Heterogeneous investments induced by emotions promote cooperation in public goods games

Emotion plays an important role in heterogeneous investments and has some direct effects on the cooperation behaviour of a player in a public goods game (PGG). How this irrational factor affects the heterogeneous investments and what level of cooperators in players with emotions are still unknown to us. Here, the heterogeneous investments induced by emotions into a PGG were introduced. The emotional index was firstly quantified by considering a memory-cumulative effect, and then an investment formula was proposed based on this emotional index. At last, the effect of emotions on the cooperation behaviour in a PGG was investigated. Results show that the heterogeneous investments induced by emotions can improve cooperation significantly in a PGG, and that an increase of the memory length, the emotional increment, or the memory discounting factor can improve the cooperation level.

An inverse problem approach to determine possible memory length of fractional differential equations

It is a fundamental problem to determine a starting point in fractional differential equations which reveals the memory length in real life modeling. This paper describes it by an inverse problem. Fixed point theorems such as Krasnoselskii’s and Schauder type’s and nonlinear alternative for single–valued mappings are presented. Through existence analysis of the inverse problem, the range of the initial value points and the memory length of fractional differential equations are obtained. Finally, three examples are demonstrated to support the theoretical results and numerical solutions are provided.

Green Roof Hydrological Modelling With GRU And LSTM Networks

Green Roofs (GRs) are becoming more popular as a low-impact building option. They have the potential to minimize peak stormwater runoff while also increasing the quality of runoff from buildings. Improvement of hydrological models for the simulation of GRs will aid design of individual roofs as well as city scale planning that relies on the predicted impacts of widespread GR implementation. Machine learning (ML) has exploded in popularity in recent years, owing to considerable increases in processing power and data availability. However, there are no studies focusing on the use of ML in hydrological simulation of GRs. We focus on two types of ML-based model: long short-term memory (LSTM) and gated recurrent unit (GRU) in modelling hydrological performance of GRs, with sequence input and a single output (SISO), and synced sequence input and output (SSIO) architectures. According to the results of this paper, LSTM and GRU are useful tools for the modelling of GRs. As the time window length (memory length, time step length of input data) increases, SISO appears to have a higher overall forecast accuracy. SSIO delivers the best overall performance, when the SSIO is close to, or even exceeds, the maximum window size.

Fragmentation in trader preferences among multiple markets: market coexistence versus single market dominance

Technological advancement has led to an increase in the number and type of trading venues and a diversification of goods traded. These changes have re-emphasized the importance of understanding the effects of market competition: does proliferation of trading venues and increased competition lead to dominance of a single market or coexistence of multiple markets? In this paper, we address these questions in a stylized model of zero-intelligence traders who make repeated decisions at which of three available markets to trade. We analyse the model numerically and analytically and find that the traders’ decision parameters—memory length and how strongly decisions are based on past success—make the key difference between consolidated and fragmented steady states of the population of traders. All three markets coexist with equal shares of traders only when either learning is too weak and traders choose randomly, or when markets are identical. In the latter case, the population of traders fragments across the markets. With different markets, we note that market dominance is the more typical scenario. Overall we show that, contrary to previous research emphasizing the role of traders’ heterogeneity, market coexistence can emerge simply as a consequence of co-adaptation of an initially homogeneous population of traders.

A Generic FPGA Implementation of the Fractional-Order Derivative and Its Application

In this paper, a generic FPGA implementation of the Grunwald-Letnikov definition of fractional-order derivative is presented, where the parameters are adjustable without changing the Verilog HDL code. Besides, there is no strict limit on the range of parameters and no need to pre-store coefficients to approximate the binomial coefficients. The memory length changes dynamically to reduce the number of calculation times. When the memory length becomes large, the advantages of this method will be more noticeable. Theoretically, it is a more generic FPGA algorithm not only suitable for the short memory principle, but also for the general Grunwald-Letnikov definition. In addition, a multi-scroll fractional-order NEW-SPROTT-41 system is designed by using a square family function. Its stability is simply analyzed, and the proposed FPGA implementation is applied to the proposed system. What’s more, the integrated logic analyzer(ILA) is used to capture internal signals of the FPGA without an oscilloscope. The experimental results are consistent with the numeric simulation results very well.

Influence of some ARFIMA model parameters on the accuracy of financial time series forecasting

The influence of ARFIMA model parameters on the accuracy of financial time series forecasting on the example of artificially generated long memory series and daily log returns of RTS index is investigated. The investigated parameters are deviation of the integration order value from its «true» value, as well as the memory «length» considered by the model. Based on the research results, some practical recommendations for modeling using ARFIMA have been formulated.