entanglement requirements. Our framework encompasses various codes including the previously known entanglement-assisted quantum LDPC codes having the best error correction performance and many new codes with better block error rates in simulations over the depolarizing channel. We also determine important parameters of several well-known classes of quantum and classical LDPC codes for previously unsettled cases.Comment: 20 pages, 5 figures. Final version appearing in Physical Review

Smart elements in combinatorial group testing problems

In combinatorial group testing problems Questioner needs to find a special element $x \in [n]$ by testing subsets of $[n]$. Tapolcai et al. introduced a new model, where each element knows the answer for those queries that contain it and each element should be able to identify the special one. Using classical results of extremal set theory we prove that if $\mathcal{F}_n \subset 2^{[n]}$ solves the non-adaptive version of this problem and has minimal cardinality, then $$\lim_{n \rightarrow \infty} \frac{|\mathcal{F}_n|}{\log_2 n} = \log_{(3/2)}2.$$ This improves results by Tapolcai et al. We also consider related models inspired by secret sharing models, where the elements should share information among them to find out the special one. Finally the adaptive versions of the different models are investigated

Mission-driven entrepreneurship in ecosystems for sustainable systems change

De wereld is in verandering, we leven in een tijd van transitie. De schaal van de economische, sociale, ecologische en bestuurlijke uitdagingen die voor ons staan, is ongeëvenaard. De bevolking groeit in de richting van 9 miljard, de verstedelijking blijft toenemen, de risico’s van klimaatverandering nemen toe en de daarmee gepaarde energie-, water- en voedselveiligheid. Daarom volstaat vandaag de dag ‘business as usual’ niet meer. Dit promotieonderzoek baseert zich op de veronderstelling dat veel van de gangbare organiseerprincipes, zoals hiërarchie en strikte functie-verdeling, niet goed passen bij veel van de huidige maatschappelijke vraagstukken. Vanuit deze veronderstelling hebben we een vijflagenmodel ontwikkeld, welke gebaseerd is op de principes van systeemdenken. In dit proefschrift was speciale aandacht voor het meso-niveau (het ecosysteem), de onmisbare schakel die het micro-niveau (individuele missie-gedreven ondernemers) en het macro-niveau (duurzame systeemverandering) met elkaar verbindt. Dit proefschrift laat zien dat missie-gedreven ondernemers inspirerende change agents zijn in het systeem met hun onderneming als vehikel voor verandering. Voor grootschaligere systeemverandering naar een meer duurzame economie is het echter nodig samen te werken in ecosystemen. Het idee hierbij is dat er een vergaande samenwerking ontstaat tussen uiteenlopende organisaties, zowel uit de private als de publieke sector, zowel grote bedrijven en kleinere ondernemers. Deze organisaties overschrijden daarmee de grenzen van de traditionele industrieën en zijn in plaats daarvan georganiseerd rond een specifiek vraagstuk of thema. Samenwerken in ecosystemen gaat echter niet vanzelf, er zijn specifieke kennis en vaardigheden nodig, zoals systeemdenken, netwerkbenaderingen binnen en tussen organisaties, en het leiden van meerpartijenoverleg.In this time of systems change entrepreneurs can contribute to finding solutions for challenges the world faces. Focusing on technology is not sufficient, when we do not address organizing principles to change the way of doing business and stimulating innovation. This PhD research has been carried out with the assumption that current and still dominant organizing principles based on hierarchies in business and society are inadequate or even counter-effective in achieving a more sustainable economy. Thereto, this dissertation introduces a five-layered conceptual model based on systems thinking that offers a guidance to identify and analyze the organizing principles needed for sustainable systems change. The main aim of this research was to obtain in-depth insights into how this conceptual model works in practice, with an emphasis on the meso-level (ecosystem) and how this level connects the micro-level (mission-driven entrepreneur) and macro-level (sustainable systems change). The research has found that the ecosystem indeed plays an important role in leveraging the initiatives of mission-driven entrepreneurs for sustainable systems change. New skills and knowledge are needed in order to effectively apply organizational principles, such as deep collaboration and networking, to working in ecosystems. This dissertation shows that mission-driven entrepreneurs are inspiring change agents in the system with their company as a vehicle for change. However, for more systemic change needed for a sustainable economy, it is necessary to work together in ecosystems. The idea here is that there will be a far-reaching collaboration between various organizations, both from the private and the public sector, both large companies and smaller enterprises. These organizations therewith transcend the boundaries of traditional industries and are instead organized around a specific issue or theme. However, collaboration in ecosystems does not happen by itself; specific knowledge and skills are needed, such as systems thinking, network approaches, and leading multiparty dialogues