EERTREE: An Efficient Data Structure for Processing Palindromes in Strings

We propose a new linear-size data structure which provides a fast access to all palindromic substrings of a string or a set of strings. This structure inherits some ideas from the construction of both the suffix trie and suffix tree. Using this structure, we present simple and efficient solutions for a number of problems involving palindromes.Comment: 21 pages, 2 figures. Accepted to IWOCA 201

Intergenerational equity and the discount rate for cost-benefit analysis

For two independent principles of intergenerational equity, the implied discount rate equals the growth rate of real per-capita income, say 2%, thus falling right into the range suggested by the U.S. Offce of Management and Budget. To prove this, we develop a simple tool to evaluate small policy changes affecting several generations, by reducing the dynamic problem to a static one. A necessary condition is time-invariance, which is satisfied by any common solution concept in an overlapping generations model with exogenous growth. This tool is applied to derive the discount rate for cost-benefit analysis under two different utilitarian welfare functions: classical and relative. It is only with relative utilitarianism that the discount rate is well-defined for a heterogeneous society, is corroborated by an independent principle equating values of hugrowth rate of real per-capita income.social welfare function, social welfare functional, overlapping generations, exogenous growth, policy reform, intergenerational equity, intergenerational fairness, cost-benefit analysis, discount rate, social discount rate, utilitarianism, relative utilitarianism, welfarism.

INTERGENERATIONAL EQUITY AND THE DISCOUNT RATE FOR POLICY ANALYSIS

For two independent principles of intergenerational equity, the implied discount rate equals the growth rate of real per capita income, say, 2%, thus falling right into the range suggested by the U.S. Office of Management and Budget. To prove this, we develop a simple tool to evaluate small policy changes affecting several generations, by reducing the dynamic problem to a static one. A necessary condition is time invariance, which is satisfied by any common solution concept in an overlapping-generations model with exogenous growth. This tool is applied to derive the discount rate for cost-benefit analysis under two different utilitarian welfare functions: classical and relative. It is only with relative utilitarianism, and assuming time-invariance of the set of alternatives (policies), that the discount rate is well defined for a heterogeneous society at a balanced growth equilibrium, is corroborated by an independent principle equating values of human lives, and equals the growth rate of real per-capita income.Overlapping Generations, Policy Reform, Intergenerational Equity, Cost-Benefit Analysis, Discount Rate, Utilitarianism

Separate control over the local and the asymptotic behaviour in L_p spaces

We introduce 2 parameter variants L_{p,q} of the Lebesgue spaces, to gain separate control on the asymptotic behaviour (p) and the local behaviour (q). Thus they behave with respect to p like the spaces ell_p and with respect to q like the spaces L_q on a probability space. Convolution behaves very well on those spaces.

Intergenerational equity and the discount rate for cost-benefit analysis

For two independent principles of intergenerational equity, the implied discount rate equals the growth rate of real per-capital income, say 2%, thus falling right into the range suggested by the U.S. Office of Management and Budget. To prove this, we develop a simple tool to evaluate small policy changes affecting several generations, by reducing the dynamic problem to a static one. A necessary condition is time-invariance, which is statisfied by any common solution concept in an overlapping generations model with exogenous growth. This tool is applied to derive the discount rate for cost-benefit analysis under two different utilitarian welfare functions : classical and relative. It is only with relative utilitarianism that the discount rate is well-defined for a heterogeneous society, is corroborated by an independent principle equation values of human lives, and equals the growth rate of real per-capital income.Social welfare function; social welfare functional; overlapping generations; exogenous growth; policy reform; intergenerational equity; intergenerational fairness; cost-benefit analysis; discount rate; social discount rate; utilitarianism; relative utilitarianism; welfarism

BANACH FAMILIES AND THE IMPLICIT FUNCTION THEOREM

We generalise the classical implicit function theorem (IFT) for a family of Banach spaces, with the resulting implicit function having derivatives that are locally Lipschitz to very strong operator norms.Banach spaces, Implicit Function Theorem

Causes and Consequences of Risk Aversion in Middle Adulthood

I analyze how risk aversion may affect decision-making over time, what effects risk aversion may have on decisions, and whether one’s level of risk aversion varies over time. I find that risk preferences correlate with certain maternal factors, income, depression, and ethnicity. Risk aversion correlates with financial and health decisions

Necessary and Sufficient Conditions for Determinacy of Asymptotically Stationary Equilibria in Olg Models

We propose a criterion for determining whether a local policy analysis can be made in a given equilibrium in an overlapping generations model. The criterion can be applied to models with infinite past and future as well as those with a truncated past. The equilibrium is not necessarily a steady state; for example, demographic and type composition of the population or individuals’ endowments can change over time. However, asymptotically, the equilibrium should be stationary. The two limiting stationary paths at either end of the timeline do not have to be the same. If they are, conditions for local uniqueness are far more stringent for an economy with a truncated past as compared to its counterpart with an infinite past. In addition, we illustrate our main result using a text-book model with a single physical good, a two-period life-cycle and a single type of consumer. In this model we show how to calculate a response to a policy change using the implicit function theorem

Palindromic k-Factorization in Pure Linear Time

Given a string s of length n over a general alphabet and an integer k, the problem is to decide whether s is a concatenation of k nonempty palindromes. Two previously known solutions for this problem work in time O(kn) and O(nlog n) respectively. Here we settle the complexity of this problem in the word-RAM model, presenting an O(n)-time online deciding algorithm. The algorithm simultaneously finds the minimum odd number of factors and the minimum even number of factors in a factorization of a string into nonempty palindromes. We also demonstrate how to get an explicit factorization of s into k palindromes with an O(n)-time offline postprocessing