Maze-solving by natural phenomena is a symbolic result of the autonomous optimization induced by ... more Maze-solving by natural phenomena is a symbolic result of the autonomous optimization induced by a natural system. We present a method for finding the shortest path on a maze consisting of a bipartite graph using a discrete-time quantum walk, which is a toy model of many kinds of quantum systems. By evolving the amplitude distribution according to the quantum walk on a kind of network with sinks, which is the exit of the amplitude, the amplitude distribution remains eternally on the paths between two self-loops indicating the start and the goal of the maze. We performed a numerical analysis of some simple cases and found that the shortest paths were detected by the chain of the maximum trapped densities in most cases of bipartite graphs. The counterintuitive dependence of the convergence steps on the size of the structure of the network was observed in some cases, implying that the asymmetry of the network accelerates or decelerates the convergence process. The relation between the ...
Uncovering causal interdependencies from observational data is one of the great challenges of a n... more Uncovering causal interdependencies from observational data is one of the great challenges of a nonlinear time series analysis. In this paper, we discuss this topic with the help of an information-theoretic concept known as Rényi’s information measure. In particular, we tackle the directional information flow between bivariate time series in terms of Rényi’s transfer entropy. We show that by choosing Rényi’s parameter α, we can appropriately control information that is transferred only between selected parts of the underlying distributions. This, in turn, is a particularly potent tool for quantifying causal interdependencies in time series, where the knowledge of “black swan” events, such as spikes or sudden jumps, are of key importance. In this connection, we first prove that for Gaussian variables, Granger causality and Rényi transfer entropy are entirely equivalent. Moreover, we also partially extend these results to heavy-tailed α-Gaussian variables. These results allow establis...
We analyze the impact of the exogenous economic shocks in the agent-based Model of Employment, Pr... more We analyze the impact of the exogenous economic shocks in the agent-based Model of Employment, Production and Consumption (EPC). The EPC model mimics the economic activity, where two types of agents—citizens and organizations—interact between each other. We consider two types of economics shocks: First, we switch between two types of ownership—direct and proxy. Second, we consider the subsidy to organizations, which pass a certain threshold. The results suggest that the economic activity in the model shows several phases based on the ownership structure and threshold level. In addition, there exists sharp boundaries between the phases. Consequently, such results support the existence of non-linear transitions between phases, where we observe both the phase transition of the first and second kind. Our results thus suggest that the economy-like system may reveal a non-linear features with number of different phases as well as different transitions between them leading to the fragility...
A model of the distribution of wealth in society will be presented. The model is based on an agen... more A model of the distribution of wealth in society will be presented. The model is based on an agent-based Monte Carlo simulation where interaction (exchange of wealth) is allowed along the edges of a small-world network. The interaction is like inelastic scattering and it is characterized by two constants. Simulations of the model show that the distribution behaves as a power-law and it agrees with results of Pareto.
ABSTRACT The recent crisis revived interest in financial transaction taxes (FTTs) as a means to o... more ABSTRACT The recent crisis revived interest in financial transaction taxes (FTTs) as a means to offset negative risk externalities. However, up-to-date academic research does not provide sufficient insights into the effects of transaction taxes on financial markets as the literature has here-to-fore been focused too narrowly on Gaussian variance as a measure of volatility. In this paper, we ar- gue that it is imperative to understand the relationship between price jumps, Gaussian variance, and FTTs. While Gaussian variance is not necessarily a problem in itself, the non-normality of return distribution caused by price jumps affects not only the performance of many risk-hedging algorithms but directly influences the frequency of catastrophic market events. To study the aforementioned relationship, we use an agent-based model of financial mar- kets. Its results show that FTTs may increase the variance while decreasing the impact of price jumps. This result implies that regulators may face a trade-off between overall variance and price jumps when designing optimal tax. However, the results are not robust to the size of the artificial market as non-linearities emerge when the size of the market is increased.
We examine the operation of a device for a public quantum key distribution network. The recipient... more We examine the operation of a device for a public quantum key distribution network. The recipients attempt to determine whether or not their individual key copies, which are a sequence of coherent states, are identical. To quantify the success of the protocol we use ...
... While our study [41,42] was limited on the simplest one-dimensional directed topology of the ... more ... While our study [41,42] was limited on the simplest one-dimensional directed topology of the ... ER case, for scale-free substrate the scale-free structure of the imita-tion network does not ... are typical to our approach, especially the structure of imitation domains and influence of the ...
Maze-solving by natural phenomena is a symbolic result of the autonomous optimization induced by ... more Maze-solving by natural phenomena is a symbolic result of the autonomous optimization induced by a natural system. We present a method for finding the shortest path on a maze consisting of a bipartite graph using a discrete-time quantum walk, which is a toy model of many kinds of quantum systems. By evolving the amplitude distribution according to the quantum walk on a kind of network with sinks, which is the exit of the amplitude, the amplitude distribution remains eternally on the paths between two self-loops indicating the start and the goal of the maze. We performed a numerical analysis of some simple cases and found that the shortest paths were detected by the chain of the maximum trapped densities in most cases of bipartite graphs. The counterintuitive dependence of the convergence steps on the size of the structure of the network was observed in some cases, implying that the asymmetry of the network accelerates or decelerates the convergence process. The relation between the ...
Uncovering causal interdependencies from observational data is one of the great challenges of a n... more Uncovering causal interdependencies from observational data is one of the great challenges of a nonlinear time series analysis. In this paper, we discuss this topic with the help of an information-theoretic concept known as Rényi’s information measure. In particular, we tackle the directional information flow between bivariate time series in terms of Rényi’s transfer entropy. We show that by choosing Rényi’s parameter α, we can appropriately control information that is transferred only between selected parts of the underlying distributions. This, in turn, is a particularly potent tool for quantifying causal interdependencies in time series, where the knowledge of “black swan” events, such as spikes or sudden jumps, are of key importance. In this connection, we first prove that for Gaussian variables, Granger causality and Rényi transfer entropy are entirely equivalent. Moreover, we also partially extend these results to heavy-tailed α-Gaussian variables. These results allow establis...
We analyze the impact of the exogenous economic shocks in the agent-based Model of Employment, Pr... more We analyze the impact of the exogenous economic shocks in the agent-based Model of Employment, Production and Consumption (EPC). The EPC model mimics the economic activity, where two types of agents—citizens and organizations—interact between each other. We consider two types of economics shocks: First, we switch between two types of ownership—direct and proxy. Second, we consider the subsidy to organizations, which pass a certain threshold. The results suggest that the economic activity in the model shows several phases based on the ownership structure and threshold level. In addition, there exists sharp boundaries between the phases. Consequently, such results support the existence of non-linear transitions between phases, where we observe both the phase transition of the first and second kind. Our results thus suggest that the economy-like system may reveal a non-linear features with number of different phases as well as different transitions between them leading to the fragility...
A model of the distribution of wealth in society will be presented. The model is based on an agen... more A model of the distribution of wealth in society will be presented. The model is based on an agent-based Monte Carlo simulation where interaction (exchange of wealth) is allowed along the edges of a small-world network. The interaction is like inelastic scattering and it is characterized by two constants. Simulations of the model show that the distribution behaves as a power-law and it agrees with results of Pareto.
ABSTRACT The recent crisis revived interest in financial transaction taxes (FTTs) as a means to o... more ABSTRACT The recent crisis revived interest in financial transaction taxes (FTTs) as a means to offset negative risk externalities. However, up-to-date academic research does not provide sufficient insights into the effects of transaction taxes on financial markets as the literature has here-to-fore been focused too narrowly on Gaussian variance as a measure of volatility. In this paper, we ar- gue that it is imperative to understand the relationship between price jumps, Gaussian variance, and FTTs. While Gaussian variance is not necessarily a problem in itself, the non-normality of return distribution caused by price jumps affects not only the performance of many risk-hedging algorithms but directly influences the frequency of catastrophic market events. To study the aforementioned relationship, we use an agent-based model of financial mar- kets. Its results show that FTTs may increase the variance while decreasing the impact of price jumps. This result implies that regulators may face a trade-off between overall variance and price jumps when designing optimal tax. However, the results are not robust to the size of the artificial market as non-linearities emerge when the size of the market is increased.
We examine the operation of a device for a public quantum key distribution network. The recipient... more We examine the operation of a device for a public quantum key distribution network. The recipients attempt to determine whether or not their individual key copies, which are a sequence of coherent states, are identical. To quantify the success of the protocol we use ...
... While our study [41,42] was limited on the simplest one-dimensional directed topology of the ... more ... While our study [41,42] was limited on the simplest one-dimensional directed topology of the ... ER case, for scale-free substrate the scale-free structure of the imita-tion network does not ... are typical to our approach, especially the structure of imitation domains and influence of the ...
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