Computing in Additive Networks with Bounded-Information Codes

This paper studies the theory of the additive wireless network model, in which the received signal is abstracted as an addition of the transmitted signals. Our central observation is that the crucial challenge for computing in this model is not high contention, as assumed previously, but rather guaranteeing a bounded amount of \emph{information} in each neighborhood per round, a property that we show is achievable using a new random coding technique. Technically, we provide efficient algorithms for fundamental distributed tasks in additive networks, such as solving various symmetry breaking problems, approximating network parameters, and solving an \emph{asymmetry revealing} problem such as computing a maximal input. The key method used is a novel random coding technique that allows a node to successfully decode the received information, as long as it does not contain too many distinct values. We then design our algorithms to produce a limited amount of information in each neighborhood in order to leverage our enriched toolbox for computing in additive networks

Beeping a Maximal Independent Set

We consider the problem of computing a maximal independent set (MIS) in an extremely harsh broadcast model that relies only on carrier sensing. The model consists of an anonymous broadcast network in which nodes have no knowledge about the topology of the network or even an upper bound on its size. Furthermore, it is assumed that an adversary chooses at which time slot each node wakes up. At each time slot a node can either beep, that is, emit a signal, or be silent. At a particular time slot, beeping nodes receive no feedback, while silent nodes can only differentiate between none of its neighbors beeping, or at least one of its neighbors beeping. We start by proving a lower bound that shows that in this model, it is not possible to locally converge to an MIS in sub-polynomial time. We then study four different relaxations of the model which allow us to circumvent the lower bound and find an MIS in polylogarithmic time. First, we show that if a polynomial upper bound on the network size is known, it is possible to find an MIS in O(log^3 n) time. Second, if we assume sleeping nodes are awoken by neighboring beeps, then we can also find an MIS in O(log^3 n) time. Third, if in addition to this wakeup assumption we allow sender-side collision detection, that is, beeping nodes can distinguish whether at least one neighboring node is beeping concurrently or not, we can find an MIS in O(log^2 n) time. Finally, if instead we endow nodes with synchronous clocks, it is also possible to find an MIS in O(log^2 n) time.Comment: arXiv admin note: substantial text overlap with arXiv:1108.192

Walks of molecular motors in two and three dimensions

Molecular motors interacting with cytoskeletal filaments undergo peculiar random walks consisting of alternating sequences of directed movements along the filaments and diffusive motion in the surrounding solution. An ensemble of motors is studied which interacts with a single filament in two and three dimensions. The time evolution of the probability distribution for the bound and unbound motors is determined analytically. The diffusion of the motors is strongly enhanced parallel to the filament. The analytical expressions are in excellent agreement with the results of Monte Carlo simulations.Comment: 7 pages, 2 figures, to be published in Europhys. Let

The Potential of Restarts for ProbSAT

This work analyses the potential of restarts for probSAT, a quite successful algorithm for k-SAT, by estimating its runtime distributions on random 3-SAT instances that are close to the phase transition. We estimate an optimal restart time from empirical data, reaching a potential speedup factor of 1.39. Calculating restart times from fitted probability distributions reduces this factor to a maximum of 1.30. A spin-off result is that the Weibull distribution approximates the runtime distribution for over 93% of the used instances well. A machine learning pipeline is presented to compute a restart time for a fixed-cutoff strategy to exploit this potential. The main components of the pipeline are a random forest for determining the distribution type and a neural network for the distribution's parameters. ProbSAT performs statistically significantly better than Luby's restart strategy and the policy without restarts when using the presented approach. The structure is particularly advantageous on hard problems.Comment: Eurocast 201

Finite size effects and error-free communication in Gaussian channels

The efficacy of a specially constructed Gallager-type error-correcting code to communication in a Gaussian channel is being examined. The construction is based on the introduction of complex matrices, used in both encoding and decoding, which comprise sub-matrices of cascading connection values. The finite size effects are estimated for comparing the results to the bounds set by Shannon. The critical noise level achieved for certain code-rates and infinitely large systems nearly saturates the bounds set by Shannon even when the connectivity used is low

Statistical Physics of Irregular Low-Density Parity-Check Codes

Low-density parity-check codes with irregular constructions have been recently shown to outperform the most advanced error-correcting codes to date. In this paper we apply methods of statistical physics to study the typical properties of simple irregular codes. We use the replica method to find a phase transition which coincides with Shannon's coding bound when appropriate parameters are chosen. The decoding by belief propagation is also studied using statistical physics arguments; the theoretical solutions obtained are in good agreement with simulations. We compare the performance of irregular with that of regular codes and discuss the factors that contribute to the improvement in performance.Comment: 20 pages, 9 figures, revised version submitted to JP

The Integrated Behavioural Model for Water, Sanitation, and Hygiene: a systematic review of behavioural models and a framework for designing and evaluating behaviour change interventions in infrastructure-restricted settings.

BACKGROUND: Promotion and provision of low-cost technologies that enable improved water, sanitation, and hygiene (WASH) practices are seen as viable solutions for reducing high rates of morbidity and mortality due to enteric illnesses in low-income countries. A number of theoretical models, explanatory frameworks, and decision-making models have emerged which attempt to guide behaviour change interventions related to WASH. The design and evaluation of such interventions would benefit from a synthesis of this body of theory informing WASH behaviour change and maintenance. METHODS: We completed a systematic review of existing models and frameworks through a search of related articles available in PubMed and in the grey literature. Information on the organization of behavioural determinants was extracted from the references that fulfilled the selection criteria and synthesized. Results from this synthesis were combined with other relevant literature, and from feedback through concurrent formative and pilot research conducted in the context of two cluster-randomized trials on the efficacy of WASH behaviour change interventions to inform the development of a framework to guide the development and evaluation of WASH interventions: the Integrated Behavioural Model for Water, Sanitation, and Hygiene (IBM-WASH). RESULTS: We identified 15 WASH-specific theoretical models, behaviour change frameworks, or programmatic models, of which 9 addressed our review questions. Existing models under-represented the potential role of technology in influencing behavioural outcomes, focused on individual-level behavioural determinants, and had largely ignored the role of the physical and natural environment. IBM-WASH attempts to correct this by acknowledging three dimensions (Contextual Factors, Psychosocial Factors, and Technology Factors) that operate on five-levels (structural, community, household, individual, and habitual). CONCLUSIONS: A number of WASH-specific models and frameworks exist, yet with some limitations. The IBM-WASH model aims to provide both a conceptual and practical tool for improving our understanding and evaluation of the multi-level multi-dimensional factors that influence water, sanitation, and hygiene practices in infrastructure-constrained settings. We outline future applications of our proposed model as well as future research priorities needed to advance our understanding of the sustained adoption of water, sanitation, and hygiene technologies and practices

Relaxation time for a dimer covering with height representation

This paper considers the Monte Carlo dynamics of random dimer coverings of the square lattice, which can be mapped to a rough interface model. Two kinds of slow modes are identified, associated respectively with long-wavelength fluctuations of the interface height, and with slow drift (in time) of the system-wide mean height. Within a continuum theory, the longest relaxation time for either kind of mode scales as the system size N. For the real, discrete model, an exact lower bound of O(N) is placed on the relaxation time, using variational eigenfunctions corresponding to the two kinds of continuum modes.Comment: 12 pages, LaTeX; 1 figure in PostScript file; to appear, J. Stat. Phys. Sections and subsections were reshuffled to improve presentation, some text added on quantum-dimer model, fully-frustrated Ising model, and application to general class of "height" model