Connections between the Sznajd Model with General Confidence Rules and graph theory

The Sznajd model is a sociophysics model, that is used to model opinion propagation and consensus formation in societies. Its main feature is that its rules favour bigger groups of agreeing people. In a previous work, we generalized the bounded confidence rule in order to model biases and prejudices in discrete opinion models. In that work, we applied this modification to the Sznajd model and presented some preliminary results. The present work extends what we did in that paper. We present results linking many of the properties of the mean-field fixed points, with only a few qualitative aspects of the confidence rule (the biases and prejudices modelled), finding an interesting connection with graph theory problems. More precisely, we link the existence of fixed points with the notion of strongly connected graphs and the stability of fixed points with the problem of finding the maximal independent sets of a graph. We present some graph theory concepts, together with examples, and comparisons between the mean-field and simulations in Barab\'asi-Albert networks, followed by the main mathematical ideas and appendices with the rigorous proofs of our claims. We also show that there is no qualitative difference in the mean-field results if we require that a group of size q>2, instead of a pair, of agreeing agents be formed before they attempt to convince other sites (for the mean-field, this would coincide with the q-voter model).Comment: 15 pages, 18 figures. To be submitted to Physical Revie

A Generalized Sznajd Model

In the last decade the Sznajd Model has been successfully employed in modeling some properties and scale features of both proportional and majority elections. We propose a new version of the Sznajd model with a generalized bounded confidence rule - a rule that limits the convincing capability of agents and that is essential to allow coexistence of opinions in the stationary state. With an appropriate choice of parameters it can be reduced to previous models. We solved this new model both in a mean-field approach (for an arbitrary number of opinions) and numerically in a Barabasi-Albert network (for three and four opinions), studying the transient and the possible stationary states. We built the phase portrait for the special cases of three and four opinions, defining the attractors and their basins of attraction. Through this analysis, we were able to understand and explain discrepancies between mean-field and simulation results obtained in previous works for the usual Sznajd Model with bounded confidence and three opinions. Both the dynamical system approach and our generalized bounded confidence rule are quite general and we think it can be useful to the understanding of other similar models.Comment: 19 pages with 8 figures. Submitted to Physical Review

Reduction of NOx Emissions in a Single Cylinder Diesel Engine Using SNCR with In-Cylinder Injection of Aqueous Urea

The subject of this study is the effect of in-cylinder selective non-catalytic reduction (SNCR) of NOx emissions in diesel exhaust gas by means of direct injection of aqueous urea ((NH2)2CO) into the combustion chamber. A single cylinder diesel test engine was modified to accept an electronically controlled secondary common rail injection system to deliver the aqueous urea directly into the cylinder during engine operation. Direct in-cylinder injection was chosen in order to ensure precise delivery of the reducing agent without the risk of any premature reactions taking place. Unlike direct in-cylinder injection of neat water, aqueous urea also works as a reducing agent by breaking down into ammonia (NH3) and Cyanuric Acid ((HOCN)3). These compounds serve as the primary reducing agents in the NOx reduction mechanism explored here. The main reducing agent, aqueous urea, was admixed with glycerol (C3H8O3) in an 80-20 ratio, by weight, to function as a lubricant for the secondary injector. The aqueous urea injection timing and duration is critical to the reduction of NOx emissions due to the dependence of SNCR NOx reduction on critical factors such as temperature, pressure, reducing agent to NOx ratio, Oxygen and radical content, residence time and NH3 slip. From scoping engine tests at loads of 40 percent and 80 percent at 1500 rpm, an aqueous urea injection strategy was developed. The final injection strategy chosen was four molar ratios, 4.0, 2.0, 1.0 and 0.5 with five varying injection timings of 60, 20, 10, 0, and -30 degrees after top dead center (ATDC). In addition to the base line and aqueous urea tests, water injection and an 80-20 water-glycerol solution reduction agent tests were also conducted to compare the effects of said additives as well. The comparison of baseline and SNCR operation was expected to show that the urea acted as a reducing agent, lowering NOx emissions up to 100% (based on exhaust stream studies) in the diesel exhaust gas without the aid of a catalyst. The data collected from the engine tests showed that the aqueous urea-glycerol solution secondary had no effect on the reduction of NOx and even resulted in an increase of up to 5% in some tests. This was due to the low average in-cylinder temperature as well as a short residence time, prohibiting the reduction reaction from taking place. The neat water and water-glycerol solution secondary injection was found to have a reduction effect of up to 59% on NOx production in the emissions due to the evaporative cooling effect and increased heat capacity of the water

Ripple Protocol performance improvement: Small world theory applied to cross border payments

In the context of faster and cheaper international money transfers, this paper makes an analysis of the Ripple Protocol Consensus Algorithm (RPCA) and provides an improved algorithm that takes advantage of the network topology when it holds several sub-networks with poor connections between them. RPCA reaches consensus based on a trusted list of nodes, which this paper theorizes to fit the small world concept from social networks. Network nodes are analyzed statically in order to add new nodes to interconnect clusters. The method used to measure the improvement is through simulation and calculated the algorithm response time with and without the added nodes. This paper achieves a performance improvement between 23 ms and 457 ms for networks of between 50 and 2000 nodes. In the context of high frequency trading, a small milliseconds improvement makes the difference for a transaction to be accepted or not.Sociedad Argentina de Informática e Investigación Operativ