Optimal Response to a Demographic Shock

We examine the optimal policy response to an exogenously given demographic shock. Such a shock affects negatively the financing of retirement pensions, and we use optimal fiscal policy in order to determine the optimal strategy of the social security administration. Our approach provides specific policy responses in an environment that guarantees the financial sustainability of existing retirement pensions. At the same time, pensions will be financed in a way that by construction generates no welfare losses for any of the cohorts in our economy. In contrast to existing literature we endogenously determine optimal policies rather than exploring implications of exogenously given policies. Our results show that the optimal strategy is based in the following ingredients: elimination of compulsory retirement, a change in the structure of labor income taxation and a temporary increase in the level of government debt.

Multiple Hypothesis Testing in Pattern Discovery

The problem of multiple hypothesis testing arises when there are more than one hypothesis to be tested simultaneously for statistical significance. This is a very common situation in many data mining applications. For instance, assessing simultaneously the significance of all frequent itemsets of a single dataset entails a host of hypothesis, one for each itemset. A multiple hypothesis testing method is needed to control the number of false positives (Type I error). Our contribution in this paper is to extend the multiple hypothesis framework to be used with a generic data mining algorithm. We provide a method that provably controls the family-wise error rate (FWER, the probability of at least one false positive) in the strong sense. We evaluate the performance of our solution on both real and generated data. The results show that our method controls the FWER while maintaining the power of the test.Comment: 28 page

Moments in graphs

Let $G$ be a connected graph with vertex set $V$ and a {\em weight function} $\rho$ that assigns a nonnegative number to each of its vertices. Then, the {\em $\rho$-moment} of $G$ at vertex $u$ is defined to be M_G^{\rho}(u)=\sum_{v\in V} \rho(v)\dist (u,v) , where \dist(\cdot,\cdot) stands for the distance function. Adding up all these numbers, we obtain the {\em $\rho$-moment of $G$}: M_G^{\rho}=\sum_{u\in V}M_G^{\rho}(u)=1/2\sum_{u,v\in V}\dist(u,v)[\rho(u)+\rho(v)]. This parameter generalizes, or it is closely related to, some well-known graph invariants, such as the {\em Wiener index} $W(G)$, when $\rho(u)=1/2$ for every $u\in V$, and the {\em degree distance} $D'(G)$, obtained when $\rho(u)=\delta(u)$, the degree of vertex $u$. In this paper we derive some exact formulas for computing the $\rho$-moment of a graph obtained by a general operation called graft product, which can be seen as a generalization of the hierarchical product, in terms of the corresponding $\rho$-moments of its factors. As a consequence, we provide a method for obtaining nonisomorphic graphs with the same $\rho$-moment for every $\rho$ (and hence with equal mean distance, Wiener index, degree distance, etc.). In the case when the factors are trees and/or cycles, techniques from linear algebra allow us to give formulas for the degree distance of their product

Spectral Estimation of Conditional Random Graph Models for Large-Scale Network Data

Generative models for graphs have been typically committed to strong prior assumptions concerning the form of the modeled distributions. Moreover, the vast majority of currently available models are either only suitable for characterizing some particular network properties (such as degree distribution or clustering coefficient), or they are aimed at estimating joint probability distributions, which is often intractable in large-scale networks. In this paper, we first propose a novel network statistic, based on the Laplacian spectrum of graphs, which allows to dispense with any parametric assumption concerning the modeled network properties. Second, we use the defined statistic to develop the Fiedler random graph model, switching the focus from the estimation of joint probability distributions to a more tractable conditional estimation setting. After analyzing the dependence structure characterizing Fiedler random graphs, we evaluate them experimentally in edge prediction over several real-world networks, showing that they allow to reach a much higher prediction accuracy than various alternative statistical models.Comment: Appears in Proceedings of the Twenty-Eighth Conference on Uncertainty in Artificial Intelligence (UAI2012

La marca de 'vulgar' en el DRAE: de Autoridades a 1992

Tradicionalment els diccionaris han recollit una sèrie de comentaris referents a l'ús i, alhora, s'han mostrat reticents a admetre tot un conjunt de paraules considerades 'malsonants'. El present treball examina aquesta qüestió en el Diccionario de la Lengua Española, de la Real Academia, en dues vessants: el desenvolupament de la marca de vulgar des del Diccionario de Autoridades (1726-1739) fins a l'última edició (1992), i l'estat d'aquesta marca en l'actualitat. S'han d'assenyalar unes edicions fonamentals, en aquest desenvolupament, a més de Autoridades: l'edició de 1780, primera en un volum, on les marques es codifiquen per mitjà d'abreviatures; la de 1817, on s'elimina la marca de 'vulgar'; la de 1925, on es restitueix aquesta marca; i les últimes edicions, amb una més gran incorporació d'aquest lèxic, fins arribar a les 269 accepcions de l'edició de 1992. Les marques de 'vulgar' es poden caracteritzar en tres grups: aquelles que designen conceptes objecte de tabú, aquelles que pertanyen al lèxic de grups marginals i arcaismes vigents a zones rurals. El resultat és un conjunt heterogeni, producte de la reconeguda dificultat per establir un sistema de marques lexicogràficament acceptable. L'alternativa ha de ser una simplificació del sistema de marques i una més gran fonamentació sociolingüística.Traditionally dictionaries have recorded a series of comments on usage and at the same time have been unwilling to accept a whole range of words considered to be 'offensive'. This study undertakes a twofold examination of this question in the Diccionario de la Lengua Española of the Real Academia: the development of the label 'vulgar' from the Diccionario de Autoridades (1726-1739) to the latest edition (1992) and the present day state of such labelling. Autoridades aside, certain editions which are fundamental to this development should be mentioned: the first single volume edition in 1780, in which the labels are codified by means of abbreviations; the 1817 edition in which the 'vulgar' entries are excluded; the 1925 edition which reinstated this entry type; and the more recent editions which include a wider range of this type of lexis, accepting up to 269 meanings in the 1992 edition. Words labelled as 'vulgar' can be classified in three groups: those that refer to taboo concepts, those that belong to the lexis of marginal groups, and archaisms that still prevail in rural areas. The result is a heterogeneous block, a product of the recognised difficulty to establish a labelling system that is lexicographically acceptable. The alternative must be a simplification of the labelling system and a greater sociolinguistics base

Gravity in the Randall-Sundrum Brane World

We discuss the weak gravitational field created by isolated matter sources in the Randall-Sundrum brane-world. In the case of two branes of opposite tension, linearized Brans-Dicke (BD) gravity is recovered on either wall, with different BD parameters. On the wall with positive tension the BD parameter is larger than 3000 provided that the separation between walls is larger than 4 times the AdS radius. For the wall of negative tension, the BD parameter is always negative but greater than -3/2. In either case, shadow matter from the other wall gravitates upon us. For equal Newtonian mass, light deflection from shadow matter is 25 % weaker than from ordinary matter. Hence, the effective mass of a clustered object containing shadow dark matter would be underestimated if naively measured through its lensing effect. For the case of a single wall of positive tension, Einstein gravity is recovered on the wall to leading order, and if the source is stationary the field stays localized near the wall. We calculate the leading Kaluza-Klein corrections to the linearized gravitational field of a non-relativistic spherical object and find that the metric is different from the Schwarzschild solution at large distances. We believe that our linearized solution corresponds to the field far from the horizon after gravitational collapse of matter on the brane.Comment: 8 pages, 1 figure. Replaced with revised version to be published in Phys. Rev. Lett. Some comments adde

Solutions to the cosmological constant problems

We critically review several recent approaches to solving the two cosmological constant problems. The "old" problem is the discrepancy between the observed value of $\Lambda$ and the large values suggested by particle physics models. The second problem is the "time coincidence" between the epoch of galaxy formation $t_G$ and the epoch of $\Lambda$-domination t_\L. It is conceivable that the "old" problem can be resolved by fundamental physics alone, but we argue that in order to explain the "time coincidence" we must account for anthropic selection effects. Our main focus here is on the discrete-$\Lambda$ models in which $\Lambda$ can change through nucleation of branes. We consider the cosmology of this type of models in the context of inflation and discuss the observational constraints on the model parameters. The issue of multiple brane nucleation raised by Feng {\it et. al.} is discussed in some detail. We also review continuous-\L models in which the role of the cosmological constant is played by a slowly varying potential of a scalar field. We find that both continuous and discrete models can in principle solve both cosmological constant problems, although the required values of the parameters do not appear very natural. M-theory-motivated brane models, in which the brane tension is determined by the brane coupling to the four-form field, do not seem to be viable, except perhaps in a very tight corner of the parameter space. Finally, we point out that the time coincidence can also be explained in models where $\Lambda$ is fixed, but the primordial density contrast $Q=\delta\rho/\rho$ is treated as a random variable.Comment: 30 pages, 3 figures, two notes adde

On Almost Distance-Regular Graphs

2010 Mathematics Subject Classification: 05E30, 05C50;distance-regular graph;walk-regular graph;eigenvalues;predistance polynomial