Solving the subset-sum problem with a light-based device

We propose a special computational device which uses light rays for solving the subset-sum problem. The device has a graph-like representation and the light is traversing it by following the routes given by the connections between nodes. The nodes are connected by arcs in a special way which lets us to generate all possible subsets of the given set. To each arc we assign either a number from the given set or a predefined constant. When the light is passing through an arc it is delayed by the amount of time indicated by the number placed in that arc. At the destination node we will check if there is a ray whose total delay is equal to the target value of the subset sum problem (plus some constants).Comment: 14 pages, 6 figures, Natural Computing, 200

A Survey on Continuous Time Computations

We provide an overview of theories of continuous time computation. These theories allow us to understand both the hardness of questions related to continuous time dynamical systems and the computational power of continuous time analog models. We survey the existing models, summarizing results, and point to relevant references in the literature

Methanogens, sulphate and heavy metals: a complex system

Anaerobic digestion (AD) is a well-established technology used for the treatment of wastes and wastewaters with high organic content. During AD organic matter is converted stepwise to methane-containing biogasa renewable energy carrier. Methane production occurs in the last AD step and relies on methanogens, which are rather sensitive to some contaminants commonly found in wastewaters (e.g. heavy metals), or easily outcompeted by other groups of microorganisms (e.g. sulphate reducing bacteria, SRB). This review gives an overview of previous research and pilot-scale studies that shed some light on the effects of sulphate and heavy metals on methanogenesis. Despite the numerous studies on this subject, comparison is not always possible due to differences in the experimental conditions used and parameters explained. An overview of the possible benefits of methanogens and SRB co-habitation is also covered. Small amounts of sulphide produced by SRB can precipitate with metals, neutralising the negative effects of sulphide accumulation and free heavy metals on methanogenesis. Knowledge on how to untangle and balance sulphate reduction and methanogenesis is crucial to take advantage of the potential for the utilisation of biogenic sulphide as a metal detoxification agent with minimal loss in methane production in anaerobic digesters.The research was financially supported by the People Program (Marie Curie Actions) of the European Union's Seventh Framework Programme FP7/2007-2013 under REA agreement 289193

Ω in number theory

We present a new method for expressing Chaitin's random real, Ω, through Diophantine equations. Where Chaitin's method causes a particular quantity to express the bits of Ω by fluctuating between finite and infinite values, in our method this quantity is always finite and the bits of Ω are expressed in its fluctuations between odd and even values, allowing for some interesting developments. We then use exponential Diophantine equations to simplify this result and finally show how both methods can also be used to create polynomials which express the bits of Ω in the number of positive values they assume

On the Possibilities of Hypercomputing Supertasks

This paper investigates the view that digital hypercomputing is a good reason for rejection or re-interpretation of the Church-Turing thesis. After suggestion that such re-interpretation is historically problematic and often involves attack on a straw man (the ‘maximality thesis’), it discusses proposals for digital hypercomputing with Zeno-machines , i.e. computing machines that compute an infinite number of computing steps in finite time, thus performing supertasks. It argues that effective computing with Zeno-machines falls into a dilemma: either they are specified such that they do not have output states, or they are specified such that they do have output states, but involve contradiction. Repairs though non-effective methods or special rules for semi-decidable problems are sought, but not found. The paper concludes that hypercomputing supertasks are impossible in the actual world and thus no reason for rejection of the Church-Turing thesis in its traditional interpretation