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.

The evolution and consequences of sex-specific reproductive variance.

Natural selection favors alleles that increase the number of offspring produced by their carriers. But in a world that is inherently uncertain within generations, selection also favors alleles that reduce the variance in the number of offspring produced. If previous studies have established this principle, they have largely ignored fundamental aspects of sexual reproduction and therefore how selection on sex-specific reproductive variance operates. To study the evolution and consequences of sex-specific reproductive variance, we present a population-genetic model of phenotypic evolution in a dioecious population that incorporates previously neglected components of reproductive variance. First, we derive the probability of fixation for mutations that affect male and/or female reproductive phenotypes under sex-specific selection. We find that even in the simplest scenarios, the direction of selection is altered when reproductive variance is taken into account. In particular, previously unaccounted for covariances between the reproductive outputs of different individuals are expected to play a significant role in determining the direction of selection. Then, the probability of fixation is used to develop a stochastic model of joint male and female phenotypic evolution. We find that sex-specific reproductive variance can be responsible for changes in the course of long-term evolution. Finally, the model is applied to an example of parental-care evolution. Overall, our model allows for the evolutionary analysis of social traits in finite and dioecious populations, where interactions can occur within and between sexes under a realistic scenario of reproduction.

Natural selection on fecundity variance in subdivided populations: kin selection meets bet hedging.

In a series of seminal articles in 1974, 1975, and 1977, J. H. Gillespie challenged the notion that the "fittest" individuals are those that produce on average the highest number of offspring. He showed that in small populations, the variance in fecundity can determine fitness as much as mean fecundity. One likely reason why Gillespie's concept of within-generation bet hedging has been largely ignored is the general consensus that natural populations are of large size. As a consequence, essentially no work has investigated the role of the fecundity variance on the evolutionary stable state of life-history strategies. While typically large, natural populations also tend to be subdivided in local demes connected by migration. Here, we integrate Gillespie's measure of selection for within-generation bet hedging into the inclusive fitness and game theoretic measure of selection for structured populations. The resulting framework demonstrates that selection against high variance in offspring number is a potent force in large, but structured populations. More generally, the results highlight that variance in offspring number will directly affect various life-history strategies, especially those involving kin interaction. The selective pressures on three key traits are directly investigated here, namely within-generation bet hedging, helping behaviors, and the evolutionary stable dispersal rate. The evolutionary dynamics of all three traits are markedly affected by variance in offspring number, although to a different extent and under different demographic conditions.

Analysis of experiments in square lattice with emphasis on variance components. i. Individual analysis

This paper focused on four alternatives of analysis of experiments in square lattice as far as the estimation of variance components and some genetic parameters are concerned: 1) intra-block analysis with adjusted treatment and blocks within unadjusted repetitions; 2) lattice analysis as complete randomized blocks; 3) intrablock analysis with unadjusted treatment and blocks within adjusted repetitions; 4) lattice analysis as complete randomized blocks, by utilizing the adjusted means of treatments, obtained from the analysis with recovery of interblock information, having as mean square of the error the mean effective variance of this same analysis with recovery of inter-block information. For the four alternatives of analysis, the estimators and estimates were obtained for the variance components and heritability coefficients. The classification of material was also studied. The present study suggests that for each experiment and depending of the objectives of the analysis, one should observe which alternative of analysis is preferable, mainly in cases where a negative estimate is obtained for the variance component due to effects of blocks within adjusted repetitions.

Analysis of variance of primary data on plant growth analysis

Plant growth analysis presents difficulties related to statistical comparison of growth rates, and the analysis of variance of primary data could guide the interpretation of results. The objective of this work was to evaluate the analysis of variance of data from distinct harvests of an experiment, focusing especially on the homogeneity of variances and the choice of an adequate ANOVA model. Data from five experiments covering different crops and growth conditions were used. From the total number of variables, 19% were originally homoscedastic, 60% became homoscedastic after logarithmic transformation, and 21% remained heteroscedastic after transformation. Data transformation did not affect the F test in one experiment, whereas in the other experiments transformation modified the F test usually reducing the number of significant effects. Even when transformation has not altered the F test, mean comparisons led to divergent interpretations. The mixed ANOVA model, considering harvest as a random effect, reduced the number of significant effects of every factor which had the F test modified by this model. Examples illustrated that analysis of variance of primary variables provides a tool for identifying significant differences in growth rates. The analysis of variance imposes restrictions to experimental design thereby eliminating some advantages of the functional growth analysis.

Exemplar-based interpolation of sparsely sampled images

A nonlocal variational formulation for interpolating a sparsel sampled image is introduced in this paper. The proposed variational formulation, originally motivated by image inpainting problems, encouragesthe transfer of information between similar image patches, following the paradigm of exemplar-based methods. Contrary to the classical inpaintingproblem, no complete patches are available from the sparse imagesamples, and the patch similarity criterion has to be redefined as here proposed. Initial experimental results with the proposed framework, at very low sampling densities, are very encouraging. We also explore somedepartures from the variational setting, showing a remarkable ability to recover textures at low sampling densities.

A(-infinity)-interpolation in the ball

We give a necessary and sufficient condition for a sequence [ak}k in the unit ball of C° to be interpolating for the class A~°° of holomorphic functions with polynomial growth. The condition, which goes along the lines of the ones given by Berenstein and Li for some weighted spaces of entire functions and by Amar for H°° functions in the ball, is given in terms of the derivatives of m > n functions F Fm e A~°° vanishing on {ak)k.

Software for interpolation of vegetative growth of yerba mate plants in 3D

The objective of this work was to build mock-ups of complete yerba mate plants in several stages of development, using the InterpolMate software, and to compute photosynthesis on the interpolated structure. The mock-ups of yerba-mate were first built in the VPlants software for three growth stages. Male and female plants grown in two contrasting environments (monoculture and forest understory) were considered. To model the dynamic 3D architecture of yerba-mate plants during the biennial growth interval between two subsequent prunings, data sets of branch development collected in 38 dates were used. The estimated values obtained from the mock-ups, including leaf photosynthesis and sexual dimorphism, are very close to those observed in the field. However, this similarity was limited to reconstructions that included growth units from original data sets. The modeling of growth dynamics enables the estimation of photosynthesis for the entire yerba mate plant, which is not easily measurable in the field. The InterpolMate software is efficient for building yerba mate mock-ups.

Increasing the efficiency of disparity computation by interpolation

Tässä diplomityössä tutkitaan dispariteettikartan laskennan tehostamista interpoloimalla. Kolmiomittausta käyttämällä stereokuvasta muodostetaan ensin harva dispariteettikartta, jonka jälkeen koko kuvan kattava dispariteettikartta muodostetaan interpoloimalla. Kolmiomittausta varten täytyy tietää samaa reaalimaailman pistettä vastaavat kuvapisteet molemmissa kameroissa. Huolimatta siitä, että vastaavien pisteiden hakualue voidaan pienentää kahdesta ulottuvuudesta yhteen ulottuvuuteen käyttämällä esimerkiksi epipolaarista geometriaa, on laskennallisesti tehokkaampaa määrittää osa dispariteetikartasta interpoloimalla, kuin etsiä vastaavia kuvapisteitä stereokuvista. Myöskin johtuen stereonäköjärjestelmän kameroiden välisestä etäisyydestä, kaikki kuvien pisteet eivät löydy toisesta kuvasta. Näin ollen on mahdotonta määrittää koko kuvan kattavaa dispariteettikartaa pelkästään vastaavista pisteistä. Vastaavien pisteiden etsimiseen tässä työssä käytetään dynaamista ohjelmointia sekä korrelaatiomenetelmää. Reaalimaailman pinnat ovat yleisesti ottaen jatkuvia, joten geometrisessä mielessä on perusteltua approksimoida kuvien esittämiä pintoja interpoloimalla. On myöskin olemassa tieteellistä näyttöä, jonkamukaan ihmisen stereonäkö interpoloi objektien pintoja.

Covariance Matrix Estimation and Mean-Variance Optimization in application to International Diversification

Tutkimus keskittyy kansainväliseen hajauttamiseen suomalaisen sijoittajan näkökulmasta. Tutkimuksen toinen tavoite on selvittää tehostavatko uudet kovarianssimatriisiestimaattorit minimivarianssiportfolion optimointiprosessia. Tavallisen otoskovarianssimatriisin lisäksi optimoinnissa käytetään kahta kutistusestimaattoria ja joustavaa monimuuttuja-GARCH(1,1)-mallia. Tutkimusaineisto koostuu Dow Jonesin toimialaindekseistä ja OMX-H:n portfolioindeksistä. Kansainvälinen hajautusstrategia on toteutettu käyttäen toimialalähestymistapaa ja portfoliota optimoidaan käyttäen kahtatoista komponenttia. Tutkimusaieisto kattaa vuodet 1996-2005 eli 120 kuukausittaista havaintoa. Muodostettujen portfolioiden suorituskykyä mitataan Sharpen indeksillä. Tutkimustulosten mukaan kansainvälisesti hajautettujen investointien ja kotimaisen portfolion riskikorjattujen tuottojen välillä ei ole tilastollisesti merkitsevää eroa. Myöskään uusien kovarianssimatriisiestimaattoreiden käytöstä ei synnytilastollisesti merkitsevää lisäarvoa verrattuna otoskovarianssimatrisiin perustuvaan portfolion optimointiin.

The influence of the quality of government institutions on entrepreneurial motivation: exploring the variance across countries

Despite the increasing understanding of the relationships between institutions and entrepreneurship, the influence of the quality of government institutions on entrepreneurship is less addressed. This paper focuses on this critical determinant of entrepreneurship in developing and developed countries. Drawing from institutional theory we hypothesize and empirically assess the role of the quality of institutions in entrepreneurial activity. We examine how the quality of government institutions influences the rate of necessity-based entrepreneurial activity across countries and over time by using a cross-sectional time-series approach on data from the Global Entrepreneurship Monitor (GEM) database covering the years 2001–2011. Our results suggest that higher economic development associated with better quality of institutions reduces the prevalence of necessity-based entrepreneurship. Our findings imply that developing countries must rationally organize their functions, and seek to remove unnecessary barriers, decrease political instability, and controls that hamper entrepreneurial activity

Ecological and physiological variance in T-cell mediated immune response in Cory's shearwaters

T-cell mediated immune response (CMI) hasbeen widely studied in relation to individual andfitness components in birds. However, few studieshave simultaneously examined individual and socialfactors and habitat-mediated variance in theimmunity of chicks and adults from the samepopulation and in the same breeding season. Weinvestigated ecological and physiological variancein CMI of male and female nestlings and adults in abreeding population of Cory's Shearwaters(Calonectrisdiomedea) in theMediterranean Sea. Explanatory variables includedindividual traits (body condition, carbon andnitrogen stable isotope ratios, plasma totalproteins, triglycerides, uric acid, osmolarity,β-hydroxy-butyrate, erythrocyte meancorpuscular diameter, hematocrit, andhemoglobin) and burrow traits(temperature, isolation, and physicalstructure). During incubation, immune responseof adult males was significantly greater than thatof females. Nestlings exhibited a lower immuneresponse than adults. Ecological and physiologicalfactors affecting immune response differed betweenadults and nestlings. General linear models showedthat immune response in adult males was positivelyassociated with burrow isolation, suggesting thatmales breeding at higher densities suffer immunesystem suppression. In contrast, immune response inchicks was positively associated with bodycondition and plasma triglyceride levels.Therefore, adult immune response appears to beassociated with social stress, whereas a trade-offbetween immune function and fasting capability mayexist for nestlings. Our results, and those fromprevious studies, provide support for anasymmetrical influence of ecological andphysiological factors on the health of differentage and sex groups within a population, and for theimportance of simultaneously considering individualand population characteristics in intraspecificstudies of immune response.