Lei Xu

On languages generated by spiking neural P systems with weights

National Natural Science Foundation of China [61202011, 61272152, 61033003, 91130034, 61320106005]; Ph.D. Programs Foundation of Ministry of Education of China [20120121120039, 20120142130008]; Natural Science Foundation of Hubei Province [2011CDA027]

Feedback from nature: an optimal distributed algorithm for maximal independent set selection

Maximal Independent Set selection is a fundamental problem in distributed computing. A novel probabilistic algorithm for this problem has recently been proposed by Afek et al, inspired by the study of the way that developing cells in the fly become specialised. The algorithm they propose is simple and robust, but not as efficient as previous approaches: the expected time complexity is O(log2 n). Here we first show that the approach of Afek et al cannot achieve better efficiency than this across all networks, no matter how the global probability values are chosen. However, we then propose a new algorithm that incorporates another important feature of the biological system: the probability value at each node is adapted using local feedback from neighbouring nodes. Our new algorithm retains all the advantages of simplicity and robustness, but also achieves the optimal efficiency of O(log n) expected time. The new algorithm also has only a constant message complexity per node.

Patterns from nature

A well-established problem in global optimization is the problem of colouring the vertices of an arbitrary graph using the minimal number of colours, such that adjacent vertices are assigned different colours. One way to restrict the number of colours used is to allow only greedy colourings. A greedy colouring is an assignment of colours to the vertices of a graph that can be obtained by an algorithm that considers each vertex in turn and assigns the first colour that is not already assigned to some neighbour. An optimal colouring can always be obtained in this way, by choosing an appropriate order on the vertices.Recently, a new bio-inspired approach to distributed pattern formation has been proposed, based on modelling the neurological development of the fruit fly. Building on that approach, we propose a new simple randomised algorithm for distributed greedy colouring using only local processing at the vertices and messages along the edges. In our approach the processors exchange only simple messages representing potential colour values and each processor has minimal graph knowledge. We discuss two variations of this algorithm, and investigate their time complexity and message complexity both theoretically and experimentally.In addition, we show experimentally that the number of colours used turns out to be optimal or near-optimal for many standard graph colouring benchmarks. Thus, for distributed networks, our algorithm serves as an effective heuristic approach to computing a colouring with a small number of colours.

Simple neural-like p systems for maximal independent set selection

Membrane systems (P systems) are distributed computing models inspired by living cells where a collection of processors jointly achieves a computing task. The problem of maximal independent set (MIS) selection in a graph is to choose a set of nonadjacent nodes to which no further nodes can be added. In this letter, we design a class of simple neural-like P systems to solve the MIS selection problem efficiently in a distributed way. This new class of systems possesses two features that are attractive for both distributed computing and membrane computing: first, the individual processors do not need any information about the overall size of the graph; second, they communicate using only one-bit messages.

Simple Algorithms for Distributed Leader Election in Anonymous Synchronous Rings and Complete Networks Inspired by Neural Development in Fruit Flies

Leader election in anonymous rings and complete networks is a very practical problem in distributed computing. Previous algorithms for this problem are generally designed for a classical message passing model where complex messages are exchanged. However, the need to send and receive complex messages makes such algorithms less practical for some real applications. We present some simple synchronous algorithms for distributed leader election in anonymous rings and complete networks that are inspired by the development of the neural system of the fruit fly. Our leader election algorithms all assume that only one-bit messages are broadcast by nodes in the network and processors are only able to distinguish between silence and the arrival of one or more messages. These restrictions allow implementations to use a simpler message-passing architecture. Even with these harsh restrictions our algorithms are shown to achieve good time and message complexity both analytically and experimentally.

Modelling to Contain Pandemic Influenza A (H1N1) with Stochastic Membrane Systems: A Work-in-Progress Paper

Pandemic influenza A (H1N1) has spread rapidly across the globe. In the event of pandemic influenza A (H1N1), decision-makers are required to act in the face of substantial uncertainties. Simulation models can be used to project the effectiveness of mitigation strategies. Since nature is very complex, the perfect model that explains it will be complex too. Membrane system (P system) can be a perfect model modelling ecological system. This paper briefly describes stochastic membrane systems for modelling spread of pandemic influenza A (H1N1) in an isolated geographical region. The model is based on a discrete and stochastic modelling framework in the area of Membrane Computing. This model can be a useful tool for the prediction of infectious diseases within predefined areas, and the evaluation of intervention strategies.

Led by nature: Distributed leader election in anonymous networks

Leader election in anonymous rings and complete networks is a very practical problem in distributed computing. Previous algorithms for his problem are generally designed for a classical message passing model where complex messages are exchanged. However, he need to send and receive complex messages makes such algorithms less practical for some real applications. Inspired by biological cell signalling, we present in his paper some simple approaches to distributed leader election in anonymous rings and complete networks. Our leader election algorithms all assume only one-bi messages are broadcast by nodes in he network and processors are only able o distinguish between silence and he arrival of one or more messages. Even with these harsh restrictions our algorithms are shown to achieve good time and message complexity both analytically and experimentally.