The dynamic counter-based broadcast for mobile ad hoc networks

Broadcasting is a fundamental operation in mobile ad hoc networks (MANETs) crucial to the successful deployment of MANETs in practice. Simple flooding is the most basic broadcasting technique where each node rebroadcasts any received packet exactly once. Although flooding is ideal for its simplicity and high reachability it has a critical disadvantage in that it tends to generate excessive collision and consumes the medium by unneeded and redundant packets. A number of broadcasting schemes have been proposed in MANETs to alleviate the drawbacks of flooding while maintaining a reasonable level of reachability. These schemes mainly fall into two categories: stochastic and deterministic. While the former employs a simple yet effective probabilistic principle to reduce redundant rebroadcasts the latter typically requires sophisticated control mechanisms to reduce excessive broadcast. The key danger with schemes that aim to reduce redundant broadcasts retransmissions is that they often do so at the expense of a reachability threshold which can be required in many applications. Among the proposed stochastic schemes, is counter-based broadcasting. In this scheme redundant broadcasts are inhibited by criteria related to the number of duplicate packets received. For this scheme to achieve optimal reachability, it requires fairly stable and known nodal distributions. However, in general, a MANETs‟ topology changes continuously and unpredictably over time. Though the counter-based scheme was among the earliest suggestions to reduce the problems associated with broadcasting, there have been few attempts to analyse in depth the performance of such an approach in MANETs. Accordingly, the first part of this research, Chapter 3, sets a baseline study of the counter-based scheme analysing it under various network operating conditions. The second part, Chapter 4, attempts to establish the claim that alleviating existing stochastic counter-based scheme by dynamically setting threshold values according to local neighbourhood density improves overall network efficiency. This is done through the implementation and analysis of the Dynamic Counter-Based (DCB) scheme, developed as part of this work. The study shows a clear benefit of the proposed scheme in terms of average collision rate, saved rebroadcasts and end-to-end delay, while maintaining reachability. The third part of this research, Chapter 5, evaluates dynamic counting and tests its performance in some approximately realistic scenarios. The examples chosen are from the rapidly developing field of Vehicular Ad hoc Networks (VANETs). The schemes are studied under metropolitan settings, involving nodes moving in streets and lanes with speed and direction constraints. Two models are considered and implemented: the first assuming an unobstructed open terrain; the other taking account of buildings and obstacles. While broadcasting is a vital operation in most MANET routing protocols, investigation of stochastic broadcast schemes for MANETs has tended to focus on the broadcast schemes, with little examination on the impact of those schemes in specific applications, such as route discovery in routing protocols. The fourth part of this research, Chapter 6, evaluates the performance of the Ad hoc On-demand Distance Vector (AODV) routing protocol with a route discovery mechanism based on dynamic-counting. AODV was chosen as it is widely accepted by the research community and is standardised by the MANET IETF working group. That said, other routing protocols would be expected to interact in a similar manner. The performance of the AODV routing protocol is analysed under three broadcasting mechanisms, notably AODV with flooding, AODV with counting and AODV with dynamic counting. Results establish that a noticeable advantage, in most considered metrics can be achieved using dynamic counting with AODV compared to simple counting or traditional flooding. In summary, this research analysis the Dynamic Counter-Based scheme under a range of network operating conditions and applications; and demonstrates a clear benefit of the scheme when compared to its predecessors under a wide range of considered conditions

Answering Conjunctive Queries under Updates

We consider the task of enumerating and counting answers to $k$-ary conjunctive queries against relational databases that may be updated by inserting or deleting tuples. We exhibit a new notion of q-hierarchical conjunctive queries and show that these can be maintained efficiently in the following sense. During a linear time preprocessing phase, we can build a data structure that enables constant delay enumeration of the query results; and when the database is updated, we can update the data structure and restart the enumeration phase within constant time. For the special case of self-join free conjunctive queries we obtain a dichotomy: if a query is not q-hierarchical, then query enumeration with sublinear$^\ast$ delay and sublinear update time (and arbitrary preprocessing time) is impossible. For answering Boolean conjunctive queries and for the more general problem of counting the number of solutions of k-ary queries we obtain complete dichotomies: if the query's homomorphic core is q-hierarchical, then size of the the query result can be computed in linear time and maintained with constant update time. Otherwise, the size of the query result cannot be maintained with sublinear update time. All our lower bounds rely on the OMv-conjecture, a conjecture on the hardness of online matrix-vector multiplication that has recently emerged in the field of fine-grained complexity to characterise the hardness of dynamic problems. The lower bound for the counting problem additionally relies on the orthogonal vectors conjecture, which in turn is implied by the strong exponential time hypothesis. $^\ast)$ By sublinear we mean $O(n^{1-\varepsilon})$ for some $\varepsilon>0$, where $n$ is the size of the active domain of the current database

Haldane Statistics in the Finite Size Entanglement Spectra of Laughlin States

We conjecture that the counting of the levels in the orbital entanglement spectra (OES) of finite-sized Laughlin Fractional Quantum Hall (FQH) droplets at filling $\nu=1/m$ is described by the Haldane statistics of particles in a box of finite size. This principle explains the observed deviations of the OES counting from the edge-mode conformal field theory counting and directly provides us with a topological number of the FQH states inaccessible in the thermodynamic limit- the boson compactification radius. It also suggests that the entanglement gap in the Coulomb spectrum in the conformal limit protects a universal quantity- the statistics of the state. We support our conjecture with ample numerical checks.Comment: 4.1 pages, published versio

Cross-Document Pattern Matching

We study a new variant of the string matching problem called cross-document string matching, which is the problem of indexing a collection of documents to support an efficient search for a pattern in a selected document, where the pattern itself is a substring of another document. Several variants of this problem are considered, and efficient linear-space solutions are proposed with query time bounds that either do not depend at all on the pattern size or depend on it in a very limited way (doubly logarithmic). As a side result, we propose an improved solution to the weighted level ancestor problem

Dynamic alpha power modulations and slow negative potentials track natural shifts of spatio‐temporal attention

Alpha power modulations and slow negative potentials have previously been associated with anticipatory processes in spatial and temporal top-down attention. In typical experimental designs, however, neural responses triggered by transient stimulus onsets can interfere with attention-driven activity patterns and our interpretation of such. Here, we investigated these signatures of spatio-temporal attention in a dynamic paradigm free from potentially confounding stimulus-driven activity using electroencephalography. Participants attended the cued side of a bilateral stimulus rotation and mentally counted how often one of two remembered sample orientations (i.e., the target) was displayed while ignoring the uncued side and non-target orientation. Afterwards, participants performed a delayed match-to-sample task, in which they indicated if the orientation of a probe stimulus matched the corresponding sample orientation (previously target or non-target). We observed dynamic alpha power reductions and slow negative waves around task-relevant points in space and time (i.e., onset of the target orientation in the cued hemifield) over posterior electrodes contralateral to the locus of attention. In contrast to static alpha power lateralization, these dynamic signatures correlated with subsequent memory performance (primarily detriments for matching probes of the non-target orientation), suggesting a preferential allocation of attention to task-relevant locations and time points at the expense of reduced resources and impaired performance for information outside the current focus of attention. Our findings suggest that humans can naturally and dynamically focus their attention at relevant points in space and time and that such spatio-temporal attention shifts can be reflected by dynamic alpha power modulations and slow negative potentials

Research in the development effort of an improved multiplier phototube Seventh quarterly report

Test data on effective photocathode size, response uniformity, and pulse amplitude distribution of multiplier phototube

An Open Source Approach for Modern Teaching Methods: The Interactive TGUI System

In order to facilitate teaching complex topics in an interactive way, the authors developed a computer-assisted teaching system, a graphical user interface named TGUI (Teaching Graphical User Interface). TGUI was introduced at the beginning of 2009 in the Austrian Journal of Statistics (Dinges and Templ 2009) as being an effective instrument to train and teach staff on mathematical and statistical topics. While the fundamental principles were retained, the current TGUI system has been undergone a complete redesign. The ultimate goal behind the reimplementation was to share the advantages of TGUI and provide teachers and people who need to hold training courses with a strong tool that can enrich their lectures with interactive features. The idea was to go a step beyond the current modular blended-learning systems (see, e.g., Da Rin 2003) or the related teaching techniques of classroom-voting (see, e.g., Cline 2006). In this paper the authors have attempted to exemplify basic idea and concept of TGUI by means of statistics seminars held at Statistics Austria. The powerful open source software R (R Development Core Team 2010a) is the backend for TGUI, which can therefore be used to process even complex statistical contents. However, with specifically created contents the interactive TGUI system can be used to support a wide range of courses and topics. The open source R packages TGUICore and TGUITeaching are freely available from the Comprehensive R Archive Network at http://CRAN.R-project.org/.

Dynamic Boolean Formula Evaluation

We present a linear space data structure for Dynamic Evaluation of k-CNF Boolean Formulas which achieves O(m^{1-1/k}) query and variable update time where m is the number of clauses in the formula and clauses are of size at most a constant k. Our algorithm is additionally able to count the total number of satisfied clauses. We then show how this data structure can be parallelized in the PRAM model to achieve O(log m) span (i.e. parallel time) and still O(m^{1-1/k}) work. This parallel algorithm works in the stronger Binary Fork model. We then give a series of lower bounds on the problem including an average-case result showing the lower bounds hold even when the updates to the variables are chosen at random. Specifically, a reduction from k-Clique shows that dynamically counting the number of satisfied clauses takes time at least n^{(2?-3)/6 ?{2k} -1 -o(?k)}, where 2 ? ? < 2.38 is the matrix multiplication constant. We show the Combinatorial k-Clique Hypothesis implies a lower bound of m^{(1-k^{-1/2})(1-o(1))} which suggests our algorithm is close to optimal without involving Matrix Multiplication or new techniques. We next give an average-case reduction to k-clique showing the prior lower bounds hold even when the updates are chosen at random. We use our conditional lower bound to show any Binary Fork algorithm solving these problems requires at least ?(log m) span, which is tight against our algorithm in this model. Finally, we give an unconditional linear space lower bound for Dynamic k-CNF Boolean Formula Evaluation

Differentially Private Algorithms for Graphs Under Continual Observation

Differentially private algorithms protect individuals in data analysis scenarios by ensuring that there is only a weak correlation between the existence of the user in the data and the result of the analysis. Dynamic graph algorithms maintain the solution to a problem (e.g., a matching) on an evolving input, i.e., a graph where nodes or edges are inserted or deleted over time. They output the value of the solution after each update operation, i.e., continuously. We study (event-level and user-level) differentially private algorithms for graph problems under continual observation, i.e., differentially private dynamic graph algorithms. We present event-level private algorithms for partially dynamic counting-based problems such as triangle count that improve the additive error by a polynomial factor (in the length $T$ of the update sequence) on the state of the art, resulting in the first algorithms with additive error polylogarithmic in $T$. We also give $\varepsilon$-differentially private and partially dynamic algorithms for minimum spanning tree, minimum cut, densest subgraph, and maximum matching. The additive error of our improved MST algorithm is $O(W \log^{3/2}T / \varepsilon)$, where $W$ is the maximum weight of any edge, which, as we show, is tight up to a $(\sqrt{\log T} / \varepsilon)$-factor. For the other problems, we present a partially-dynamic algorithm with multiplicative error $(1+\beta)$ for any constant $\beta > 0$ and additive error $O(W \log(nW) \log(T) / (\varepsilon \beta) )$. Finally, we show that the additive error for a broad class of dynamic graph algorithms with user-level privacy must be linear in the value of the output solution's range