A Tale of Two Tails: Peakedness Properties in Inheritance Models of Evolutionary Theory

In this paper, we study transmission of traits through generations in multifactorial inheritance models with sex- and time-dependent heritability. We further analyze the implications of these models under heavy-tailedness of traits' distributions. Among other results, we show that in the case of a trait (for instance, a medical or behavioral disorder or a phenotype with significant heritability affecting human capital in an economy) with not very thick-tailed initial density, the trait distribution becomes increasingly more peaked, that is, increasingly more concentrated and unequally spread, with time. But these patterns are reversed for traits with sufficiently heavy-tailed initial distributions (e. g. , a medical or behavioral disorder for which there is no strongly expressed risk group or a relatively equally distributed ability with significant genetic influence). Such traits' distributions become less peaked over time and increasingly more spread in the population. In addition, we study the intergenerational transmission of the sex ratio in models of threshold (e. g. , polygenic or temperature-dependent) sex determination with long-tailed sex-determining traits. Among other results, we show that if the distribution of the sex determining trait is not very thick-tailed, then several properties of these models are the same as in the case of log-concave densities analyzed by Karlin (1984, 1992). In particular, the excess of males (females) among parents leads to the same pattern for the population of the offspring. Thus, the excess of one sex over the other one accumulates with time and the sex ratio in the total alive population cannot stabilize at the balanced sex ratio value of 1/2. We further show that the above properties are reversed for sufficiently heavy-tailed distributions of sex determining traits. In such settings, the sex ratio of the offspring oscillates around the balanced sex ratio value and an excess of males (females) in the initial period leads to an excess of females (males) offspring next period. Therefore, the sex ratio in the total living population can, in fact, stabilize at 1/2. Interestingly, these results are related, in particular, to the analysis of correlation between human sex ratios and socioeconomic status of parents as well as to the study of the variation of the sex ratio due to parental hormonal levels. The proof of the results in the paper is based on the general results on majorization properties of heavy-tailed distributions obtained recently in Ibragimov (2004) and several their extensions derived in this work.

International Diversification: A Copula Approach

.Diversification; Copula; Correlation Complexity; Downside Risk; Systemic Risk

A Survey of Performance Evaluation and Control for Self-Similar Network Traffic

This paper surveys techniques for the recognition and treatment of self-similar network or internetwork traffic. Various researchers have reported traffic measurements that demonstrate considerable burstiness on a range of time scales with properties of self-similarity. Rapid technological development has widened the scope of network and Internet applications and, in turn, increased traffic volume. The exponential growth of the number of servers, as well as the number of users, causes Internet performance to be problematic as a result of the significant impact that long-range dependent traffic has on buffer requirements. Consequently, accurate and reliable measurement, analysis and control of Internet traffic are vital. The most significant techniques for performance evaluation include theoretical analysis, simulation, and empirical study based on measurement. In this research, we discuss existing and recent developments in performance evaluation and control tools used in network traffic engineering

Heavy-tailedness and Threshold Sex Determination.

This paper studies the properties of the sex ratio in two-period models of threshold (e.g., polygenic or temperature-dependent) sex determination under heavy-tailedness in the framework of possibly skewed stable distributions and their convolutions. We show that if the initial distribution of the sex determining trait in such settings is moderately heavy-tailed and has a finite first moment, then an excess of males (females) in the first period leads to the same pattern in the second period. Thus, the excess of one sex over the other one accumulates over two generations and the sex ratio in the total alive population in the second period cannot stabilize at the balanced sex ratio value of 1/2. These properties are reversed for extremely heavy-tailed initial distributions of sex determining traits with infinite first moments. In such settings, the sex ratio of the offspring oscillates around the balanced sex ratio value and an excess of males (females) in the first period leads to an excess of females (males) in the second period. In addition, the sex ratio in the total living population in the second period can stabilize at 1/2 for some extremely heavy-tailed initial distributions of the sex determining trait. The results in the paper are shown to also hold for bounded sex determining phenotypes.Economic

Thou shalt not diversity: Why "Two of Every Sort"?

This paper presents a study of the intertemporal propagation of distributional properties of phenotypes in general polygenic multisex inheritance models with sex- and time-dependent heritabilities. It further analyzes the implications of these models under heavy-tailedness of traits' initial distributions. Our results suggest the optimality of a flexible asexual/binary mating system. Switching between asexual and binary inheritance mechanisms allows the population effectively to achieve a fast suppression of negative traits and a fast dispersion of positive traits, regardless of the distributional properties of the phenotypes in the initial period.Economic

International Diversification: An Extreme Value Approach

.Diversification; Downside Risk; Correlation Complexity; Extreme Value; Systemic Risk

Robust Risk Management. Accounting for Nonstationarity and Heavy Tails

In the ideal Black-Scholes world, financial time series are assumed 1) stationary (time homogeneous) and 2) having conditionally normal distribution given the past. These two assumptions have been widely-used in many methods such as the RiskMetrics, one risk management method considered as industry standard. However these assumptions are unrealistic. The primary aim of the paper is to account for nonstationarity and heavy tails in time series by presenting a local exponential smoothing approach, by which the smoothing parameter is adaptively selected at every time point and the heavy-tailedness of the process is considered. A complete theory addresses both issues. In our study, we demonstrate the implementation of the proposed method in volatility estimation and risk management given simulated and real data. Numerical results show the proposed method delivers accurate and sensitive estimates.Exponential Smoothing, Spatial Aggregation.

Fractional integration and fat tails for realized covariance kernels

We introduce a new fractionally integrated model for covariance matrix dynamics based on the long-memory behavior of daily realized covariance matrix kernels. We account for fat tails in the data by an appropriate distributional assumption. The covariance matrix dynamics are formulated as a numerically efficient matrix recursion that ensures positive definiteness under simple parameter constraints. Using intraday stock data over the period 2001-2012, we construct realized covariance kernels and show that the new fractionally integrated model statistically and economically outperforms recent alternatives such as the multivariate HEAVY model and the multivariate HAR model. In addition, the long-memory behavior is more important during non-crisis periods