Generating trees for permutations avoiding generalized patterns

We construct generating trees with with one, two, and three labels for some classes of permutations avoiding generalized patterns of length 3 and 4. These trees are built by adding at each level an entry to the right end of the permutation, which allows us to incorporate the adjacency condition about some entries in an occurrence of a generalized pattern. We use these trees to find functional equations for the generating functions enumerating these classes of permutations with respect to different parameters. In several cases we solve them using the kernel method and some ideas of Bousquet-Mélou [2]. We obtain refinements of known enumerative results and find new ones.

Generalized factor models: a bayesian approach

There is recent interest in the generalization of classical factor models in which the idiosyncratic factors are assumed to be orthogonal and there are identification restrictions on cross-sectional and time dimensions. In this study, we describe and implement a Bayesian approach to generalized factor models. A flexible framework is developed to determine the variations attributed to common and idiosyncratic factors. We also propose a unique methodology to select the (generalized) factor model that best fits a given set of data. Applying the proposed methodology to the simulated data and the foreign exchange rate data, we provide a comparative analysis between the classical and generalized factor models. We find that when there is a shift from classical to generalized, there are significant changes in the estimates of the structures of the covariance and correlation matrices while there are less dramatic changes in the estimates of the factor loadings and the variation attributed to common factors.

Generalized multiresolution analyses with given multiplicity functions

Generalized multiresolution analyses are increasing sequences of subspaces of a Hilbert space H that fail to be multiresolution analyses in the sense of wavelet theory because the core subspace does not have an orthonormal basis generated by a fixed scaling function. Previous authors have studied a multiplicity function m which, loosely speaking, measures the failure of the GMRA to be an MRA. When the Hilbert space H is L2(Rn), the possible multiplicity functions have been characterized by Baggett and Merrill. Here we start with a function m satisfying a consistency condition which is known to be necessary, and build a GMRA in an abstract Hilbert space with multiplicity function m.

Labor supply response to international migration and remittances in the Republic of Haiti

The Republic of Haiti is the prime international remittances recipient country in the Latin American and Caribbean (LAC) region relative to its gross domestic product (GDP). The downside of this observation may be that this country is also the first exporter of skilled workers in the world by population size. The present research uses a zero-altered negative binomial (with logit inflation) to model households' international migration decision process, and endogenous regressors' Amemiya Generalized Least Squares method (instrumental variable Tobit, IV-Tobit) to account for selectivity and endogeneity issues in assessing the impact of remittances on labor market outcomes. Results are in line with what has been found so far in this literature in terms of a decline of labor supply in the presence of remittances. However, the impact of international remittances does not seem to be important in determining recipient households' labor participation behavior, particularly for women.

The effects of the generalized use of iodized salt on occupational patterns in Switzerland.

This paper examines the impact of salt iodization in Switzerland in the 1920s and 1930s on occupational patterns of cohorts born after the intervention. The generalized use of iodized salt successfully combatted iodine deficiency disorders, which were previously endemic in some areas of Switzerland. The most important effect of universal prophylaxis by means of iodized salt was the eradication of mental retardation inflicted in utero by lack of iodine. This paper looks for evidence of increased cognitive ability of those treated with iodine in utero by examining the occupational choice and characteristics of occupations chosen by cohorts born after the intervention. By exploiting variation in pre-existing conditions and in the timing of the intervention, I find that cohorts born in previously highly-deficient areas after the introduction of iodized salt self-selected into higher-paying occupations. I also find that the characteristics of occupations in those areas changed, and that cohorts born after the intervention engaged to a higher degree in occupations with higher cognitive demands, whereas they opted out of physical-labor-intensive occupations.

Nowcasting Scottish GDP Growth

The delays in the release of macroeconomic variables such as GDP mean that policymakers do not know their current values. Thus, nowcasts, which are estimates of current values of macroeconomic variables, are becoming increasingly popular. This paper takes up the challenge of nowcasting Scottish GDP growth. Nowcasting in Scotland, currently a government office region within the United Kingdom, is complicated due to data limitations. For instance, key nowcast predictors such as industrial production are unavailable. Accordingly, we use data on some non-traditional variables and investigate whether UK aggregates can help nowcast Scottish GDP growth. Such data limitations are shared by many other sub-national regions, so we hope this paper can provide lessons for other regions interested in developing nowcasting models.

Nondictatorial Arrovian Social Welfare Functions: An Integer Programming Approach

In the line opened by Kalai and Muller (1997), we explore new conditions on prefernce domains which make it possible to avoid Arrow's impossibility result. In our main theorem, we provide a complete characterization of the domains admitting nondictorial Arrovian social welfare functions with ties (i.e. including indifference in the range) by introducing a notion of strict decomposability. In the proof, we use integer programming tools, following an approach first applied to social choice theory by Sethuraman, Teo and Vohra ((2003), (2006)). In order to obtain a representation of Arrovian social welfare functions whose range can include indifference, we generalize Sethuraman et al.'s work and specify integer programs in which variables are allowed to assume values in the set {0, 1/2, 1}: indeed, we show that, there exists a one-to-one correspondence between solutions of an integer program defined on this set and the set of all Arrovian social welfare functions - without restrictions on the range.

Integer Programming on Domains Containing Inseparable Ordered Paris

Using the integer programming approach introduced by Sethuraman, Teo, and Vohra (2003), we extend the analysis of the preference domains containing an inseparable ordered pair, initiated by Kalai and Ritz (1978). We show that these domains admit not only Arrovian social welfare functions \without ties," but also Arrovian social welfare functions \with ties," since they satisfy the strictly decomposability condition introduced by Busetto, Codognato, and Tonin (2012). Moreover, we go further in the comparison between Kalai and Ritz (1978)'s inseparability and Arrow (1963)'s single-peak restrictions, showing that the former condition is more \respectable," in the sense of Muller and Satterthwaite (1985).

Aging and motor programming: differential effects according to the selection of action

There are controversial reports about the effect of aging on movement preparation, and it is unclear to which extent cognitive and/or motor related cerebral processes may be affected. This study examines the age effects on electro-cortical oscillatory patterns during various motor programming tasks, in order to assess potential differences according to the mode of action selection. Twenty elderly (EP, 60-84 years) and 20 young (YP, 20-29 years) participants with normal cognition underwent 3 pre-cued response tasks (S1-S2 paradigm). S1 carried either complete information on response side (Full; stimulus-driven motor preparation), no information (None; general motor alertness), or required free response side selection (Free; internally-driven motor preparation). Electroencephalogram (EEG) was recorded using 64 surface electrodes. Alpha (8-12 Hz) desynchronization (ERD)/synchronization (ERS) and motor-related amplitude asymmetries (MRAA) were analyzed during the S1-S2 interval. Reaction times (RTs) to S2 were slower in EP than YP, and in None than in the other 2 tasks. There was an Age x Task interaction due to increased RTs in Free compared to Full in EP only. Central bilateral and midline activation (alpha ERD) was smaller in EP than YP in None. In Full just before S2, readiness to move was reflected by posterior midline inhibition (alpha ERS) in both groups. In Free, such inhibition was present only in YP. Moreover, MRAA showed motor activity lateralization in both groups in Full, but only in YP in Free. The results indicate reduced recruitment of motor regions for motor alertness in the elderly. They further show less efficient cerebral processes subtending free selection of movement in elders, suggesting reduced capacity for internally-driven action with age.

A numerical algorithm for finding solutions of a generalized Nash equilibrium problem

A family of nonempty closed convex sets is built by using the data of the Generalized Nash equilibrium problem (GNEP). The sets are selected iteratively such that the intersection of the selected sets contains solutions of the GNEP. The algorithm introduced by Iusem-Sosa (2003) is adapted to obtain solutions of the GNEP. Finally some numerical experiments are given to illustrate the numerical behavior of the algorithm.

The Multiple-partners assignment game with heterogeneous sales and multi-unit demands: competitive equilibria

A multiple-partners assignment game with heterogeneous sales and multiunit demands consists of a set of sellers that own a given number of indivisible units of (potentially many different) goods and a set of buyers who value those units and want to buy at most an exogenously fixed number of units. We define a competitive equilibrium for this generalized assignment game and prove its existence by using only linear programming. In particular, we show how to compute equilibrium price vectors from the solutions of the dual linear program associated to the primal linear program defined to find optimal assignments. Using only linear programming tools, we also show (i) that the set of competitive equilibria (pairs of price vectors and assignments) has a Cartesian product structure: each equilibrium price vector is part of a competitive equilibrium with all optimal assignments, and vice versa; (ii) that the set of (restricted) equilibrium price vectors has a natural lattice structure; and (iii) how this structure is translated into the set of agents' utilities that are attainable at equilibrium.

On Cooperative solutions of a generalized assignment game: limit theorems to the set of competitive equilibria

We study two cooperative solutions of a market with indivisible goods modeled as a generalized assignment game: Set-wise stability and Core. We first establish that the Set-wise stable set is contained in the Core and it contains the non-empty set of competitive equilibrium payoffs. We then state and prove three limit results for replicated markets. First, the sequence of Cores of replicated markets converges to the set of competitive equilibrium payoffs when the number of replicas tends to infinity. Second, the Set-wise stable set of a two-fold replicated market already coincides with the set of competitive equilibrium payoffs. Third, for any number of replicas there is a market with a Core payoff that is not a competitive equilibrium payoff.

Generalized inductive limits of quasidiagonal C*-algebras

If A is a unital quasidiagonal C*-algebra, we construct a generalized inductive limit BA which is simple, unital and inherits many structural properties from A. If A is the unitization of a non-simple purely infinite algebra (e.g., the cone over a Cuntz algebra), then BA is tracially AF which, among other things, lends support to a conjecture of Toms.

Generalized descriptive set theory and classification theory

Descriptive set theory is mainly concerned with studying subsets of the space of all countable binary sequences. In this paper we study the generalization where countable is replaced by uncountable. We explore properties of generalized Baire and Cantor spaces, equivalence relations and their Borel reducibility. The study shows that the descriptive set theory looks very different in this generalized setting compared to the classical, countable case. We also draw the connection between the stability theoretic complexity of first-order theories and the descriptive set theoretic complexity of their isomorphism relations. Our results suggest that Borel reducibility on uncountable structures is a model theoretically natural way to compare the complexity of isomorphism relations.