Foundations of utilitarianism under risk and variable population.

Utilitarianism is the most prominent social welfare function in economics. We present three new axiomatic characterizations of utilitarian (that is, additively-separable) social welfare functions in a setting where there is risk over both population size and individuals' welfares. We first show that, given uncontroversial basic axioms, Blackorby et al.'s (1998) Expected Critical-Level Generalized Utilitarianism is equivalent to a new axiom holding that it is better to allocate higher utility-conditional-on-existence to possible people who have a higher probability of existence. The other two characterizations extend and clarify classic axiomatizations of utilitarianism from settings with either social risk or variable-population, considered alone.

Dynamical properties of single species stage structured model with Michaelis-Menten type harvesting on adult population and linear harvesting on juvenile population.

A very common and effective way for investigating future demographics is the study of stage structured models. The focus of this article is to propose a modified model to study the impact of population harvesting on their juvenile and adult stages, and analyze the dynamical properties from both qualitative and numerical perspective. It studies single species stage structured model with linear harvesting on juvenile group and Michaelis-Menten type harvesting on adult group. We exploit general ideas in mathematical modeling process to study the dynamical properties and their biological, ecological, and economic implications. It discusses that bi-stability phenomena may exist, global asymptotic stability at boundary equilibrium points and internal equilibrium points are investigated from construction of suitable Lyapunov and Dulac functions. It has been observed that a suitable linear harvesting on juvenile population can feasibly be carry out along with Michaelis-Menten type harvesting on adult population without endangering extinction of any group of population.

AVALANCHES IN A SHORT-MEMORY EXCITABLE NETWORK.

We study propagation of avalanches in a certain excitable network. The model is a particular case of the one introduced in [24], and is mathematically equivalent to an endemic variation of the Reed-Frost epidemic model introduced in [28]. Two types of heuristic approximation are frequently used for models of this type in applications, a branching process for avalanches of a small size at the beginning of the process and a deterministic dynamical system once the avalanche spreads to a significant fraction of a large network. In this paper we prove several results concerning the exact relation between the avalanche model and these limits, including rates of convergence and rigorous bounds for common characteristics of the model.

Favorite Sites of a Persistent Random Walk.

We consider favorite (i.e., most visited) sites of a symmetric persistent random walk on ℤ , a discrete-time process typified by the correlation of its directional history. We show that the cardinality of the set of favorite sites is eventually at most three. This is a generalization of a result by Tóth for a simple random walk, used to partially prove a longstanding conjecture by Erdos and Róvósz. The original conjecture asserting that for the simple random walk on integers the cardinality of the set of favorite sites is eventually at most two was recently disproved by Ding and Shen.

Covariance estimation via fiducial inference.

As a classical problem, covariance estimation has drawn much attention from the statistical community for decades. Much work has been done under the frequentist and the Bayesian frameworks. Aiming to quantify the uncertainty of the estimators without having to choose a prior, we have developed a fiducial approach to the estimation of covariance matrix. Built upon the Fiducial Berstein-von Mises Theorem (Sonderegger and Hannig 2014), we show that the fiducial distribution of the covariate matrix is consistent under our framework. Consequently, the samples generated from this fiducial distribution are good estimators to the true covariance matrix, which enable us to define a meaningful confidence region for the covariance matrix. Lastly, we also show that the fiducial approach can be a powerful tool for identifying clique structures in covariance matrices.

Efficient numerical computation of the basic reproduction number for structured populations.

As widely known, the basic reproduction number plays a key role in weighing birth/infection and death/recovery processes in several models of population dynamics. In this general setting, its characterization as the spectral radius of next generation operators is rather elegant, but simultaneously poses serious obstacles to its practical determination. In this work we address the problem numerically by reducing the relevant operators to matrices through a pseudospectral collocation, eventually computing the sought quantity by solving finite-dimensional eigenvalue problems. The approach is illustrated for two classes of models, respectively from ecology and epidemiology. Several numerical tests demonstrate experimentally important features of the method, like fast convergence and influence of the smoothness of the models' coefficients. Examples of robust analysis of instances of specific models are also presented to show potentialities and ease of application.

Unbalanced sex ratios in Germany caused by World War II and their effect on fertility: A life cycle perspective.

This paper analyzes the effects of permanently unbalanced sex ratios in Germany caused by World War II on fertility outcomes over the life cycle. Using Census records linked with individual biography data, our analysis confirms the commonly found short-term pattern of decreased fertility rates due to a stark imbalance of the sex ratio. Yet, the long-term effects of such an imbalance crucially depend on when in the life cycle fertility is evaluated. We find that female cohorts with low sex ratios have fewer children at younger ages and a larger fraction remains childless. While childlessness remains higher throughout their life cycle, mothers from affected cohorts catch up and even overcompensate at later ages with respect to the number of children. Our preferred reading of this result is that with low sex ratios women select themselves into late motherhood according to their fertility preferences. This interpretation is consistent with the finding that women from affected cohorts expand their childbearing period and accept lower quality matches in the marriage market. Our findings have important implications for understanding the long-term consequences of large population shocks.

Retirement Effect on Health Status and Health Behaviors in Urban China.

This paper analyzes the causal impact of retirement in China on Body Mass Index (BMI) and weight, which are a good gauge of the risk for some diseases. Many middle income developing countries are aging very rapidly and may have to adjust the retirement age to have financially feasible government budgets. It is important to know and understand any plausible health consequences of raising the retirement age in developing countries, and which sub-populations within these countries may be most affected. By using 2011, 2013 and 2015 waves of the China Health and Retirement Longitudinal Study (CHARLS), our identification strategy uses variation in China's mandatory retirement age with a fuzzy discontinuity design to examine an exogenous shock to retirement behavior. Our study finds that retirement will increase weight and BMI among men. This effect is much larger for men with low education. The channel may be that men with low education drink more and take less vigorous exercises after they get retired. Retirement does not affect weight and BMI for women. These effects are robust with different definitions of retirement, narrow retirement bandwidth for samples as well as dropping samples with rural Hukou.

Redistributive effects of different pension systems when longevity varies by socioeconomic status.

We propose a general analytical framework to model the redistributive features of alternative pension systems when individuals face ex ante differences in mortality. Differences in life expectancy between high and low socioeconomic groups are often large and have widened recently in many countries. Such longevity gaps affect the actuarial fairness and progressivity of public pension systems. However, behavioral responses to longevity and policy complicate analysis of possible reforms. Here we consider how various pension systems would perform in an OLG setting with heterogeneous longevity and ability. We evaluate redistributive effects of three Notional Defined Contribution plans and three Defined Benefit plans, calibrated on the US case. Compared to a benchmark non-redistributive plan that accounts for differences in mortality, US Social Security reduces regressivity from longevity differences, but would require group-specific life tables to achieve progressivity. Moreover, without separate life tables, despite apparent accounting gains, lower income groups would suffer welfare losses and higher income groups would enjoy welfare gains through indirect effects of pension systems on labor supply.

Estimation in additive models and ANOVA-like applications.

A well-known property of cumulant generating function is used to estimate the first four order cumulants, using least-squares estimators. In the case of additive models, empirical best linear unbiased predictors are also obtained. Pairs of independent and identically distributed models associated with the treatments of a base design are used to obtain unbiased estimators for the fourth-order cumulants. An application to real data is presented, showing the good behaviour of the least-squares estimators and the great flexibility of our approach.

Considering the sample sizes as truncated Poisson random variables in mixed effects models.

When applying analysis of variance, the sample sizes may not be previously known, so it is more appropriate to consider them as realizations of random variables. A motivating example is the collection of observations during a fixed time span in a study comparing, for example, several pathologies of patients arriving at a hospital. This paper extends the theory of analysis of variance to those situations considering mixed effects models. We will assume that the occurrences of observations correspond to a counting process and the sample dimensions have Poisson distribution. The proposed approach is applied to a study of cancer patients.

On ballistic deposition process on a strip.

We revisit the model of the ballistic deposition studied in [5] and prove several combinatorial properties of the random tree structure formed by the underlying stochastic process. Our results include limit theorems for the number of roots and the empirical average of the distance between two successive roots of the underlying tree-like structure as well as certain intricate moments calculations.

Modal Propellant Gauging: High-resolution and non-invasive gauging of both settled and unsettled liquids in reduced gravity.

The modal response of a liquid-filled tank to external acoustic excitation can be used to infer with high resolution the mass of contained liquid, the mass flow rate of liquids into and out of the tank, and changes in tank pressure. Both contained liquid mass and internal ullage pressure affect the modal response of the tank walls through fluid mass-loading of the tank walls and pressure-induced wall stiffening, respectively. Modal Propellant Gauging refers to the technology that exploits these shifts in modal frequencies to infer the mass of propellant in a tank. MPG is a non-invasive gauging technology that has demonstrated gauging resolutions of 1% for settled propellants and 2-3% for unsettled, sloshing propellants. Extensive parabolic flight testing of the MPG system on model tanks has been conducted to validate the technology in reduced gravity. MPG testing on a qualification tank for the Orion Program's European Service Module has also been conducted and is reported here. Finite element modeling of the Orion ESM ″upper" tank is discussed and compared with measurement data. Three computational approaches to mass determination, Peak Tracking, Point Sensor, and Spectral Density methods, are described here. Use cases are defined and analyzed in the context of the Orion ESM Qualification tank data, and an implementation scheme for continuous mass gauging on the Orion ESM is discussed.

Structural Variability from Noisy Tomographic Projections.

In cryo-electron microscopy, the three-dimensional (3D) electric potentials of an ensemble of molecules are projected along arbitrary viewing directions to yield noisy two-dimensional images. The volume maps representing these potentials typically exhibit a great deal of structural variability, which is described by their 3D covariance matrix. Typically, this covariance matrix is approximately low rank and can be used to cluster the volumes or estimate the intrinsic geometry of the conformation space. We formulate the estimation of this covariance matrix as a linear inverse problem, yielding a consistent least-squares estimator. For n images of size N-by-N pixels, we propose an algorithm for calculating this covariance estimator with computational complexity O ( n N 4 + κ N 6 log N ) , where the condition number κ is empirically in the range 10-200. Its efficiency relies on the observation that the normal equations are equivalent to a deconvolution problem in six dimensions. This is then solved by the conjugate gradient method with an appropriate circulant preconditioner. The result is the first computationally efficient algorithm for consistent estimation of the 3D covariance from noisy projections. It also compares favorably in runtime with respect to previously proposed nonconsistent estimators. Motivated by the recent success of eigenvalue shrinkage procedures for high-dimensional covariance matrix estimation, we incorporate a shrinkage procedure that improves accuracy at lower signal-to-noise ratios. We evaluate our methods on simulated datasets and achieve classification results comparable to state-of-the-art methods in shorter running time. We also present results on clustering volumes in an experimental dataset, illustrating the power of the proposed algorithm for practical determination of structural variability.

NETWORK-ENSEMBLE COMPARISONS WITH STOCHASTIC REWIRING AND VON NEUMANN ENTROPY.

Assessing whether a given network is typical or atypical for a random-network ensemble (i.e., network-ensemble comparison) has widespread applications ranging from null-model selection and hypothesis testing to clustering and classifying networks. We develop a framework for network-ensemble comparison by subjecting the network to stochastic rewiring. We study two rewiring processes-uniform and degree-preserved rewiring-which yield random-network ensembles that converge to the Erdos-Rényi and configuration-model ensembles, respectively. We study convergence through von Neumann entropy (VNE)-a network summary statistic measuring information content based on the spectra of a Laplacian matrix-and develop a perturbation analysis for the expected effect of rewiring on VNE. Our analysis yields an estimate for how many rewires are required for a given network to resemble a typical network from an ensemble, offering a computationally efficient quantity for network-ensemble comparison that does not require simulation of the corresponding rewiring process.

Optimal Population and Exhaustible Resource Constraints.

A large literature considers the optimal size and growth rate of the human population, trading off the utility value of additional people with the costs of a larger population. In this literature, an important parameter is the social weight placed on population size; a standard result is that a planner with a larger weight on population chooses larger population levels and growth rates. We demonstrate that this result is conditionally overturned when an exhaustible resource constraint is introduced: if the discount rate is small enough, the optimal population today decreases with the welfare weight on population size. That is, a more total-utilitarian social planner could prefer a smaller population today than a more average-utilitarian social planner. We also present a numerical illustration applied to the case of climate change, where we show that under plausible real-world parameter values, our result matters for the direction and magnitude of optimal population policy.

Discrete maximal regularity of time-stepping schemes for fractional evolution equations.

In this work, we establish the maximal [Formula: see text]-regularity for several time stepping schemes for a fractional evolution model, which involves a fractional derivative of order [Formula: see text], [Formula: see text], in time. These schemes include convolution quadratures generated by backward Euler method and second-order backward difference formula, the L1 scheme, explicit Euler method and a fractional variant of the Crank-Nicolson method. The main tools for the analysis include operator-valued Fourier multiplier theorem due to Weis (Math Ann 319:735-758, 2001. doi:10.1007/PL00004457) and its discrete analogue due to Blunck (Stud Math 146:157-176, 2001. doi:10.4064/sm146-2-3). These results generalize the corresponding results for parabolic problems.

Marriage and Health: Selection, Protection, and Assortative Mating.

Using data from the Panel Study of Income Dynamics (PSID) and the Medical Expenditure Panel Survey (MEPS), we analyze the health gap between married and unmarried individuals of working-age. Controlling for observables, we find a gap that peaks at 10 percentage points at ages 55-59 years. The marriage health gap is similar for men and women. If we allow for unobserved heterogeneity in innate health (permanent and age-dependent), potentially correlated with timing and likelihood of marriage, we find that the effect of marriage on health disappears below age 40 years, while about 5 percentage points difference between married and unmarried individuals remains at older ages (55-59 years). This indicates that the observed gap is mainly driven by selection into marriage at younger ages, but there might be a protective effect of marriage at older ages. Exploring the mechanisms behind this result, we find that better innate health is associated with a higher probability of marriage and a lower probability of divorce, and there is strong assortative mating among couples by innate health. We also find that married individuals are more likely to have a healthier behavior compared to unmarried ones. Finally, we find that health insurance is critical for the beneficial effect of marriage.

Spectral shift functions and Dirichlet-to-Neumann maps.

The spectral shift function of a pair of self-adjoint operators is expressed via an abstract operator-valued Titchmarsh-Weyl m-function. This general result is applied to different self-adjoint realizations of second-order elliptic partial differential operators on smooth domains with compact boundaries and Schrödinger operators with compactly supported potentials. In these applications the spectral shift function is determined in an explicit form with the help of (energy parameter dependent) Dirichlet-to-Neumann maps.

On Aharonov-Bohm Operators with Two Colliding Poles.

We consider Aharonov-Bohm operators with two poles and prove sharp asymptotics for simple eigenvalues as the poles collapse at an interior point out of nodal lines of the limit eigenfunction.