Discrete Distributions in the Tardos Scheme, Revisited

The Tardos scheme is a well-known traitor tracing scheme to protect copyrighted content against collusion attacks. The original scheme contained some suboptimal design choices, such as the score function and the distribution function used for generating the biases. Skoric et al. previously showed that a symbol-symmetric score function leads to shorter codes, while Nuida et al. obtained the optimal distribution functions for arbitrary coalition sizes. Later, Nuida et al. showed that combining these results leads to even shorter codes when the coalition size is small. We extend their analysis to the case of large coalitions and prove that these optimal distributions converge to the arcsine distribution, thus showing that the arcsine distribution is asymptotically optimal in the symmetric Tardos scheme. We also present a new, practical alternative to the discrete distributions of Nuida et al. and give a comparison of the estimated lengths of the fingerprinting codes for each of these distributions.Comment: 5 pages, 2 figure

The Collatz conjecture and De Bruijn graphs

We study variants of the well-known Collatz graph, by considering the action of the 3n+1 function on congruence classes. For moduli equal to powers of 2, these graphs are shown to be isomorphic to binary De Bruijn graphs. Unlike the Collatz graph, these graphs are very structured, and have several interesting properties. We then look at a natural generalization of these finite graphs to the 2-adic integers, and show that the isomorphism between these infinite graphs is exactly the conjugacy map previously studied by Bernstein and Lagarias. Finally, we show that for generalizations of the 3n+1 function, we get similar relations with 2-adic and p-adic De Bruijn graphs.Comment: 9 pages, 8 figure

Binomial collisions and near collisions

We describe efficient algorithms to search for cases in which binomial coefficients are equal or almost equal, give a conjecturally complete list of all cases where two binomial coefficients differ by 1, and give some identities for binomial coefficients that seem to be new.Comment: 7 page

Some Diophantine equations from finite group theory: Φm(x)=2pn−1\Phi_m(x)=2p^n-1

We show that the equation in the title (with $\Phi_m$ the $m$th cyclotomic polynomial) has no integer solution with $n\ge 1$ in the cases $(m,p)=(15,41), (15,5581),(10,271)$. These equations arise in a recent group theoretical investigation by Z. Akhlaghi, M. Khatami and B. Khosravi.Comment: 17 pages, slightly extended version is available as Max-Planck preprint MPIM 2009-6

Solving exponential diophantine equations using lattice basis reduction algorithms

Let S be the set of all positive integers with prime divisors from a fixed finite set of primes. Algorithms are given for solving the diophantine inequality 0< x − y < yδ in x, y S for fixed δ (0, 1), and for the diophantine equation x + Y = z in x, y, z S. The method is based on multi-dimensional diophantine approximation, in the real and p-adic case, respectively. The main computational tool is the L3-Basis Reduction Algorithm. Elaborate examples are presented

Data Minimisation in Communication Protocols: A Formal Analysis Framework and Application to Identity Management

With the growing amount of personal information exchanged over the Internet, privacy is becoming more and more a concern for users. One of the key principles in protecting privacy is data minimisation. This principle requires that only the minimum amount of information necessary to accomplish a certain goal is collected and processed. "Privacy-enhancing" communication protocols have been proposed to guarantee data minimisation in a wide range of applications. However, currently there is no satisfactory way to assess and compare the privacy they offer in a precise way: existing analyses are either too informal and high-level, or specific for one particular system. In this work, we propose a general formal framework to analyse and compare communication protocols with respect to privacy by data minimisation. Privacy requirements are formalised independent of a particular protocol in terms of the knowledge of (coalitions of) actors in a three-layer model of personal information. These requirements are then verified automatically for particular protocols by computing this knowledge from a description of their communication. We validate our framework in an identity management (IdM) case study. As IdM systems are used more and more to satisfy the increasing need for reliable on-line identification and authentication, privacy is becoming an increasingly critical issue. We use our framework to analyse and compare four identity management systems. Finally, we discuss the completeness and (re)usability of the proposed framework

The introduction and evaluation of telehealth into a mental health service

Introduction: This two-year project involves the introduction and evaluation of telehealth into a mental health service. Phase 1 of the project explores stakeholders’ views on how telehealth in the form of video conferencing could be used to link-up inpatient and community services. Aims and objectives: Identify issues regarding: •• Quality of care •• Length of inpatient stay •• Access, communication, and relationship between inpatient, CMHT staff, service-users, carers •• Unproductive staff time, travel time and cost •• Telehealth for therapeutic work Methods: These were: •• Focus groups, interviews with: staff, service-users •• Literature review •• Piloting of video conferencing facilities Results: The main findings were: •• Focus groups/interviews: (a) isolation of different teams; (b) communication, relationship between teams; (c) staff, service-users’ views on telehealth •• Literature review: identified relevant articles from 2000 onwards on the effectiveness of telehealth in mental health services and guidelines on the uses of video conferencing. •• Utilising the findings of (i) and (ii) to make recommendation. •• Initial findings from the pilot will be presented Conclusions: The combined findings from the focus groups and literature review have identified ways of introducing and evaluating telehealth to the service: •• Per site: 1 meeting room with 1 large screen for team activities (e.g. ward rounds). •• Per site: 1 dedicated computer with web-cam for quickly arranged, 1-1 calls (e.g. professional-professional, practice sharing)

Sedimentological characteristics of a late Miovene Contourite Channel System (The Rifian Corridor, Morocco)

Bottom currents are widely and increasingly more often recognized in deep-marine environments. However, the processes driving and controlling these bottom currents remain poorly understood. This partially results from their occurrence in near inaccessible deep-marine environments. Consequently, our knowledge of bottom currents significantly depends on studying their deposits.Idealized facies of bottom current deposits (contourites) have been established for fine-grained contourite drifts in modern deep-marine sedimentary environments however, their sand-rich counter parts, related to stronger bottom-currents, have remained more elusive. Equivalent contourite facies in the ancient record have only been scarcely recognized, hindering the development of models that can be applied to industry geosciences and the reconstruction of past ocean circulation.This Thesis presents a multidisciplinary field-focussed study on contourite deposits from the late Miocene Rifian Corridor in Morocco. A detailed geological analysis was carried out in the study area to characterise the paleogeographic setting and to analyse the potential of outcrops having a contouritic origin. Four sections were selected for detailed sedimentological analysis, including the characterisation of morphological, sedimentological, petrological, and ichnological elements. The results of these characterisations allowed us to reconstruct the newly identified contourite channel system associated to the late Miocene Mediterranean Outflow Water (paleo-MOW). Detailed facies analysis enables the characterisation of different contourite elements and the proposal of a novel contourite facies model.The new findings of this research project furthermore include the characterisation of control factors on the behaviour of overflow, and thus the controls on bottom-current formation and their evolution. These control factors range from tectonically induced re-configuration of overflow controlling geological features, multi-scale orbitally controlled climate change and its effects on overflow behaviour as well as a strong modulation by tides. Unravelling these control factors from the sedimentary record, enabled the evaluation of the evolution of contourite depositional systems. This in-turn allows for the predictability of bottom-current induced sedimentary systems and strategies for both energy geosciences and hydrocarbon exploration