Testing Linear-Invariant Non-Linear Properties

We consider the task of testing properties of Boolean functions that are invariant under linear transformations of the Boolean cube. Previous work in property testing, including the linearity test and the test for Reed-Muller codes, has mostly focused on such tasks for linear properties. The one exception is a test due to Green for "triangle freeness": a function f:\cube^{n}\to\cube satisfies this property if $f(x),f(y),f(x+y)$ do not all equal 1, for any pair x,y\in\cube^{n}. Here we extend this test to a more systematic study of testing for linear-invariant non-linear properties. We consider properties that are described by a single forbidden pattern (and its linear transformations), i.e., a property is given by $k$ points v_{1},...,v_{k}\in\cube^{k} and f:\cube^{n}\to\cube satisfies the property that if for all linear maps L:\cube^{k}\to\cube^{n} it is the case that $f(L(v_{1})),...,f(L(v_{k}))$ do not all equal 1. We show that this property is testable if the underlying matroid specified by $v_{1},...,v_{k}$ is a graphic matroid. This extends Green's result to an infinite class of new properties. Our techniques extend those of Green and in particular we establish a link between the notion of "1-complexity linear systems" of Green and Tao, and graphic matroids, to derive the results.Comment: This is the full version; conference version appeared in the proceedings of STACS 200

The critical window for the classical Ramsey-Tur\'an problem

The first application of Szemer\'edi's powerful regularity method was the following celebrated Ramsey-Tur\'an result proved by Szemer\'edi in 1972: any K_4-free graph on N vertices with independence number o(N) has at most (1/8 + o(1)) N^2 edges. Four years later, Bollob\'as and Erd\H{o}s gave a surprising geometric construction, utilizing the isoperimetric inequality for the high dimensional sphere, of a K_4-free graph on N vertices with independence number o(N) and (1/8 - o(1)) N^2 edges. Starting with Bollob\'as and Erd\H{o}s in 1976, several problems have been asked on estimating the minimum possible independence number in the critical window, when the number of edges is about N^2 / 8. These problems have received considerable attention and remained one of the main open problems in this area. In this paper, we give nearly best-possible bounds, solving the various open problems concerning this critical window.Comment: 34 page

Knowledge management in future organizations

publishedVersio

Label-free electrochemical monitoring of DNA ligase activity

This study presents a simple, label-free electrochemical technique for the monitoring of DNA ligase activity. DNA ligases are enzymes that catalyze joining of breaks in the backbone of DNA and are of significant scientific interest due to their essential nature in DNA metabolism and their importance to a range of molecular biological methodologies. The electrochemical behavior of DNA at mercury and some amalgam electrodes is strongly influenced by its backbone structure, allowing a perfect discrimination between DNA molecules containing or lacking free ends. This variation in electrochemical behavior has been utilized previously for a sensitive detection of DNA damage involving the sugar-phosphate backbone breakage. Here we show that the same principle can be utilized for monitoring of a reverse process, i.e., the repair of strand breaks by action of the DNA ligases. We demonstrate applications of the electrochemical technique for a distinction between ligatable and unligatable breaks in plasmid DNA using T4 DNA ligase, as well as for studies of the DNA backbone-joining activity in recombinant fragments of E. coli DNA ligase

On certain other sets of integers

We show that if A is a subset of {1,...,N} containing no non-trivial three-term arithmetic progressions then |A|=O(N/ log^{3/4-o(1)} N).Comment: 29 pp. Corrected typos. Added definitions for some non-standard notation and remarks on lower bound

How to Create an Innovation Accelerator

Too many policy failures are fundamentally failures of knowledge. This has become particularly apparent during the recent financial and economic crisis, which is questioning the validity of mainstream scholarly paradigms. We propose to pursue a multi-disciplinary approach and to establish new institutional settings which remove or reduce obstacles impeding efficient knowledge creation. We provided suggestions on (i) how to modernize and improve the academic publication system, and (ii) how to support scientific coordination, communication, and co-creation in large-scale multi-disciplinary projects. Both constitute important elements of what we envision to be a novel ICT infrastructure called "Innovation Accelerator" or "Knowledge Accelerator".Comment: 32 pages, Visioneer White Paper, see http://www.visioneer.ethz.c

The use of routine outcome measures in two child and adolescent mental health services: a completed audit cycle

Background: Routine outcome measurement (ROM) is important for assessing the clinical effectiveness of health services and for monitoring patient outcomes. Within Child and Adolescent Mental Health Services (CAMHS) in the UK the adoption of ROM in CAMHS has been supported by both national and local initiatives (such as government strategies, local commissioning policy, and research). Methods: With the aim of assessing how these policies and initiatives may have influenced the uptake of ROM within two different CAMHS we report the findings of two case-note audits: a baseline audit conducted in January 2011 and a re-audit conducted two years later in December 2012-February 2013. Results: The findings show an increase in both the single and repeated use of outcome measures from the time of the original audit, with repeated use (baseline and follow-up) of the Health of the Nation Outcome Scale for Children and Adolescents (HoNOSCA) scale increasing from 10% to 50% of cases. Re-audited case-notes contained more combined use of different outcome measures, with greater consensus on which measures to use. Outcome measures that were applicable across a wide range of clinical conditions were more likely to be used than symptom-specific measures, and measures that were completed by the clinician were found more often than measures completed by the service user. Conclusions: The findings show a substantial improvement in the use of outcome measures within CAMHS. These increases in use were found across different service organisations which were subject to different types of local service priorities and drivers

Mathematical practice, crowdsourcing, and social machines

The highest level of mathematics has traditionally been seen as a solitary endeavour, to produce a proof for review and acceptance by research peers. Mathematics is now at a remarkable inflexion point, with new technology radically extending the power and limits of individuals. Crowdsourcing pulls together diverse experts to solve problems; symbolic computation tackles huge routine calculations; and computers check proofs too long and complicated for humans to comprehend. Mathematical practice is an emerging interdisciplinary field which draws on philosophy and social science to understand how mathematics is produced. Online mathematical activity provides a novel and rich source of data for empirical investigation of mathematical practice - for example the community question answering system {\it mathoverflow} contains around 40,000 mathematical conversations, and {\it polymath} collaborations provide transcripts of the process of discovering proofs. Our preliminary investigations have demonstrated the importance of "soft" aspects such as analogy and creativity, alongside deduction and proof, in the production of mathematics, and have given us new ways to think about the roles of people and machines in creating new mathematical knowledge. We discuss further investigation of these resources and what it might reveal. Crowdsourced mathematical activity is an example of a "social machine", a new paradigm, identified by Berners-Lee, for viewing a combination of people and computers as a single problem-solving entity, and the subject of major international research endeavours. We outline a future research agenda for mathematics social machines, a combination of people, computers, and mathematical archives to create and apply mathematics, with the potential to change the way people do mathematics, and to transform the reach, pace, and impact of mathematics research.Comment: To appear, Springer LNCS, Proceedings of Conferences on Intelligent Computer Mathematics, CICM 2013, July 2013 Bath, U

Small doubling in groups

Let A be a subset of a group G = (G,.). We will survey the theory of sets A with the property that |A.A| <= K|A|, where A.A = {a_1 a_2 : a_1, a_2 in A}. The case G = (Z,+) is the famous Freiman--Ruzsa theorem.Comment: 23 pages, survey article submitted to Proceedings of the Erdos Centenary conferenc