scholarly journals Power laws in the Roman Empire: a survival analysis

2021 ◽  
Vol 8 (7) ◽  
pp. 210850
Author(s):  
P. L. Ramos ◽  
L. F. Costa ◽  
F. Louzada ◽  
F. A. Rodrigues
Keyword(s):  
Roman Empire ◽  
Power Law ◽  
Political Institutions ◽  
Survival Data ◽  
Power Laws ◽  
Data Types ◽  
Ancient Civilizations ◽  
Long Term Survivors ◽  
Power Law Distributions

The Roman Empire shaped western civilization, and many Roman principles are embodied in modern institutions. Although its political institutions proved both resilient and adaptable, allowing it to incorporate diverse populations, the Empire suffered from many conflicts. Indeed, most emperors died violently, from assassination, suicide or in battle. These conflicts produced patterns in the length of time that can be identified by statistical analysis. In this paper, we study the underlying patterns associated with the reign of the Roman emperors by using statistical tools of survival data analysis. We consider all the 175 Roman emperors and propose a new power-law model with change points to predict the time-to-violent-death of the Roman emperors. This model encompasses data in the presence of censoring and long-term survivors, providing more accurate predictions than previous models. Our results show that power-law distributions can also occur in survival data, as verified in other data types from natural and artificial systems, reinforcing the ubiquity of power-law distributions. The generality of our approach paves the way to further related investigations not only in other ancient civilizations but also in applications in engineering and medicine.

scholarly journals POWER-LAW DISTRIBUTIONS IN CIRCULATING MONEY: EFFECT OF PREFERENTIAL BEHAVIOR

2004 ◽  
Vol 18 (17n19) ◽  
pp. 2725-2729 ◽  
Author(s):  
NING DING ◽  
YOUGUI WANG ◽  
JUN XU ◽  
NING XI
Keyword(s):  
Computer Simulation ◽  
Statistical Mechanics ◽  
Power Law ◽  
Power Laws ◽  
Generation Mechanism ◽  
Holding Time ◽  
Simulation Results ◽  
Power Law Distributions ◽  
Money Circulation

We introduce preferential behavior into the study on statistical mechanics of money circulation. The computer simulation results show that the preferential behavior can lead to power laws on distributions over both holding time and amount of money held by agents. However, some constraints are needed in generation mechanism to ensure the robustness of power-law distributions.

scholarly journals A BAYESIAN WEIBULL ANALYSIS OF BREAST CANCER DATA WITH LONG-TERM SURVIVORS IN PARANA STATE, BRAZIL

2021 ◽  
Vol 39 (2) ◽  
pp. 293-310
Author(s):  
Talita Evelin Nabarrete Tristão de MORAES ◽  
Isolde PREVIDELLI ◽  
Giovani Loiola da SILVA
Keyword(s):  
Breast Cancer ◽  
Survival Data ◽  
White Women ◽  
Age Groups ◽  
Population Based ◽  
Breast Cancer Data ◽  
Weibull Regression ◽  
Cancer Data ◽  
Long Term Survivors

Breast cancer is one of the most common diseases among women worldwide with about 25% of new cases each year. In Brazil, 59,700 new cases of breast cancer were expected in 2019, according to the Brazilian National Cancer Institute (INCA). Survival analysis has been an useful tool for the identifying the risk and prognostic factors for cancer patients. This work aims to characterize the prognostic value of demographic, clinical and pathological variables in relation to the survival time of 2,092 patients diagnosed with breast cancer in Parana State, Brazil, from 2004 to 2016. In this sense, we propose a Bayesian analysis of survival data with long-term survivors by using Weibull regression models through integrated nested Laplace approximations (INLA). The results point to a proportion of long-term survivors around 57:6% in the population under study. In regard to potential risk factors, we namely concluded that 40-50 year age group has superior survival than younger and older age groups, white women have higher breast cancer risk than other races, and marital status decreases that risk. Caution on the general use of these results is nevertheless advised, since we have analyzed population-based breast cancer data without proper monitoring by a healthprofessional.

scholarly journals Nadarajah-Haghighi Model for Survival Data With Long Term Survivors in the Presence of Right Censored Data

2021 ◽  
pp. 695-709
Author(s):  
Umar Usman ◽  
Shamsuddeen Suleiman ◽  
Bello Magaji Arkilla ◽  
Yakubu Aliyu
Keyword(s):  
Survival Data ◽  
Likelihood Estimation ◽  
Estimation Procedure ◽  
Right Censoring ◽  
Right Censored Data ◽  
Term Survival ◽  
Proposed Model ◽  
Cure Fraction ◽  
Long Term Survivors

In this paper, a new long term survival model called Nadarajah-Haghighi model for survival data with long term survivors was proposed. The model is used in fitting data where the population of interest is a mixture of individuals that are susceptible to the event of interest and individuals that are not susceptible to the event of interest. The statistical properties of the proposed model including quantile function, moments, mean and variance were provided. Maximum likelihood estimation procedure was used to estimate the parameters of the model assuming right censoring. Furthermore, Bayesian method of estimation was also employed in estimating the parameters of the model assuming right censoring. Simulations study was performed in order to ascertain the performances of the MLE estimators. Random samples of different sample sizes were generated from the model with some arbitrary values for the parameters for 5%, 1:3% and 1:5% cure fraction values. Bias, standard error and mean square error were used as discrimination criteria. Additionally, we compared the performance of the proposed model with some competing models. The results of the applications indicates that the proposed model is more efficient than the models compared with. Finally, we fitted some models considering type of treatment as a covariate. It was observed that the covariate  have effect on the shape parameter of the proposed model.

Environmental Stress Models

2003 ◽  
Author(s):  
M. E. J. Newman ◽  
R. G. Palmer
Keyword(s):  
Critical Phenomena ◽  
Power Law ◽  
Species Interactions ◽  
Fossil Record ◽  
Biotic Interactions ◽  
Power Laws ◽  
Fixed Number ◽  
Stress Models ◽  
Fossil Data ◽  
Power Law Distributions

In chapters 2 to 4 we discussed several models of extinction which make use of ideas drawn from the study of critical phenomena. The primary impetus for this approach was the observation of apparent power-law distributions in a variety of statistics drawn from the fossil record, as discussed in section 1.2; in other branches of science such power laws are often indicators of critical processes. However, there are also a number of other mechanisms by which power laws can arise, including random multiplicative processes (Montroll and Shlesinger 1982; Sornette and Cont 1997), extremal random processes (Sibani and Littlewood 1993), and random barrier-crossing dynamics (Sneppen 1995). Thus the existence of power-law distributions in the fossil data is not on its own sufficient to demonstrate the presence of critical phenomena in extinction processes. Critical models also assume that extinction is caused primarily by biotic effects such as competition and predation, an assumption which is in disagreement with the fossil record. As discussed in section 1.2.2.1, all the plausible causes for specific prehistoric extinctions are abiotic in nature. Therefore an obvious question to ask is whether it is possible to construct models in which extinction is caused by abiotic environmental factors, rather than by critical fluctuations arising out of biotic interactions, but which still give power-law distributions of the relevant quantities. Such models have been suggested by Newman (1996, 1997) and by Manrubia and Paczuski (1998). Interestingly, both of these models are the result of attempts at simplifying models based on critical phenomena. Newman's model is a simplification of the model of Newman and Roberts (see section 3.6), which included both biotic and abiotic effects; the simplification arises from the realization that the biotic part can be omitted without losing the power-law distributions. Manrubia and Paczuski's model was a simplification of the connection model of Solé and Manrubia (see section 4.1), but in fact all direct species-species interactions were dropped, leaving a model which one can regard as driven only by abiotic effects. We discuss these models in turn. The model proposed by Newman (1996, 1997) has a fixed number N of species which in the simplest case are noninteracting.

POWER LAWS, WEAK lp ESTIMATE AND WAVELET DE-NOISING

Fractals ◽  
2000 ◽  
Vol 08 (01) ◽  
pp. 73-83
Author(s):  
TOMOHIRO MATSUOKA ◽  
TOSHIHIDE UENO ◽  
TAKASHI ADACHI ◽  
MASAMI OKADA
Keyword(s):  
Power Law ◽  
Power Laws ◽  
Mild Assumption ◽  
Lp Estimate ◽  
Scaling Argument ◽  
Power Law Distributions

Data with power law distributions are studied by a scaling argument. Then related weak lp sequences are characterized. As an application we can show in a transparent way that the wavelet de-noising theory holds under a mild assumption which is given by means of weak lp (quasi-)norms.

SIMPLE MODELS OF WAITING LISTS

2003 ◽  
Vol 06 (02) ◽  
pp. 215-222 ◽  
Author(s):  
G. J. RODGERS ◽  
Y. J. YAP ◽  
T. P. YOUNG
Keyword(s):  
Power Law ◽  
Empirical Studies ◽  
Length Distribution ◽  
Power Laws ◽  
Waiting Lists ◽  
Waiting List ◽  
Power Law Distributions ◽  
Simple Models

Motivated by recent empirical studies of the length distribution of hospital waiting lists, we introduce and solve a set of models that imitate the formation of waiting lists. Patients arriving in the system must choose a waiting list to join, based on its length. At the same time patients leave the lists as they get served. The model illustrates how the power-law distributions found in the empirical studies might arise, but indicates that the mechanism causing the power-laws is unlikely to be the preferential behavior of patients or their physicians.

scholarly journals Power-Law Neuronal Fluctuations in a Recurrent Network Model of Parametric Working Memory

2006 ◽  
Vol 95 (2) ◽  
pp. 1099-1114 ◽  
Author(s):  
Paul Miller ◽  
Xiao-Jing Wang
Keyword(s):  
Working Memory ◽  
Power Law ◽  
Neural Coding ◽  
Power Spectra ◽  
Power Laws ◽  
Recurrent Network ◽  
Persistent Activity ◽  
External Stimulation ◽  
Tuning Curves

In a working memory system, persistent activity maintains information in the absence of external stimulation, therefore the time scale and structure of correlated neural fluctuations reflect the intrinsic microcircuit dynamics rather than direct responses to sensory inputs. Here we show that a parametric working memory model capable of graded persistent activity is characterized by arbitrarily long correlation times, with Fano factors and power spectra of neural activity described by the power laws of a random walk. Collective drifts of the mnemonic firing pattern induce long-term noise correlations between pairs of cells, with the sign (positive or negative) and amplitude proportional to the product of the gradients of their tuning curves. None of the power-law behavior was observed in a variant of the model endowed with discrete bistable neural groups, where noise fluctuations were unable to cause long-term changes in rate. Therefore such behavior can serve as a probe for a quasi-continuous attractor. We propose that the unusual correlated fluctuations have important implications for neural coding in parametric working memory circuits.

A new parametric model for survival data with long-term survivors

2004 ◽  
Vol 23 (22) ◽  
pp. 3525-3543 ◽  
Author(s):  
Quanxi Shao ◽  
Xian Zhou
Keyword(s):  
Survival Data ◽  
Parametric Model ◽  
Long Term Survivors
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