Towards Optimal Synchronous Counting

Consider a complete communication network of $n$ nodes, where the nodes receive a common clock pulse. We study the synchronous $c$-counting problem: given any starting state and up to $f$ faulty nodes with arbitrary behaviour, the task is to eventually have all correct nodes counting modulo $c$ in agreement. Thus, we are considering algorithms that are self-stabilizing despite Byzantine failures. In this work, we give new algorithms for the synchronous counting problem that (1) are deterministic, (2) have linear stabilisation time in $f$, (3) use a small number of states, and (4) achieve almost-optimal resilience. Prior algorithms either resort to randomisation, use a large number of states, or have poor resilience. In particular, we achieve an exponential improvement in the space complexity of deterministic algorithms, while still achieving linear stabilisation time and almost-linear resilience.Comment: 17 pages, 2 figure

Interoceptive Ingredients of Body Ownership: Affective Touch and Cardiac Awareness in the Rubber Hand Illusion

This document is the Accepted Manuscript version of the following article: Laura Crucianelli, Charlotte Krahe, Paul M. Jenkinson, Aikaterini (Katerina) Fotopoulou, 'Interoceptive Ingredients of Body Ownership: Affective Touch and Cardiac Awareness in the Rubber Hand Illusion', Cortex, first published online 1 May 2017, available at doi: https://doi.org/10.1016/j.cortex.2017.04.018. © 2017 Elsevier Ltd. All rights reserved.The sense of body ownership represents a fundamental aspect of bodily self-consciousness. Using multisensory integration paradigms, recent studies have shown that both exteroceptive and interoceptive information contribute to our sense of body ownership. Interoception refers to the physiological sense of the condition of the body, including afferent signals that originate inside the body and outside the body. However, it remains unclear whether individual sensitivity to interoceptive modalities is unitary or differs between modalities. It is also unclear whether the effect of interoceptive information on body ownership is caused by exteroceptive ‘visual capture’ of these modalities, or by bottom-up processing of interoceptive information. This study aimed to test these questions in two separate samples. In the first experiment (N = 76), we examined the relationship between two different interoceptive modalities, namely cardiac awareness based on a heartbeat counting task, and affective touch perception based on stimulation of a specialized C tactile (CT) afferent system. This is an interoceptive modality of affective and social significance. In a second experiment (N = 63), we explored whether ‘off-line’ trait interoceptive sensitivity based on a heartbeat counting task would modulate the extent to which CT affective touch influences the multisensory process during the rubber hand illusion (RHI). We found that affective touch enhanced the subjective experience of body ownership during the RHI. Nevertheless, interoceptive sensitivity, as measured by a heartbeat counting task, did not modulate this effect, nor did it relate to the perception of ownership or of CT-optimal affective touch more generally. By contrast, this trait measure of interoceptive sensitivity appeared most relevant when the multisensory context of interoception was ambiguous, suggesting that the perception of interoceptive signals and their effects on body ownership may depend on individual abilities to regulate the balance of interoception and exteroception in given contexts.Peer reviewedFinal Accepted Versio

Synchronous Counting and Computational Algorithm Design

Consider a complete communication network on $n$ nodes, each of which is a state machine. In synchronous 2-counting, the nodes receive a common clock pulse and they have to agree on which pulses are "odd" and which are "even". We require that the solution is self-stabilising (reaching the correct operation from any initial state) and it tolerates $f$ Byzantine failures (nodes that send arbitrary misinformation). Prior algorithms are expensive to implement in hardware: they require a source of random bits or a large number of states. This work consists of two parts. In the first part, we use computational techniques (often known as synthesis) to construct very compact deterministic algorithms for the first non-trivial case of $f = 1$. While no algorithm exists for $n < 4$, we show that as few as 3 states per node are sufficient for all values $n \ge 4$. Moreover, the problem cannot be solved with only 2 states per node for $n = 4$, but there is a 2-state solution for all values $n \ge 6$. In the second part, we develop and compare two different approaches for synthesising synchronous counting algorithms. Both approaches are based on casting the synthesis problem as a propositional satisfiability (SAT) problem and employing modern SAT-solvers. The difference lies in how to solve the SAT problem: either in a direct fashion, or incrementally within a counter-example guided abstraction refinement loop. Empirical results suggest that the former technique is more efficient if we want to synthesise time-optimal algorithms, while the latter technique discovers non-optimal algorithms more quickly.Comment: 35 pages, extended and revised versio

Fast and compact self-stabilizing verification, computation, and fault detection of an MST

This paper demonstrates the usefulness of distributed local verification of proofs, as a tool for the design of self-stabilizing algorithms.In particular, it introduces a somewhat generalized notion of distributed local proofs, and utilizes it for improving the time complexity significantly, while maintaining space optimality. As a result, we show that optimizing the memory size carries at most a small cost in terms of time, in the context of Minimum Spanning Tree (MST). That is, we present algorithms that are both time and space efficient for both constructing an MST and for verifying it.This involves several parts that may be considered contributions in themselves.First, we generalize the notion of local proofs, trading off the time complexity for memory efficiency. This adds a dimension to the study of distributed local proofs, which has been gaining attention recently. Specifically, we design a (self-stabilizing) proof labeling scheme which is memory optimal (i.e., $O(\log n)$ bits per node), and whose time complexity is $O(\log ^2 n)$ in synchronous networks, or $O(\Delta \log ^3 n)$ time in asynchronous ones, where $\Delta$ is the maximum degree of nodes. This answers an open problem posed by Awerbuch and Varghese (FOCS 1991). We also show that $\Omega(\log n)$ time is necessary, even in synchronous networks. Another property is that if $f$ faults occurred, then, within the requireddetection time above, they are detected by some node in the $O(f\log n)$ locality of each of the faults.Second, we show how to enhance a known transformer that makes input/output algorithms self-stabilizing. It now takes as input an efficient construction algorithm and an efficient self-stabilizing proof labeling scheme, and produces an efficient self-stabilizing algorithm. When used for MST, the transformer produces a memory optimal self-stabilizing algorithm, whose time complexity, namely, $O(n)$, is significantly better even than that of previous algorithms. (The time complexity of previous MST algorithms that used $\Omega(\log^2 n)$ memory bits per node was $O(n^2)$, and the time for optimal space algorithms was $O(n|E|)$.) Inherited from our proof labelling scheme, our self-stabilising MST construction algorithm also has the following two properties: (1) if faults occur after the construction ended, then they are detected by some nodes within $O(\log ^2 n)$ time in synchronous networks, or within $O(\Delta \log ^3 n)$ time in asynchronous ones, and (2) if $f$ faults occurred, then, within the required detection time above, they are detected within the $O(f\log n)$ locality of each of the faults. We also show how to improve the above two properties, at the expense of some increase in the memory

The Parallelism Motifs of Genomic Data Analysis

Genomic data sets are growing dramatically as the cost of sequencing continues to decline and small sequencing devices become available. Enormous community databases store and share this data with the research community, but some of these genomic data analysis problems require large scale computational platforms to meet both the memory and computational requirements. These applications differ from scientific simulations that dominate the workload on high end parallel systems today and place different requirements on programming support, software libraries, and parallel architectural design. For example, they involve irregular communication patterns such as asynchronous updates to shared data structures. We consider several problems in high performance genomics analysis, including alignment, profiling, clustering, and assembly for both single genomes and metagenomes. We identify some of the common computational patterns or motifs that help inform parallelization strategies and compare our motifs to some of the established lists, arguing that at least two key patterns, sorting and hashing, are missing

Brain-Switches for Asynchronous Brain−Computer Interfaces: A Systematic Review

A brain–computer interface (BCI) has been extensively studied to develop a novel communication system for disabled people using their brain activities. An asynchronous BCI system is more realistic and practical than a synchronous BCI system, in that, BCI commands can be generated whenever the user wants. However, the relatively low performance of an asynchronous BCI system is problematic because redundant BCI commands are required to correct false-positive operations. To significantly reduce the number of false-positive operations of an asynchronous BCI system, a two-step approach has been proposed using a brain-switch that first determines whether the user wants to use an asynchronous BCI system before the operation of the asynchronous BCI system. This study presents a systematic review of the state-of-the-art brain-switch techniques and future research directions. To this end, we reviewed brain-switch research articles published from 2000 to 2019 in terms of their (a) neuroimaging modality, (b) paradigm, (c) operation algorithm, and (d) performance

Survey-propagation decimation through distributed local computations

We discuss the implementation of two distributed solvers of the random K-SAT problem, based on some development of the recently introduced survey-propagation (SP) algorithm. The first solver, called the "SP diffusion algorithm", diffuses as dynamical information the maximum bias over the system, so that variable nodes can decide to freeze in a self-organized way, each variable making its decision on the basis of purely local information. The second solver, called the "SP reinforcement algorithm", makes use of time-dependent external forcing messages on each variable, which let the variables get completely polarized in the direction of a solution at the end of a single convergence. Both methods allow us to find a solution of the random 3-SAT problem in a range of parameters comparable with the best previously described serialized solvers. The simulated time of convergence towards a solution (if these solvers were implemented on a distributed device) grows as log(N).Comment: 18 pages, 10 figure