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.

EMPIRICAL LAWS OF A STOCK PRICE INDEX AND A STOCHASTIC MODEL

2003 ◽  
Vol 06 (03) ◽  
pp. 303-312 ◽  
Author(s):  
TAISEI KAIZOJI ◽  
MICHIYO KAIZOJI
Keyword(s):  
Stochastic Model ◽  
Power Law ◽  
Stock Prices ◽  
Stock Price ◽  
Price Index ◽  
Probability Function ◽  
The Other ◽  
Power Law Distribution ◽  
Exponential Distributions ◽  
Daily Data

Recent works by econo-physicists [5,8,15,19] have shown that the probability function of the share returns and the volatility satisfies a power law with an exponent close to 4. On the other hand, we investigated quantitatively the return and the volatility of the daily data of the Nikkei 225 index from 1990 to 2003, and we found that the distributions of the returns and the volatility can be accurately described by the exponential distributions [11]. We then propose a stochastic model of stock markets that can reproduce these empirical laws. In our model the fluctuations of stock prices are caused by interactions among traders. We indicate that the model can reproduce the empirical facts mentioned above. In particular, we show that the interaction strengths among traders are a key variable that can distinguish the emergence of the exponential distribution or the power-law distribution.

scholarly journals Vibration analysis of rotating porous functionally graded material beams using exact formulation

2021 ◽  
pp. 107754632110278
Author(s):  
Mohammadreza Amoozgar ◽  
Len Gelman
Keyword(s):  
Power Law ◽  
Functionally Graded Material ◽  
Material Properties ◽  
Functionally Graded ◽  
Distribution Model ◽  
Power Law Distribution ◽  
Cross Sectional ◽  
Rotating Speed ◽  
Rotating Blade ◽  
Graded Material

In this article, the exact free vibration of porous functionally graded rotating blades is investigated. The nonlinear 3D dynamics of the blade is simulated using the geometrically exact fully intrinsic beam equations, and the corresponding cross-sectional properties of the FG beam are developed. The material properties of the functionally graded material blade are graded through the thickness using a power law distribution. Furthermore, it is assumed that due to the manufacturing process, a level of porosity exists in the material which in turn can affect the material properties of the blade. Two porosity models resembling the even and uneven distributions of porosity are considered. First, the obtained results for a functionally graded material rotating blade are compared with those reported in the literature, and a very good agreement is observed. Furthermore, the effect of various parameters on the vibration of the functionally graded material beam is investigated. It is obtained that the dynamics of the rotating blade is sensitive to the type of the porosity due to manufacturing flaws. Moreover, the numerical results show that the blade length to height ratio, power law index, rotating speed and porosity distribution model affect the dynamics of the beam significantly.

scholarly journals POWER-LAW DISTRIBUTIONS BASED ON EXPONENTIAL DISTRIBUTIONS: LATENT SCALING, SPURIOUS ZIPF'S LAW, AND FRACTAL RABBITS

Fractals ◽  
2015 ◽  
Vol 23 (02) ◽  
pp. 1550009 ◽  
Author(s):  
YANGUANG CHEN
Keyword(s):  
Exponential Distribution ◽  
Power Law ◽  
Power Laws ◽  
Power Exponent ◽  
Power Law Distribution ◽  
Exponential Distributions ◽  
Real Power ◽  
The Real ◽  
Dimension Space ◽  
Power Law Distributions

The difference between the inverse power function and the negative exponential function is significant. The former suggests a complex distribution, while the latter indicates a simple distribution. However, the association of the power-law distribution with the exponential distribution has been seldom researched. This paper is devoted to exploring the relationships between exponential laws and power laws from the angle of view of urban geography. Using mathematical derivation and numerical experiments, I reveal that a power-law distribution can be created through a semi-moving average process of an exponential distribution. For the distributions defined in a one-dimension space (e.g. Zipf's law), the power exponent is 1; while for those defined in a two-dimension space (e.g. Clark's law), the power exponent is 2. The findings of this study are as follows. First, the exponential distributions suggest a hidden scaling, but the scaling exponents suggest a Euclidean dimension. Second, special power-law distributions can be derived from exponential distributions, but they differ from the typical power-law distributions. Third, it is the real power-law distributions that can be related with fractal dimension. This study discloses an inherent link between simplicity and complexity. In practice, maybe the result presented in this paper can be employed to distinguish the real power laws from spurious power laws (e.g. the fake Zipf distribution).

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 The Characteristics of Persistent Sporadic Meteor Echoes

1961 ◽  
Vol 14 (1) ◽  
pp. 89 ◽  
Author(s):  
JW Smith
Keyword(s):  
Diurnal Variation ◽  
Frequency Distribution ◽  
Mass Distribution ◽  
Power Law ◽  
Power Law Distribution ◽  
Sporadic Meteors

This paper examines the frequency distribution of the durations of nearly 8000 persistent radio echoes from sporadic meteors recorded at Adelaide during 1957. The maximum line densities in the trails formed by these meteors exceed 1013 electrons/em, corresponding to visual magnitudes < +3. As the echo duration increases, the numbers of echoes are found to fall progressively further below the numbers expected from a power-law distribution. No significant seasonal or diurnal variation in the mass distribution of the meteors examined is apparent.

scholarly journals The structure of co-publications multilayer network

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Ghislain Romaric Meleu ◽  
Paulin Yonta Melatagia
Keyword(s):  
Power Law ◽  
Degree Distribution ◽  
Preferential Attachment ◽  
Small World ◽  
Generation Model ◽  
Small World Network ◽  
Power Law Distribution ◽  
Multilayer Networks ◽  
Multilayer Network ◽  
Scientific Papers

AbstractUsing the headers of scientific papers, we have built multilayer networks of entities involved in research namely: authors, laboratories, and institutions. We have analyzed some properties of such networks built from data extracted from the HAL archives and found that the network at each layer is a small-world network with power law distribution. In order to simulate such co-publication network, we propose a multilayer network generation model based on the formation of cliques at each layer and the affiliation of each new node to the higher layers. The clique is built from new and existing nodes selected using preferential attachment. We also show that, the degree distribution of generated layers follows a power law. From the simulations of our model, we show that the generated multilayer networks reproduce the studied properties of co-publication networks.

scholarly journals Blocks Size Frequency Distribution in the Enceladus Tiger Stripes Area: Implications on Their Formative Processes

Universe ◽  
2021 ◽  
Vol 7 (4) ◽  
pp. 82
Author(s):  
Maurizio Pajola ◽  
Alice Lucchetti ◽  
Lara Senter ◽  
Gabriele Cremonese
Keyword(s):  
Frequency Distribution ◽  
Power Law ◽  
Size Frequency Distribution ◽  
Surface Stresses ◽  
Size Frequency ◽  
The One ◽  
Power Law Index ◽  
Comet 67P ◽  
South Polar ◽  
Degree Of Fragmentation

We study the size frequency distribution of the blocks located in the deeply fractured, geologically active Enceladus South Polar Terrain with the aim to suggest their formative mechanisms. Through the Cassini ISS images, we identify ~17,000 blocks with sizes ranging from ~25 m to 366 m, and located at different distances from the Damascus, Baghdad and Cairo Sulci. On all counts and for both Damascus and Baghdad cases, the power-law fitting curve has an index that is similar to the one obtained on the deeply fractured, actively sublimating Hathor cliff on comet 67P/Churyumov-Gerasimenko, where several non-dislodged blocks are observed. This suggests that as for 67P, sublimation and surface stresses favor similar fractures development in the Enceladus icy matrix, hence resulting in comparable block disaggregation. A steeper power-law index for Cairo counts may suggest a higher degree of fragmentation, which could be the result of localized, stronger tectonic disruption of lithospheric ice. Eventually, we show that the smallest blocks identified are located from tens of m to 20–25 km from the Sulci fissures, while the largest blocks are found closer to the tiger stripes. This result supports the ejection hypothesis mechanism as the possible source of blocks.

scholarly journals Power-law behavior of transcription factor dynamics at the single-molecule level implies a continuum affinity model

2021 ◽  
Author(s):  
David A Garcia ◽  
Gregory Fettweis ◽  
Diego M Presman ◽  
Ville Paakinaho ◽  
Christopher Jarzynski ◽  
...  
Keyword(s):  
Transcription Factor ◽  
Single Molecule ◽  
Power Law ◽  
Dwell Time ◽  
Specific Binding ◽  
Power Law Distribution ◽  
Single Molecule Level ◽  
Binding Behavior ◽  
Chromatin Template ◽  
Nuclear Domains

Abstract Single-molecule tracking (SMT) allows the study of transcription factor (TF) dynamics in the nucleus, giving important information regarding the diffusion and binding behavior of these proteins in the nuclear environment. Dwell time distributions obtained by SMT for most TFs appear to follow bi-exponential behavior. This has been ascribed to two discrete populations of TFs—one non-specifically bound to chromatin and another specifically bound to target sites, as implied by decades of biochemical studies. However, emerging studies suggest alternate models for dwell-time distributions, indicating the existence of more than two populations of TFs (multi-exponential distribution), or even the absence of discrete states altogether (power-law distribution). Here, we present an analytical pipeline to evaluate which model best explains SMT data. We find that a broad spectrum of TFs (including glucocorticoid receptor, oestrogen receptor, FOXA1, CTCF) follow a power-law distribution of dwell-times, blurring the temporal line between non-specific and specific binding, suggesting that productive binding may involve longer binding events than previously believed. From these observations, we propose a continuum of affinities model to explain TF dynamics, that is consistent with complex interactions of TFs with multiple nuclear domains as well as binding and searching on the chromatin template.

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