The mean-variance model from the inverse of the variance-covariance matrix

En este artículo, a partir de la inversa de la matriz de varianzas y covarianzas se obtiene el modelo Esperanza-Varianza de Markowitz siguiendo un camino más corto y matemáticamente riguroso. También se obtiene la ecuación de equilibrio del CAPM de Sharpe.

Mean first-passage time of continuous non-Markovian processes driven by colored noise

An equation for mean first-passage times of non-Markovian processes driven by colored noise is derived through an appropriate backward integro-differential equation. The equation is solved in a Bourret-like approximation. In a weak-noise bistable situation, non-Markovian effects are taken into account by an effective diffusion coefficient. In this situation, our results compare satisfactorily with other approaches and experimental data.

A comparison of mean phase difference and generalized least squares for analyzing single-case data

The present study focuses on single-case data analysis and specifically on two procedures for quantifying differences between baseline and treatment measurements The first technique tested is based on generalized least squares regression analysis and is compared to a proposed non-regression technique, which allows obtaining similar information. The comparison is carried out in the context of generated data representing a variety of patterns (i.e., independent measurements, different serial dependence underlying processes, constant or phase-specific autocorrelation and data variability, different types of trend, and slope and level change). The results suggest that the two techniques perform adequately for a wide range of conditions and researchers can use both of them with certain guarantees. The regression-based procedure offers more efficient estimates, whereas the proposed non-regression procedure is more sensitive to intervention effects. Considering current and previous findings, some tentative recommendations are offered to applied researchers in order to help choosing among the plurality of single-case data analysis techniques.

Frontshear and backshear instabilities of the mean longshore current

An analytical model based on Bowen and Holman [1989] is used to prove the existence of instabilities due to the presence of a second extremum of the background vorticity at the front side of the longshore current. The growth rate of the so-called frontshear waves depends primarily upon the frontshear but also upon the backshear and the maximum and the width of the current. Depending on the values of these parameters, either the frontshear or the backshear instabilities may dominate. Both types of waves have a cross-shore extension of the order of the width of the current, but the frontshear modes are localized closer to the coast than are the backshear modes. Moreover, under certain conditions both unstable waves have similar growth rates with close wave numbers and angular frequencies, leading to the possibility of having modulated shear waves in the alongshore direction. Numerical analysis performed on realistic current profiles confirm the behavior anticipated by the analytical model. The theory has been applied to a current profile fitted to data measured during the 1980 Nearshore Sediment Transport Studies experiment at Leadbetter Beach that has an extremum of background vorticity at the front side of the current. In this case and in agreement with field observations, the model predicts instability, whereas the theory based only on backshear instability fai led to do so.

Generation of symmetric periodic orbits by a heteroclinic loop formed by two singular points and their invariant manifolds of dimension 1 and 2 in R3

In this paper we will find a continuous of periodic orbits passing near infinity for a class of polynomial vector fields in R3. We consider polynomial vector fields that are invariant under a symmetry with respect to a plane and that possess a “generalized heteroclinic loop” formed by two singular points e+ and e− at infinity and their invariant manifolds � and . � is an invariant manifold of dimension 1 formed by an orbit going from e− to e+, � is contained in R3 and is transversal to . is an invariant manifold of dimension 2 at infinity. In fact, is the 2–dimensional sphere at infinity in the Poincar´e compactification minus the singular points e+ and e−. The main tool for proving the existence of such periodic orbits is the construction of a Poincar´e map along the generalized heteroclinic loop together with the symmetry with respect to .

Symmetric periodic orbits near heteroclinic loops at infinity for a class of polynomial vector fields

For polynomial vector fields in R3, in general, it is very difficult to detect the existence of an open set of periodic orbits in their phase portraits. Here, we characterize a class of polynomial vector fields of arbitrary even degree having an open set of periodic orbits. The main two tools for proving this result are, first, the existence in the phase portrait of a symmetry with respect to a plane and, second, the existence of two symmetric heteroclinic loops.

Symmetric periodic orbits near a heteroclinic loop in R3 formed by two singular points, a semistable periodic orbit and their invariant manifolds

In this paper we consider C1 vector fields X in R3 having a “generalized heteroclinic loop” L which is topologically homeomorphic to the union of a 2–dimensional sphere S2 and a diameter connecting the north with the south pole. The north pole is an attractor on S2 and a repeller on . The equator of the sphere is a periodic orbit unstable in the north hemisphere and stable in the south one. The full space is topologically homeomorphic to the closed ball having as boundary the sphere S2. We also assume that the flow of X is invariant under a topological straight line symmetry on the equator plane of the ball. For each n ∈ N, by means of a convenient Poincar´e map, we prove the existence of infinitely many symmetric periodic orbits of X near L that gives n turns around L in a period. We also exhibit a class of polynomial vector fields of degree 4 in R3 satisfying this dynamics.

Symmetric periodic orbits near a heteroclinic loop formed by two singular points and their invariant manifolds of dimension 1 and 2

In this paper we consider vector fields in R3 that are invariant under a suitable symmetry and that posses a “generalized heteroclinic loop” L formed by two singular points (e+ and e −) and their invariant manifolds: one of dimension 2 (a sphere minus the points e+ and e −) and one of dimension 1 (the open diameter of the sphere having endpoints e+ and e −). In particular, we analyze the dynamics of the vector field near the heteroclinic loop L by means of a convenient Poincar´e map, and we prove the existence of infinitely many symmetric periodic orbits near L. We also study two families of vector fields satisfying this dynamics. The first one is a class of quadratic polynomial vector fields in R3, and the second one is the charged rhomboidal four body problem.

The underestimation of compliance to direct help requests explained by adaptive sampling

Helping behavior is any intentional behavior that benefits another living being or group (Hogg & Vaughan, 2010). People tend to underestimate the probability that others will comply with their direct requests for help (Flynn & Lake, 2008). This implies that when they need help, they will assess the probability of getting it (De Paulo, 1982, cited in Flynn & Lake, 2008) and then they will tend to estimate one that is actually lower than the real chance, so they may not even consider worth asking for it. Existing explanations for this phenomenon attribute it to a mistaken cost computation by the help seeker, who will emphasize the instrumental cost of “saying yes”, ignoring that the potential helper also needs to take into account the social cost of saying “no”. And the truth is that, especially in face-to-face interactions, the discomfort caused by refusing to help can be very high. In short, help seekers tend to fail to realize that it might be more costly to refuse to comply with a help request rather than accepting. A similar effect has been observed when estimating trustworthiness of people. Fetchenhauer and Dunning (2010) showed that people also tend to underestimate it. This bias is reduced when, instead of asymmetric feedback (getting feedback only when deciding to trust the other person), symmetric feedback (always given) was provided. This cause could as well be applicable to help seeking as people only receive feedback when they actually make their request but not otherwise. Fazio, Shook, and Eiser (2004) studied something that could be reinforcing these outcomes: Learning asymmetries. By means of a computer game called BeanFest, they showed that people learn better about negatively valenced objects (beans in this case) than about positively valenced ones. This learning asymmetry esteemed from “information gain being contingent on approach behavior” (p. 293), which could be identified with what Fetchenhauer and Dunning mention as ‘asymmetric feedback’, and hence also with help requests. Fazio et al. also found a generalization asymmetry in favor of negative attitudes versus positive ones. They attributed it to a negativity bias that “weights resemblance to a known negative more heavily than resemblance to a positive” (p. 300). Applied to help seeking scenarios, this would mean that when facing an unknown situation, people would tend to generalize and infer that is more likely that they get a negative rather than a positive outcome from it, so, along with what it was said before, people will be more inclined to think that they will get a “no” when requesting help. Denrell and Le Mens (2011) present a different perspective when trying to explain judgment biases in general. They deviate from the classical inappropriate information processing (depicted among other by Fiske & Taylor, 2007, and Tversky & Kahneman, 1974) and explain this in terms of ‘adaptive sampling’. Adaptive sampling is a sampling mechanism in which the selection of sample items is conditioned by the values of the variable of interest previously observed (Thompson, 2011). Sampling adaptively allows individuals to safeguard themselves from experiences they went through once and turned out to lay negative outcomes. However, it also prevents them from giving a second chance to those experiences to get an updated outcome that could maybe turn into a positive one, a more positive one, or just one that regresses to the mean, whatever direction that implies. That, as Denrell and Le Mens (2011) explained, makes sense: If you go to a restaurant, and you did not like the food, you do not choose that restaurant again. This is what we think could be happening when asking for help: When we get a “no”, we stop asking. And here, we want to provide a complementary explanation for the underestimation of the probability that others comply with our direct help requests based on adaptive sampling. First, we will develop and explain a model that represents the theory. Later on, we will test it empirically by means of experiments, and will elaborate on the analysis of its results.

Synchronization of symmetric chaotic systems

This paper contains a study of the synchronization by homogeneous nonlinear driving of systems that are symmetric in phase space. The main consequence of this symmetry is the ability of the response to synchronize in more than just one way to the driving systems. These different forms of synchronization are to be understood as generalized synchronization states in which the motions of drive and response are in complete correlation, but the phase space distance between them does not converge to zero. In this case the synchronization phenomenon becomes enriched because there is multistability. As a consequence, there appear multiple basins of attraction and special responses to external noise. It is shown, by means of a computer simulation of various nonlinear systems, that: (i) the decay to the generalized synchronization states is exponential, (ii) the basins of attraction are symmetric, usually complicated, frequently fractal, and robust under the changes in the parameters, and (iii) the effect of external noise is to weaken the synchronization, and in some cases to produce jumps between the various synchronization states available

Warranties used as a mean to promote commercial FOSS

From a business standpoint, this paper describes the point of view on the question of warranties of a FOSS editor doing business in a risk-averse market segment. It is based on 15-years experience of AdaCore in the safety-critical embedded industry. However, it is not only the point of view of a provider, as it also aims at demonstrating that the interests of providers and users are aligned in this area. From a legal point of view, the enforceability of these warranties will be partly covered, as well as the articulation between the license and the warranties on one hand, and the articulation between the license and the other contracts that can be created in a business relationship on the other hand.

From symmetric glycerol derivatives to dissymmetric chlorohydrins

The anticipated worldwide increase in biodiesel production will result in an accumulation of glycerol for which there are insufficient conventional uses. The surplus of this by-product has increased rapidly during the last decade, prompting a search for new glycerol applications. We describe here the synthesis of dissymmetric chlorohydrin esters from symmetric 1,3-dichloro-2-propyl esters obtained from glycerol. We studied the influence of two solvents: 1,4-dioxane and 1-butanol and two bases: sodium carbonate and 1-butylimidazole, on the synthesis of dissymmetric chlorohydrin esters. In addition, we studied the influence of other bases (potassium and lithium carbonates) in the reaction using 1,4-dioxane as the solvent. The highest yield was obtained using 1,4-dioxane and sodium carbonate.

Giant monopole energies from a constrained relativistic mean-field approach

Background:Average energies of nuclear collective modes may be efficiently and accurately computed using a nonrelativistic constrained approach without reliance on a random phase approximation (RPA). Purpose: To extend the constrained approach to the relativistic domain and to establish its impact on the calibration of energy density functionals. Methods: Relativistic RPA calculations of the giant monopole resonance (GMR) are compared against the predictions of the corresponding constrained approach using two accurately calibrated energy density functionals. Results: We find excellent agreement at the 2% level or better between the predictions of the relativistic RPA and the corresponding constrained approach for magic (or semimagic) nuclei ranging from 16 O to 208 Pb. Conclusions: An efficient and accurate method is proposed for incorporating nuclear collective excitations into the calibration of future energy density functionals.

Symmetric or asymmetric gasoline prices? A meta-analysis approach

The analysis of price asymmetries in the gasoline market is one of the most studied in the energy economics literature. Nevertheless, the great variability of results makes it very difficult to extract conclusive results on the existence or not of asymmetries. This paper shows through a meta-analysis approach how the industry segment analysed, the quality and quantity of data, the estimator and the model used may explain this heterogeneity of results.