Segmental dynamics in entangled linear polymer melts

We present molecular dynamics (MD) and slip-springs model simulations of the chain segmental dynamics in entangled linear polymer melts. The time-dependent behavior of the segmental orientation autocorrelation functions and mean-square segmental displacements are analyzed for both flexible and semiflexible chains, with particular attention paid to the scaling relations among these dynamic quantities. Effective combination of the two simulation methods at different coarse-graining levels allows us to explore the chain dynamics for chain lengths ranging from Z ≈ 2 to 90 entanglements. For a given chain length of Z ≈ 15, the time scales accessed span for more than 10 decades, covering all of the interesting relaxation regimes. The obtained time dependence of the monomer mean square displacements, g1(t), is in good agreement with the tube theory predictions. Results on the first- and second-order segmental orientation autocorrelation functions, C1(t) and C2(t), demonstrate a clear power law relationship of C2(t) C1(t)m with m = 3, 2, and 1 in the initial, free Rouse, and entangled (constrained Rouse) regimes, respectively. The return-to-origin hypothesis, which leads to inverse proportionality between the segmental orientation autocorrelation functions and g1(t) in the entangled regime, is convincingly verified by the simulation result of C1(t) g1(t)−1 t–1/4 in the constrained Rouse regime, where for well-entangled chains both C1(t) and g1(t) are rather insensitive to the constraint release effects. However, the second-order correlation function, C2(t), shows much stronger sensitivity to the constraint release effects and experiences a protracted crossover from the free Rouse to entangled regime. This crossover region extends for at least one decade in time longer than that of C1(t). The predicted time scaling behavior of C2(t) t–1/4 is observed in slip-springs simulations only at chain length of 90 entanglements, whereas shorter chains show higher scaling exponents. The reported simulation work can be applied to understand the observations of the NMR experiments.

The structure of the optimal income tax in the quasi-linear model

Existing numerical characterizations of the optimal income tax have been based on a limited number of model specifications. As a result, they do not reveal which properties are general. We determine the optimal tax in the quasi-linear model under weaker assumptions than have previously been used; in particular, we remove the assumption of a lower bound on the utility of zero consumption and the need to permit negative labor incomes. A Monte Carlo analysis is then conducted in which economies are selected at random and the optimal tax function constructed. The results show that in a significant proportion of economies the marginal tax rate rises at low skills and falls at high. The average tax rate is equally likely to rise or fall with skill at low skill levels, rises in the majority of cases in the centre of the skill range, and falls at high skills. These results are consistent across all the specifications we test. We then extend the analysis to show that these results also hold for Cobb-Douglas utility.

'Quasi'-norm of an arithmetical convolution operator and the order of the Riemann zeta function

In this paper we study Dirichlet convolution with a given arithmetical function f as a linear mapping 'f that sends a sequence (an) to (bn) where bn = Pdjn f(d)an=d. We investigate when this is a bounded operator on l2 and ¯nd the operator norm. Of particular interest is the case f(n) = n¡® for its connection to the Riemann zeta function on the line 1, 'f is bounded with k'f k = ³(®). For the unbounded case, we show that 'f : M2 ! M2 where M2 is the subset of l2 of multiplicative sequences, for many f 2 M2. Consequently, we study the `quasi'-norm sup kak = T a 2M2 k'fak kak for large T, which measures the `size' of 'f on M2. For the f(n) = n¡® case, we show this quasi-norm has a striking resemblance to the conjectured maximal order of j³(® + iT )j for ® > 12 .

The Empirical Forcing Function as a tool for the diagnosis of large-scale atmospheric anomalies

The time-mean quasi-geostrophic potential vorticity equation of the atmospheric flow on isobaric surfaces can explicitly include an atmospheric (internal) forcing term of the stationary-eddy flow. In fact, neglecting some non-linear terms in this equation, this forcing can be mathematically expressed as a single function, called Empirical Forcing Function (EFF), which is equal to the material derivative of the time-mean potential vorticity. Furthermore, the EFF can be decomposed as a sum of seven components, each one representing a forcing mechanism of different nature. These mechanisms include diabatic components associated with the radiative forcing, latent heat release and frictional dissipation, and components related to transient eddy transports of heat and momentum. All these factors quantify the role of the transient eddies in forcing the atmospheric circulation. In order to assess the relevance of the EFF in diagnosing large-scale anomalies in the atmospheric circulation, the relationship between the EFF and the occurrence of strong North Atlantic ridges over the Eastern North Atlantic is analyzed, which are often precursors of severe droughts over Western Iberia. For such events, the EFF pattern depicts a clear dipolar structure over the North Atlantic; cyclonic (anticyclonic) forcing of potential vorticity is found upstream (downstream) of the anomalously strong ridges. Results also show that the most significant components are related to the diabatic processes. Lastly, these results highlight the relevance of the EFF in diagnosing large-scale anomalies, also providing some insight into their interaction with different physical mechanisms.

The effect of adding stinging nettle (Urtica dioica) haylage to a total mixed ration on performance and rumen function of lactating dairy cows

In vitro studies found that inclusion of dried stinging nettle (Urtica dioica) at 100 mg/g dry matter (DM) increased the pH of a rumen fluid inoculated fermentation buffer by 30% and the effect was persistent for 7 days. Our objective was to evaluate the effects of adding stinging nettle haylage to a total mixed ration on feed intake, eating and rumination activity, rumen pH, milk yield, and milk composition of lactating dairy cows. Six lactating Holstein-Friesian cows were used in a replicated 3 × 3 Latin Square design experiment with 3 treatments and 3 week periods. Treatments were a control (C) high-starch (311 g/kg DM) total mixed ration diet and two treatment diets containing 50 (N5) and 100 (N10) g nettle haylage (DM/kg) as a replacement for ryegrass silage (Lolium perenne). There was an increase (linear, P < 0.010) in the proportion of large particles and a reduction in medium (linear, P = 0.045) and fine particles (linear, P = 0.026) in the diet offered with increasing nettle inclusion. A numerical decrease (linear, P = 0.106) in DM intake (DMI) was observed as nettle inclusion in the diet increased. Milk yield averaged 20.3 kg/day and was not affected by diet. There was a decrease (quadratic, P = 0.01) in the time animals spent ruminating as nettle inclusion in the diet increased, in spite of an increase in the number of boli produced daily for the N5 diet (quadratic, P = 0.031). Animals fed the N10 diet spent less time with a rumen pH below 5.5 (P < 0.05) than cows fed the N5 diet. Averaged over an 8.5 h sampling period, there were no changes in the concentration or proportions of acetate or propionate in the rumen, but feeding nettle haylage reduced the concentrations of n-butyrate (quadratic, P < 0.001), i-butyrate (linear, P < 0.009) and n-caproate (linear, P < 0.003). Milk and fat and protein corrected milk yield were not affected when nettles replaced ryegrass silage in the diet of lactating dairy cows, despite a numerical reduction in feed intake. Rumination activity was reduced by the addition of nettle haylage to the diet, which may reflect differences in fibre structure between the nettle haylage and ryegrass silage fed. Changes observed in rumen pH suggest potential benefits of feeding nettle haylage for reducing rumen acidosis. However, the extent to which these effects were due to the fermentability and structure of the nettle haylage compared to the ryegrass silage fed, or a bioactive component of the nettles, is not certain

Comparing performance of instrumental drift correction by linear and quadratic adjusting in inductive electromagnetic data

Electromagnetic induction (EMI) method results are shown for vertical magnetic dipole (VMD) configuration by using the EM38 equipment. Performance in the location of metallic pipes and electrical cables is compared as a function of instrumental drift correction by linear and quadratic adjusting under controlled conditions. Metallic pipes and electrical cables are buried at the IAG/USP shallow geophysical test site in Sao Paulo City. Brazil. Results show that apparent electrical conductivity and magnetic susceptibility data were affected by ambient temperature variation. In order to obtain better contrast between background and metallic targets it was necessary to correct the drift. This correction was accomplished by using linear and quadratic relation between conductivity/susceptibility and temperature intending comparative studies. The correction of temperature drift by using a quadratic relation was effective, showing that all metallic targets were located as well deeper targets were also improved. (C) 2010 Elsevier B.V. All rights reserved.

Exact Search Directions for Optimization of Linear and Nonlinear Models Based on Generalized Orthonormal Functions

A novel technique for selecting the poles of orthonormal basis functions (OBF) in Volterra models of any order is presented. It is well-known that the usual large number of parameters required to describe the Volterra kernels can be significantly reduced by representing each kernel using an appropriate basis of orthonormal functions. Such a representation results in the so-called OBF Volterra model, which has a Wiener structure consisting of a linear dynamic generated by the orthonormal basis followed by a nonlinear static mapping given by the Volterra polynomial series. Aiming at optimizing the poles that fully parameterize the orthonormal bases, the exact gradients of the outputs of the orthonormal filters with respect to their poles are computed analytically by using a back-propagation-through-time technique. The expressions relative to the Kautz basis and to generalized orthonormal bases of functions (GOBF) are addressed; the ones related to the Laguerre basis follow straightforwardly as a particular case. The main innovation here is that the dynamic nature of the OBF filters is fully considered in the gradient computations. These gradients provide exact search directions for optimizing the poles of a given orthonormal basis. Such search directions can, in turn, be used as part of an optimization procedure to locate the minimum of a cost-function that takes into account the error of estimation of the system output. The Levenberg-Marquardt algorithm is adopted here as the optimization procedure. Unlike previous related work, the proposed approach relies solely on input-output data measured from the system to be modeled, i.e., no information about the Volterra kernels is required. Examples are presented to illustrate the application of this approach to the modeling of dynamic systems, including a real magnetic levitation system with nonlinear oscillatory behavior.

Fock space for fermion-like lattices and the linear Glauber model

The concept of Fock space representation is developed to deal with stochastic spin lattices written in terms of fermion operators. A density operator is introduced in order to follow in parallel the developments of the case of bosons in the literature. Some general conceptual quantities for spin lattices are then derived, including the notion of generating function and path integral via Grassmann variables. The formalism is used to derive the Liouvillian of the d-dimensional Linear Glauber dynamics in the Fock-space representation. Then the time evolution equations for the magnetization and the two-point correlation function are derived in terms of the number operator. (C) 2008 Elsevier B.V. All rights reserved.

Magnetic linear dichroism in absorption spectroscopy of EuTe

The magnetic linear dichroism (MLD) at band-edge photon energies in the Voigt geometry was calculated for EuTe. At the spin-flop transition, MLD shows a step-like increase. Above the spin-flop transition MLD slowly decreases and becomes zero when the averaged electronic charge becomes symmetric relative to the axis of light propagation. Further increase of the magnetic field causes ferromagnetic alignment of the spins along the magnetic field direction, and MLD is recovered but with an opposite sign, and reaches maximum absolute values. These results are explained by the rearrangement of the Eu(2+) spin distribution in the crystal lattice as a function of magnetic field, due to the Zeeman interaction, demonstrating that MLD can be a sensitive probe of the spin order in EuTe, and provides information that is not accessible from other magneto-optical techniques, such as magnetic circular dichroism measurement studies.

Improved testing inference in mixed linear models

Mixed linear models are commonly used in repeated measures studies. They account for the dependence amongst observations obtained from the same experimental unit. Often, the number of observations is small, and it is thus important to use inference strategies that incorporate small sample corrections. In this paper, we develop modified versions of the likelihood ratio test for fixed effects inference in mixed linear models. In particular, we derive a Bartlett correction to such a test, and also to a test obtained from a modified profile likelihood function. Our results generalize those in [Zucker, D.M., Lieberman, O., Manor, O., 2000. Improved small sample inference in the mixed linear model: Bartlett correction and adjusted likelihood. Journal of the Royal Statistical Society B, 62,827-838] by allowing the parameter of interest to be vector-valued. Additionally, our Bartlett corrections allow for random effects nonlinear covariance matrix structure. We report simulation results which show that the proposed tests display superior finite sample behavior relative to the standard likelihood ratio test. An application is also presented and discussed. (C) 2008 Elsevier B.V. All rights reserved.

Local Influence Analysis for Skew-Normal Linear Mixed Models

In this article, we consider local influence analysis for the skew-normal linear mixed model (SN-LMM). As the observed data log-likelihood associated with the SN-LMM is intractable, Cook`s well-known approach cannot be applied to obtain measures of local influence. Instead, we develop local influence measures following the approach of Zhu and Lee (2001). This approach is based on the use of an EM-type algorithm and is measurement invariant under reparametrizations. Four specific perturbation schemes are discussed. Results obtained for a simulated data set and a real data set are reported, illustrating the usefulness of the proposed methodology.

Chemical profile of rums as a function of their origin. The use of chemometric techniques for their identification

To identify chemical descriptors to distinguish Cuban from non-Cuban rums, analyses of 44 samples of rum from 15 different countries are described. To provide the chemical descriptors, analyses of the the mineral fraction, phenolic compounds, caramel, alcohols, acetic acid, ethyl acetate, ketones, and aldehydes were carried out. The analytical data were treated through the following chemometric methods: principal component analysis (PCA), partial least square-discriminate analysis (PLS-DA), and linear discriminate analysis (LDA). These analyses indicated 23 analytes as relevant chemical descriptors for the separation of rums into two distinct groups. The possibility of clustering the rum samples investigated through PCA analysis led to an accumulative percentage of 70.4% in the first three principal components, and isoamyl alcohol, n-propyl alcohol, copper, iron, 2-furfuraldehyde (furfuraldehyde), phenylmethanal (benzaldehyde), epicatechin, and vanillin were used as chemical descriptors. By applying the PLS-DA technique to the whole set of analytical data, the following analytes have been selected as descriptors: acetone, sec-butyl alcohol, isobutyl alcohol, ethyl acetate, methanol, isoamyl alcohol, magnesium, sodium, lead, iron, manganese, copper, zinc, 4-hydroxy3,5-dimethoxybenzaldehyde (syringaldehyde), methaldehyde (formaldehyde), 5-hydroxymethyl-2furfuraldehyde (5-HMF), acetalclehyde, 2-furfuraldehyde, 2-butenal (crotonaldehyde), n-pentanal (valeraldehyde), iso-pentanal (isovaleraldehyde), benzaldehyde, 2,3-butanodione monoxime, acetylacetone, epicatechin, and vanillin. By applying the LIDA technique, a model was developed, and the following analytes were selected as descriptors: ethyl acetate, sec-butyl alcohol, n-propyl alcohol, n-butyl alcohol, isoamyl alcohol, isobutyl alcohol, caramel, catechin, vanillin, epicatechin, manganese, acetalclehyde, 4-hydroxy-3-methoxybenzoic acid, 2-butenal, 4-hydroxy-3,5-dimethoxybenzoic acid, cyclopentanone, acetone, lead, zinc, calcium, barium, strontium, and sodium. This model allowed the discrimination of Cuban rums from the others with 88.2% accuracy.

Feasible estimation of generalized linear mixed models (GLMM) with weak dependency between groups

This paper presents a two-step pseudo likelihood estimation technique for generalized linear mixed models with the random effects being correlated between groups. The core idea is to deal with the intractable integrals in the likelihood function by multivariate Taylor's approximation. The accuracy of the estimation technique is assessed in a Monte-Carlo study. An application of it with a binary response variable is presented using a real data set on credit defaults from two Swedish banks. Thanks to the use of two-step estimation technique, the proposed algorithm outperforms conventional pseudo likelihood algorithms in terms of computational time.

On the differentiability of the consumer demand function

For strictly quasi concave differentiable utility functions, demand is shown to be differentiable almost everywhere if marginal utilities are pointwise Lipschitzian. For concave utility functions, demand is differentiable almost everywhere in the case of differentiable additively separable utility or in the case of quasi-linear utility.

Generalized linear mixed models for the genetic evaluation of binary reproductive traits: a simulation study

The objective of this study was to evaluate the use of probit and logit link functions for the genetic evaluation of early pregnancy using simulated data. The following simulation/analysis structures were constructed: logit/logit, logit/probit, probit/logit, and probit/probit. The percentages of precocious females were 5, 10, 15, 20, 25 and 30% and were adjusted based on a change in the mean of the latent variable. The parametric heritability (h²) was 0.40. Simulation and genetic evaluation were implemented in the R software. Heritability estimates (ĥ²) were compared with h² using the mean squared error. Pearson correlations between predicted and true breeding values and the percentage of coincidence between true and predicted ranking, considering the 10% of bulls with the highest breeding values (TOP10) were calculated. The mean ĥ² values were under- and overestimated for all percentages of precocious females when logit/probit and probit/logit models used. In addition, the mean squared errors of these models were high when compared with those obtained with the probit/probit and logit/logit models. Considering ĥ², probit/probit and logit/logit were also superior to logit/probit and probit/logit, providing values close to the parametric heritability. Logit/probit and probit/logit presented low Pearson correlations, whereas the correlations obtained with probit/probit and logit/logit ranged from moderate to high. With respect to the TOP10 bulls, logit/probit and probit/logit presented much lower percentages than probit/probit and logit/logit. The genetic parameter estimates and predictions of breeding values of the animals obtained with the logit/logit and probit/probit models were similar. In contrast, the results obtained with probit/logit and logit/probit were not satisfactory. There is need to compare the estimation and prediction ability of logit and probit link functions.