scholarly journals Power Laws Derived from a Bayesian Decision-Making Model in Non-Stationary Environments

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 718
Author(s):  
Shuji Shinohara ◽  
Nobuhito Manome ◽  
Yoshihiro Nakajima ◽  
Yukio Pegio Gunji ◽  
Toru Moriyama ◽  
...  
Keyword(s):  
Decision Making ◽  
Power Law ◽  
Power Laws ◽  
Step Length ◽  
Bayesian Decision ◽  
Power Law Distribution ◽  
Confidence Levels ◽  
Self Confidence ◽  
Lack Of Information ◽  
Wide Range

The frequency of occurrence of step length in the migratory behaviour of various organisms, including humans, is characterized by the power law distribution. This pattern of behaviour is known as the Lévy walk, and the reason for this phenomenon has been investigated extensively. Especially in humans, one possibility might be that this pattern reflects the change in self-confidence in one’s chosen behaviour. We used simulations to demonstrate that active assumptions cause changes in the confidence level in one’s choice under a situation of lack of information. More specifically, we presented an algorithm that introduced the effects of learning and forgetting into Bayesian inference, and simulated an imitation game in which two decision-making agents incorporating the algorithm estimated each other’s internal models. For forgetting without learning, each agents’ confidence levels in their own estimation remained low owing to a lack of information about the counterpart, and the agents changed their hypotheses about the opponent frequently, and the frequency distribution of the duration of the hypotheses followed an exponential distribution for a wide range of forgetting rates. Conversely, when learning was introduced, high confidence levels occasionally occurred even at high forgetting rates, and exponential distributions universally turned into power law distribution.

scholarly journals Simulation of foraging behavior using a decision-making agent with Bayesian and inverse Bayesian inference: Lévy and Brownian walk-like search patterns derived from differences in prey distributions

2021 ◽  
Author(s):  
Shuji Shinohara ◽  
Hiroshi Okamoto ◽  
Nobuhito Manome ◽  
Yukio Gunji ◽  
Yoshihiro Nakajima ◽  
...  
Keyword(s):  
Decision Making ◽  
Foraging Behavior ◽  
Power Law ◽  
Length Distribution ◽  
Step Length ◽  
Marine Organisms ◽  
Migratory Behavior ◽  
Frequency Of Occurrence ◽  
Power Law Distribution ◽  
Positive Correlation

Lévy walks, random walks where the frequency of occurrence of a linear step length follows a power-law distribution, are found in the migratory behavior of organisms at various levels, from bacteria and T cells to humans. However, it has been pointed out that in human migratory behavior, the step length series may have temporal correlation (i.e., it is not random walk) and that there is some relationship between this time dependency and the fact that the frequency distribution of step length follows the power-law distribution. Furthermore, some large marine organisms have been found to switch between Lévy and Brownian walks, wherein the frequency of occurrence of the step length is characterized by an exponential distribution (EP), depending on the difficulty of prey acquisition. However, as of now it has not been clarified how the aforementioned three phenomena arise: the positive correlation created in the step length series, the relation between the positive correlation of the step length series and the form of an individual's step length distribution, and the switching between Lévy and Brownian behavior depending on the abundance of prey. The purpose of this study is to simulate foraging behavior by three Bayesian decision-making agents: an agent simultaneously performing both knowledge learning and knowledge-based inference, an agent performing only learning, an agent performing only inference, and to analyze how the aforementioned three phenomena arise. The simulation results show that only the agent with both learning and inference has a mechanism that simultaneously causes all the phenomena. This suggests that simultaneous learning on prey distribution and inference based on the knowledge gained in exploratory behavior under incomplete information may be the key to the emergence of Lévy walk-like patterns found in humans and marine organisms.

scholarly journals Emergence of power laws in the pharmacokinetics of paclitaxel due to competing saturable processes.

2008 ◽  
Vol 11 (3) ◽  
pp. 77 ◽  
Author(s):  
Jack A Tuszynski ◽  
Rebeccah E. Marsh ◽  
Michael B. Sawyer ◽  
Kenneth J.E. Vos
Keyword(s):  
Power Law ◽  
Fractional Power ◽  
Area Under The Curve ◽  
Power Laws ◽  
Dose Dependence ◽  
Power Exponent ◽  
Least Squares Regression ◽  
Time Data ◽  
Concentration Time ◽  
Wide Range

Purpose: This study presents the results of power law analysis applied to the pharmacokinetics of paclitaxel. Emphasis is placed on the role that the power exponent can play in the investigation and quantification of nonlinear pharmacokinetics and the elucidation of the underlying physiological processes. Methods: Forty-one sets of concentration-time data were inferred from 20 published clinical trial studies, and 8 sets of area under the curve (AUC) and maximum concentration (Cmax) values as a function of dose were collected. Both types of data were tested for a power law relationship using least squares regression analysis. Results: Thirty-nine of the concentration-time curves were found to exhibit power law tails, and two dominant fractal exponents emerged. Short infusion times led to tails with a single power exponent of -1.57 ± 0.14, while long infusion times resulted in steeper tails characterized by roughly twice the exponent. The curves following intermediate infusion times were characterized by two consecutive power laws; an initial short slope with the larger alpha value was followed by a crossover to a long-time tail characterized by the smaller exponent. The AUC and Cmax parameters exhibited a power law dependence on the dose, with fractional power exponents that agreed with each other and with the exponent characterizing the shallow decline. Computer simulations revealed that a two- or three-compartment model with both saturable distribution and saturable elimination can produce the observed behaviour. Furthermore, there is preliminary evidence that the nonlinear dose-dependence is correlated with the power law tails. Conclusion: Assessment of data from published clinical trials suggests that power laws accurately describe the concentration-time curves and non-linear dose-dependence of paclitaxel, and the power exponents provide insight into the underlying drug mechanisms. The interplay between two saturable processes can produce a wide range of behaviour, including concentration-time curves with exponential, power law, and dual power law tails.

scholarly journals RESTRICTIONS ON THE HYPOTHETICAL LONG RANGE INTERACTIONS FROM THE CASIMIR-TYPE NULL EXPERIMENT WITH THREE TEST BODIES

1994 ◽  
Vol 09 (29) ◽  
pp. 2671-2680 ◽  
Author(s):  
M. BORDAG ◽  
V. M. MOSTEPANENKO ◽  
I. YU. SOKOLOV
Keyword(s):  
Long Range ◽  
Power Law ◽  
Casimir Force ◽  
Power Laws ◽  
Gravitational Attraction ◽  
Spherical Lens ◽  
Plane Plate ◽  
Wide Range ◽  
Long Range Interactions

A realistic null experiment is suggested in which the Casimir force between a plane plate and a spherical lens is compensated by the force of gravitational attraction. This configuration is shown to be very sensitive to the existence of additional hypothetical forces of Yukawa-type or power laws. From the suggested null experiment the restrictions on the Yukawa constant α can be strengthened by a factor up to 1000 in a wide range 10−8 m < λ < 10−4 m and by a factor of 10 for λ from several centimeters to several meters. For power law interactions the strengthening of restrictions by a factor of 20 is possible for the force decreasing as r−5.

scholarly journals Sliding Blocks Revisited: A Simulational Study

1998 ◽  
Vol 09 (06) ◽  
pp. 875-880 ◽  
Author(s):  
A. R. de Lima ◽  
C. Moukarzel ◽  
T. J. P. Penna
Keyword(s):  
Experimental Data ◽  
Friction Coefficient ◽  
Power Law ◽  
Computational Study ◽  
Recent Experimental Data ◽  
Power Law Distribution ◽  
Inclined Surfaces ◽  
Wide Range

A computational study of sliding blocks on inclined surfaces is presented. Assuming that the friction coefficient μ is a function of position, the probability P(λ) for the block to slide down over a length λ is numerically calculated. Our results are consistent with recent experimental data suggesting a power-law distribution of events over a wide range of displacements when the chute angle is close to the critical one, and suggest that the variation of μ along the surface is responsible for this.

HOW LONG CAN YOU ENJOY BLACKJACK WITH 100 CHIPS?

2011 ◽  
Vol 22 (10) ◽  
pp. 1161-1171
Author(s):  
TAO YANG ◽  
QIANQIAN LI ◽  
XINGANG XIA ◽  
ERBO ZHAO ◽  
GUO LIU ◽  
...  
Keyword(s):  
Decision Making ◽  
Random Walk ◽  
Power Law ◽  
Risk Taking ◽  
Real World ◽  
Power Law Distribution ◽  
Related Research ◽  
Fat Tail ◽  
Playing Time ◽  
Pathologic Gambling

Gambling-related research has implications in financial area understandings and applications. Researches in this area usually focus on pathology, risk-taking, decision-making and addiction. Few works have been done to demonstrate the distribution of the playing time before players go bankrupt. One problem is that it is difficult to get statistics in real world gambling. In this paper, we do simulations in a Blackjack game with a selected strategy. We find the distribution of playing time before players lose a certain amount of money as a power law distribution, indicating the existence of very long playing time players. We also find that double is the most important factor that causes the fat tail. Comparison shows that when removing double, split and three to two payoff, Blackjack goes back to a random walk. The increase of the number of decks somewhat decreases the average playing time. Our results may have pathologic gambling intervention implications.

scholarly journals Exploring the Citywide Human Mobility Patterns of Taxi Trips through a Topic-Modeling Analysis

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Hui Xiong ◽  
Kaiqiang Xie ◽  
Lu Ma ◽  
Feng Yuan ◽  
Rui Shen
Keyword(s):  
Power Law ◽  
Traffic Management ◽  
Large Scale ◽  
Latent Dirichlet Allocation ◽  
Topic Model ◽  
Human Mobility ◽  
Mobility Patterns ◽  
Power Law Distribution ◽  
Modeling Analysis ◽  
Wide Range

Understanding human mobility patterns is of great importance for a wide range of applications from social networks to transportation planning. Toward this end, the spatial-temporal information of a large-scale dataset of taxi trips was collected via GPS, from March 10 to 23, 2014, in Beijing. The data contain trips generated by a great portion of taxi vehicles citywide. We revealed that the geographic displacement of those trips follows the power law distribution and the corresponding travel time follows a mixture of the exponential and power law distribution. To identify human mobility patterns, a topic model with the latent Dirichlet allocation (LDA) algorithm was proposed to infer the sixty-five key topics. By measuring the variation of trip displacement over time, we find that the travel distance in the morning rush hour is much shorter than that in the other time. As for daily patterns, it shows that taxi mobility presents weekly regularity both on weekdays and on weekends. Among different days in the same week, mobility patterns on Tuesday and Wednesday are quite similar. By quantifying the trip distance along time, we find that Topic 44 exhibits dominant patterns, which means distance less than 10 km is predominant no matter what time in a day. The findings could be references for travelers to arrange trips and policymakers to formulate sound traffic management policies.

scholarly journals Power Laws in Superspreading Events: Evidence from Coronavirus Outbreaks and Implications for SIR Models

2020 ◽  
Author(s):  
Masao Fukui ◽  
Chishio Furukawa
Keyword(s):  
Power Law ◽  
Average Rate ◽  
Herd Immunity ◽  
Power Laws ◽  
Infinite Variance ◽  
Finite Variance ◽  
Fat Tails ◽  
Infection Rates ◽  
Power Law Distribution ◽  
Large Populations

AbstractWhile they are rare, superspreading events (SSEs), wherein a few primary cases infect an extraordinarily large number of secondary cases, are recognized as a prominent determinant of aggregate infection rates (ℛ0). Existing stochastic SIR models incorporate SSEs by fitting distributions with thin tails, or finite variance, and therefore predicting almost deterministic epidemiological outcomes in large populations. This paper documents evidence from recent coronavirus outbreaks, including SARS, MERS, and COVID-19, that SSEs follow a power law distribution with fat tails, or infinite variance. We then extend an otherwise standard SIR model with the estimated power law distributions, and show that idiosyncratic uncertainties in SSEs will lead to large aggregate uncertainties in infection dynamics, even with large populations. That is, the timing and magnitude of outbreaks will be unpredictable. While such uncertainties have social costs, we also find that they on average decrease the herd immunity thresholds and the cumulative infections because per-period infection rates have decreasing marginal effects. Our findings have implications for social distancing interventions: targeting SSEs reduces not only the average rate of infection (ℛ0) but also its uncertainty. To understand this effect, and to improve inference of the average reproduction numbers under fat tails, estimating the tail distribution of SSEs is vital.

DYNAMICAL EXPLANATION FOR THE EMERGENCE OF POWER LAW IN A STOCK MARKET MODEL

1996 ◽  
Vol 07 (01) ◽  
pp. 65-72 ◽  
Author(s):  
MOSHE LEVY ◽  
SORIN SOLOMON ◽  
GIVAT RAM
Keyword(s):  
Stock Market ◽  
Power Law ◽  
Wealth Distribution ◽  
Power Laws ◽  
Stationary Regime ◽  
Market Model ◽  
Self Organized ◽  
Wide Range ◽  
Self Organized Criticality ◽  
Sand Piles

Power laws are found in a wide range of different systems: From sand piles to word occurrence frequencies and to the size distribution of cities. The natural emergence of these power laws in so many different systems, which has been called self-organized criticality, seems rather mysterious and awaits a rigorous explanation. In this letter we study the stationary regime of a previously introduced dynamical microscopic model of the stock market. We find that the wealth distribution among investors spontaneously converges to a power law. We are able to explain this phenomenon by simple general considerations. We suggest that similar considerations may explain self-organized criticality in many other systems. They also explain the Levy distribution.

scholarly journals A generalized distribution interpolated between the exponential and power law distributions and applied to the walking data of the pill bug (Armadillidium vulgare)

2021 ◽  
Author(s):  
Shuji Shinohara ◽  
Hiroshi Okamoto ◽  
Toru Moriyama ◽  
Yoshihiro Nakajima ◽  
Takaharu Shokaku ◽  
...  
Keyword(s):  
Frequency Distribution ◽  
Power Law ◽  
Shape Parameter ◽  
Step Length ◽  
Distribution Model ◽  
General Distribution ◽  
Series Data ◽  
Power Law Distribution ◽  
Exponential Distributions ◽  
Special Cases

To determine whether the walking pattern of an organism is a Lévy walk or a Brownian walk, it has been compared whether the frequency distribution of linear step lengths follows a power law distribution or an exponential distribution. However, there are many cases where actual data cannot be classified into either of these categories. In this paper, we propose a general distribution that includes the power law and exponential distributions as special cases. This distribution has two parameters: One represents the exponent, similar to the power law and exponential distributions, and the other is a shape parameter representing the shape of the distribution. By introducing this distribution, an intermediate distribution model can be interpolated between the power law and exponential distributions. In this study, the proposed distribution was fitted to the frequency distribution of the step length calculated from the walking data of pill bugs. The autocorrelation coefficients were also calculated from the time-series data of the step length, and the relationship between the shape parameter and time dependency was investigated. The results showed that individuals whose step-length frequency distributions were closer to the power law distribution had stronger time dependence.

scholarly journals Rationalizing spatial exploration patterns of wild animals and humans through a temporal discounting framework

2016 ◽  
Vol 113 (31) ◽  
pp. 8747-8752 ◽  
Author(s):  
Vijay Mohan K. Namboodiri ◽  
Joshua M. Levy ◽  
Stefan Mihalas ◽  
David W. Sims ◽  
Marshall G. Hussain Shuler
Keyword(s):  
Power Law ◽  
Path Length ◽  
Temporal Discounting ◽  
Power Laws ◽  
Hyperbolic Model ◽  
Wild Animals ◽  
Power Law Distribution ◽  
Spatial Exploration ◽  
Path Lengths ◽  
Cost Of Time

Understanding the exploration patterns of foragers in the wild provides fundamental insight into animal behavior. Recent experimental evidence has demonstrated that path lengths (distances between consecutive turns) taken by foragers are well fitted by a power law distribution. Numerous theoretical contributions have posited that “Lévy random walks”—which can produce power law path length distributions—are optimal for memoryless agents searching a sparse reward landscape. It is unclear, however, whether such a strategy is efficient for cognitively complex agents, from wild animals to humans. Here, we developed a model to explain the emergence of apparent power law path length distributions in animals that can learn about their environments. In our model, the agent’s goal during search is to build an internal model of the distribution of rewards in space that takes into account the cost of time to reach distant locations (i.e., temporally discounting rewards). For an agent with such a goal, we find that an optimal model of exploration in fact produces hyperbolic path lengths, which are well approximated by power laws. We then provide support for our model by showing that humans in a laboratory spatial exploration task search space systematically and modify their search patterns under a cost of time. In addition, we find that path length distributions in a large dataset obtained from free-ranging marine vertebrates are well described by our hyperbolic model. Thus, we provide a general theoretical framework for understanding spatial exploration patterns of cognitively complex foragers.

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