Approximate Randomization of Quantum States With Fewer Bits of Key

Randomization of quantum states is the quantum analogue of the classical one-time pad. We present an improved, efficient construction of an approximately randomizing map that uses O(d/epsilon^2) Pauli operators to map any d-dimensional state to a state that is within trace distance epsilon of the completely mixed state. Our bound is a log d factor smaller than that of Hayden, Leung, Shor, and Winter (2004), and Ambainis and Smith (2004). Then, we show that a random sequence of essentially the same number of unitary operators, chosen from an appropriate set, with high probability form an approximately randomizing map for d-dimensional states. Finally, we discuss the optimality of these schemes via connections to different notions of pseudorandomness, and give a new lower bound for small epsilon.Comment: 18 pages, Quantum Computing Back Action, IIT Kanpur, March 2006, volume 864 of AIP Conference Proceedings, pages 18--36. Springer, New Yor

Compressing Sparse Sequences under Local Decodability Constraints

We consider a variable-length source coding problem subject to local decodability constraints. In particular, we investigate the blocklength scaling behavior attainable by encodings of $r$-sparse binary sequences, under the constraint that any source bit can be correctly decoded upon probing at most $d$ codeword bits. We consider both adaptive and non-adaptive access models, and derive upper and lower bounds that often coincide up to constant factors. Notably, such a characterization for the fixed-blocklength analog of our problem remains unknown, despite considerable research over the last three decades. Connections to communication complexity are also briefly discussed.Comment: 8 pages, 1 figure. First five pages to appear in 2015 International Symposium on Information Theory. This version contains supplementary materia

A New Test for Chaos

We describe a new test for determining whether a given deterministic dynamical system is chaotic or nonchaotic. (This is an alternative to the usual approach of computing the largest Lyapunov exponent.) Our method is a 0-1 test for chaos (the output is a 0 signifying nonchaotic or a 1 signifying chaotic) and is independent of the dimension of the dynamical system. Moreover, the underlying equations need not be known. The test works equally well for continuous and discrete time. We give examples for an ordinary differential equation, a partial differential equation and for a map.Comment: 10 pages, 5 figure

Sociological Knowledge and Transformation at ‘Diversity University’, UK

This chapter is based on a case study of one UK university sociology department and shows how sociology knowledge can transform the lives of ‘non-traditional’ students. The research from which the case is drawn focused on four departments teaching sociology-related subjects in universities positioned differently in UK league tables. It explored the question of the relationship between university reputation, pedagogic quality and curriculum knowledge, challenging taken-for-granted judgements about ‘quality’ and in conceptualising ‘just’ university pedagogy by taking Basil Bernstein’s ideas about how ‘powerful’ knowledge is distributed in society to illuminate pedagogy and curriculum. The project took the view that ‘power’ lies in the acquisition of specific (inter)disciplinary knowledges which allows the formation of disciplinary identities by way of developing the means to think about and act in the world in specific ways. We chose to focus on sociology because (1) university sociology is taken up by all socio-economic classes in the UK and is increasingly taught in courses in which the discipline is applied to practice; (2) it is a discipline that historically pursues social and moral ambition which assists exploration of the contribution of pedagogic quality to individuals and society beyond economic goals; (3) the researchers teach and research sociology or sociology of education - an understanding of the subjects under discussion is essential to make judgements about quality. ‘Diversity’ was one of four case study universities. It ranks low in university league tables; is located in a large, multi-cultural English inner city; and, its students are likely to come from lower socio-economic and/or ethnic minority groups, as well as being the first in their families to attend university. To make a case for transformative teaching at Diversity, the chapter draws on longitudinal interviews with students, interviews with tutors, curriculum documents, recordings of teaching, examples of student work, and a survey. It establishes what we can learn from the case of sociology at Diversity, arguing that equality, quality and transformation for individuals and society are served by a university curriculum which is research led and challenging combined with pedagogical practices which give access to difficult-to-acquire and powerful knowledge

Chaos in Symmetric Phase Oscillator Networks

Phase-coupled oscillators serve as paradigmatic models of networks of weakly interacting oscillatory units in physics and biology. The order parameter which quantifies synchronization was so far found to be chaotic only in systems with inhomogeneities. Here we show that even symmetric systems of identical oscillators may not only exhibit chaotic dynamics, but also chaotically fluctuating order parameters. Our findings imply that neither inhomogeneities nor amplitude variations are necessary to obtain chaos, i.e., nonlinear interactions of phases give rise to the necessary instabilities.Comment: 4 pages; Accepted by Physical Review Letter

"Siddhartha", the Paradox, and the Counterculture

Während Hermann Hesse vor den 1960er Jahren zu einem der vielgelesenen Autoren gehörte, führte das starke Interesse der Gegenkultur an seinem Werk zu einem wissenschaftlichen Parallelfokus auf die globale Rezeption und Einfluss Hesses. Es scheint, als ob die Forschung auf eine Stärkung von Hans Robert Jauß' zeitgenössischen Annahmen zur Rezeptionstheorie ausgerichtet waren. Jauß' Rezeptionstheorie macht verständlich, wie ein einzelner Text unzählige Gedanken, Untersuchungen und Antworten bewirken kann. Der Beitrag widmet sich daher der Frage, weshalb Siddharta gut 45 Jahre nach seinem Erscheinen für die US-amerikanische Gegenkultur von so hoher Relevanz war