Large Mean Square Research Articles

Lattice summations for spread out particles: Applications to neutral and charged systems

This work is concerned with the lattice energy of periodic assemblies of mass and charge distributions of the form, exp (-αp(2)), where α is an adjustable positive variable and p(̱) is the vector from the lattice site or average position. The energy of interaction between two distributions is the density-weighted integral of the interactions between the volume elements of each distribution. Reciprocal space lattice summation formulas derived for particles represented by gaussian smeared-out density distributions are applied to the gaussian potential and a bounded version of the soft-sphere potential for a range of exponents. Two types of spatial broadening are considered, continuous or physical broadening (PB) and broadening resulting from the time average of point particle positions, so-called "time" broadening (TB). For neutral mass distributions a reciprocal space lattice summation formula is derived which is applied to the bounded soft-sphere potential. For the charged systems, the methodology described in Heyes [J. Chem. Phys. 74, 1924 (1981)] is used, which for the PB case gives the Ewald-like formulas derived by Gingrich and Wilson [Chem. Phys. Lett. 500, 178 (2010)] using a different method. Another expression for the lattice energy of the spread out charge distributions is derived which is cast entirely in terms of a summation over the reciprocal lattice vectors, without the arbitrary charge spreading function used in the Ewald method. The effects of charge spreading on a generalized definition of the Madelung constant (M) for a selection of crystal lattices are shown to be insignificant for route mean square displacements up to values typical of melting of an ionic crystal. When the length scale of the charge distribution becomes comparable to or greater than the mean inter particle spacing, however, the effects of charge broadening on the lattice energy are shown to be significant. In the PB case, M → 0 for the uniform charge density or α → 0 limit, and M ultimately becomes negative in the TB case for a large enough root mean square displacement (or small enough α).

Extending time-dependent instrumental variable estimation to estimate the causal effect of time-dependent exposure

Objectives: The purpose of the study was to compare the traditional models with the instrumental variable estimation method to estimate the causal effect of time-dependent exposure on the time-dependent outcome in the presence of unmeasured confounders for this effect. Methods: In recent studies, the instrumental variable (IV) estimation method of exposure effect frequently was used to collect information on potentially confounding variables. This is the case in particular where the time-dependent exposure is affected by the pervious events. We develop IV estimation method to estimate the effect of time-dependent exposure or treatment on timedependent outcome. This estimation method is designed for settings in which the exposure in time t is influenced by the exposure and outcome at time t − 1. Specifically, we extend IV estimation method in 2 stages in to a situation where exposure and outcome vary over the time. We show that our approach estimation in nonlinearity/additivity model is more consistent in comparison with the classical regression estimation method. This is done through simulation studies. Results: Our estimation strategy has larger mean square error (MSE) for the effect estimate in spite of having smaller bias in comparison with the tradition regression estimation method. However, this result might be the weak correlation between the time-dependent of instrumental variable and treatment. The case where the degree of correlation between time-depended instrumental variable and treatment at time t is stronger, we have more consistent estimate of causal effect. That is, our effect estimate tended to have less bias and less MSE, and more likely to have better confidence intervals and coverage probabilities. In the simulations study, we added interaction effect between exposures and measured confounder (nonadditivity model). In this model, by changing the association between outcome and confounders through different covariates, we could obtain more consistent estimate of the causal effect through our method than the classical method. The same results have been observed in case where we consider nonlinearity relationship between confounders and treatment. Alternatively, in some cases, we have better MSE for the classical estimation method, but we must note that its confidence intervals would not include the null causal effect value. Conclusions:We sketched a model for estimating the effect of timedependent treatment in settings in which classical methods may fail because of unmeasured confounding variables. We represented time-dependent instrumental variable to control the impact of measured and unmeasured confounders. We showed, after controlling confounding variables effect, that the effect of the previous treatment of interest that we wish to estimate could play the role of confounding variables under our assumptions and should be adjusted in the analysis. We showed that our approach has less bias than the classical regression models. Moreover, the mean square error of our method is large in some cases; this might be because our method performs in 2 steps. Not so surprisingly, strong association between instrument and treatment in each time reduces bias and the mean square error of the causal effect estimator. We showed also that our estimator is more efficient in coverage probabilities and confidence intervals in nonadditivity and nonlinearity/additivity models.

Credit Lending and Errors in Variables

Credit lending institutions often obtain credit data from third parties to make lending decisions. There are three major credit data providers (credit bureaus) in the United States. The credit reports that are obtained from these sources are not the same for the same individual for many reasons. The major sources of the data for these credit bureaus are the lending institutions themselves. Nevertheless, lending institutions do not report the performance of their customers to all three bureaus for cost considerations. As a result, there is discrepancy in the credit data pulled from credit bureaus. In this paper, we argue that variables based on merged credit bureau reports are more accurate than variables based on just single-bureau reports. Models estimated using data from individual credit bureaus have larger mean square errors relative to a model estimated using the merged data. Our results also show that the merge model possesses more predictive power than any of the individual credit bureau models. This is shown using Kolmogorov-Smirnov statistic and C-statistic.

Evaluation of multiple protein docking structures using correctly predicted pairwise subunits

BackgroundMany functionally important proteins in a cell form complexes with multiple chains. Therefore, computational prediction of multiple protein complexes is an important task in bioinformatics. In the development of multiple protein docking methods, it is important to establish a metric for evaluating prediction results in a reasonable and practical fashion. However, since there are only few works done in developing methods for multiple protein docking, there is no study that investigates how accurate structural models of multiple protein complexes should be to allow scientists to gain biological insights.MethodsWe generated a series of predicted models (decoys) of various accuracies by our multiple protein docking pipeline, Multi-LZerD, for three multi-chain complexes with 3, 4, and 6 chains. We analyzed the decoys in terms of the number of correctly predicted pair conformations in the decoys.Results and conclusionWe found that pairs of chains with the correct mutual orientation exist even in the decoys with a large overall root mean square deviation (RMSD) to the native. Therefore, in addition to a global structure similarity measure, such as the global RMSD, the quality of models for multiple chain complexes can be better evaluated by using the local measurement, the number of chain pairs with correct mutual orientation. We termed the fraction of correctly predicted pairs (RMSD at the interface of less than 4.0Å) as fpair and propose to use it for evaluation of the accuracy of multiple protein docking.

Physiological Intracellular Crowdedness is Defined by the Perimeter-to-Area Ratio of Sub-Cellular Compartments

The intracellular environment is known to be a crowded and inhomogeneous space. Such an in vivo environment differs from a well-diluted, homogeneous environment for biochemical reactions. However, the effects of both crowdedness and the inhomogeneity of environment on the behavior of a mobile particle have not yet been investigated sufficiently. As described in this paper, we constructed artificial reaction spaces with fractal models, which are assumed to be non-reactive solid obstacles in a reaction space with crevices that function as operating ranges for mobile particles threading the space. Because of the homogeneity of the structures of artificial reaction spaces, the models succeeded in reproducing the physiological fractal dimension of solid structures with a smaller number of non-reactive obstacles than in the physiological condition. This incomplete compatibility was mitigated when we chose a suitable condition of a perimeter-to-area ratio of the operating range to our model. Our results also show that a simulation space is partitioned into convenient reaction compartments as an in vivo environment with the exact amount of solid structures estimated from TEM images. The characteristics of these compartments engender larger mean square displacement of a mobile particle than that of particles in smaller compartments. Subsequently, the particles start to show confined particle-like behavior. These results are compatible with our previously presented results, which predicted that a physiological environment would produce quick response and slow exhaustion reactions.

New Variable Step-Size Blind Equalization Based on Modified Constant Modulus Algorithm

This paper presents a new blind equalization algorithm based on MCMA to attain fast convergence speed and low steady-state error. The channel equalization without resorting to training sequence is called blind equalization. The CMA (Constant Modulus Algorithm) and MCMA (Modified Constant Modulus Algorithm) are two widely referenced algorithms for blind equalization of a QAM system. These algorithms exhibit very slow convergence rates and large steady-state mean square error when compared to algorithms employed in conventional equalization schemes. To obtain better results, we used varying step-size in MCMA, based on estimate of error at the output of equalizer. Simulation results show that the proposed algorithm has a better convergence rates and lower steady state error in comparison to CMA and MCMA algorithms.

Static disorders of atoms and experimental determination of Debye temperature in pyrope: Low- and high-temperature single-crystal X-ray diffraction study

Geiger (2013) argues that the large mean square displacement (MSD) of Mg in the dodecahedral site in pyrope, Mg3Al2Si3O12, originates from the dynamic disorder of Mg due to its large anisotropic thermal vibration, including anharmonic contribution, and refutes our findings that the Mg static disorder is present. His argument is based on the diffraction, spectroscopic, thermodynamic, and computational studies made mainly by him and his co-workers. However, these investigations only suggested the large anisotropy of the Mg thermal vibration, and do not necessarily prove that there is no Mg static disorder. What we must obtain is conclusive experimental proof as to whether the Mg static disorder exists or not. In the present paper, a reply to his comment (Geiger 2013), we discuss the validity of our findings (Nakatsuka et al. 2011). A “direct” method to confirm the Mg static disorder is to observe a splitting of electron density maxima around the Mg site form the structure analysis. As shown in Nakatsuka et al. (2011), we successfully observed the residual electron density maxima around the Mg site (24 c site) in the difference Fourier map at a low temperature of 97 K. In addition, the refinements assigning Mg to these electron density maxima (split-atom model refinements) yielded “the Mg positional parameters deviating significantly from the 24 c site” and provided “the atomic displacement parameters (ADPs) of Mg significantly smaller than the ones in the normal-model refinements,” assigning Mg to the 24 c site, as a consequent of the removal of the static disorder components. These are direct evidence for the presence of the Mg static disorder. In the anharmonic refinements, several of the higher-rank tensor coefficients of Mg, Al, Si, and O atoms deviated significantly from …

Replica exchange molecular dynamics simulation of structure variation from α/4β-fold to 3α-fold protein

Replica exchange molecular dynamics (REMD) simulation provides an efficient conformational sampling tool for the study of protein folding. In this study, we explore the mechanism directing the structure variation from α/4β-fold protein to 3α-fold protein after mutation by conducting REMD simulation on 42 replicas with temperatures ranging from 270 K to 710 K. The simulation began from a protein possessing the primary structure of GA88 but the tertiary structure of GB88, two G proteins with "high sequence identity." Albeit the large Cα-root mean square deviation (RMSD) of the folded protein (4.34 Å at 270 K and 4.75 Å at 304 K), a variation in tertiary structure was observed. Together with the analysis of secondary structure assignment, cluster analysis and principal component, it provides insights to the folding and unfolding pathway of 3α-fold protein and α/4β-fold protein respectively paving the way toward the understanding of the ongoings during conformational variation.

A monostatic illumination function with surface reflections from one-dimensional rough surfaces

When solving scattering or emissivity problems for rough surfaces, the shadowing effect is often taken into account. Furthermore, for rough surfaces with large root mean square slope, surface reflections of the incidence or emission ray should not be neglected, especially at large observation angles. In this paper, a model of the monostatic statistical illumination function for one-dimensional rough surfaces with single surface reflection is developed, which is based on the Smith illumination function. A Monte Carlo ray-tracing algorithm is used to evaluate the accuracy of the present model. It is shown that, when neglecting the correlation between heights and slopes of the surface, the present model agrees quite well with the Monte Carlo result. Moreover, the result is improved if the correlation between heights and slopes is taken into account. For practical purposes, an empirical factor is introduced to improve the performance of the uncorrelated first-order illumination function to avoid computing the correlated one, which takes a long computation time. Besides, the first-order illumination function is significant at large observation angles, which could be promising to overcome problems in models of surface infrared emissivity where underestimation occurs compared with experimental measurements.

The effect of post-annealing on surface acoustic wave devices based on ZnO thin films prepared by magnetron sputtering

Zinc oxide (ZnO) thin films were deposited on unheated silicon substrates via radio frequency (RF) magnetron sputtering, and the post-deposition annealing of the ZnO thin films was performed at 400°C, 600°C, 800°C, and 1000°C. The characteristics of the thin films were investigated by X-ray diffractometry (XRD), scanning electron microscopy (SEM), and atomic force microscopy (AFM). The films were then used to fabricate surface acoustic wave (SAW) resonators. The effects of post-annealing on the SAW devices are discussed in this work. Resulting in the 600°C is determined as optimal annealing temperature for SAW devices. At 400°C, the microvoids exit between the grains yield large root mean square (RMS) surface roughness and higher insertion losses in SAW devices. The highest RMS surface roughness, crack and residual stress cause a reduction of surface velocity (about 40m/s) and increase dramatically insertion loss at 1000°C. The SAW devices response becomes very weak at this temperature, the electromechanical coupling coefficient (k2) of ZnO film decrease from 3.8% at 600°C to 1.49% at 1000°C.

Wavelet weighted blood vessel distortion measure for retinal images

In this paper, a novel wavelet transform based blood vessel distortion measure (WBVDM) is proposed to assess the image quality of blood vessels in the processed retinal images. The wavelet analysis of retinal image shows that different wavelet subbands carry different information about the blood vessels. The WBVDM is defined as the sum of wavelet weighted root of the normalized mean square error of subbands expressed in percentage. The proposed WBVDM is compared with other wavelet based distortion measures such as wavelet mean square error(WMSE), Relative WMSE(Rel WMSE) and root of the normalized WMSE(RNWMSE). The results show that WBVDM performs better in capturing the blood vessel distortion. For distortion in clinically nonsignificant regions, the proposed WBVDM shows a low value of 1.1676 compared to a large mean square error value of 7.9909. The evaluation of correlation using Pearson linear correlation coefficient (PLCC) and Spearman rank order correlation coefficient (SROCC) shows a higher value for the correlation between WBVDM and subjective score. The experimental observations show that WBVDM is able to capture the distortion in blood vessels more effectively and responds weakly to the distortion inherent in the other retinal features.

Gas concentration and temperature reconstruction by genetic simulated annealing algorithm based on multi-wavelengths diode laser absorption spectroscopy

Gas concentration and temperature distribution reconstruction is realized based on tunable diode laser absorption spectroscopy. A measurement system using wavelength multiplexing technology with four absorption transitions is designed to reduce the number of projections and enrich the gas absorption measurement data. According to the nonlinear system established, a hybrid algorithm based on genetic algorithm and simulated annealing algorithm is introduced to obtain the global optimization and improve the search efficiency. A model for H2O concentration and temperature distribution in combustion is assumed, and numerical simulation is utilized to reconstruct the images with the transitions within 1.3—1.5 μm range. Both concentration and temperature distribution reconstruction results are in agreement with the model. The influence of random errors in projections on reconstruction is also analyzed. The increased error in projection would lead to larger mean square error of temperature reconstruction results, but little affect the concentration reconstruction results.

A Modified T/2 Fractionally Spaced Coordinate Transformation Blind Equalization Algorithm

When T/2 Fractionally Spaced blind Equalization Algorithm based Constant Modulus Algorithm (T/2-FSE- CMA) is employed for equalizing higher order Quadrature Amplitude Modulation signals (QAM), it has disadvantages of low convergence speed and large Mean Square Error (MSE). For overcoming these disadvantages, a Modified T/2 Fractionally Spaced blind Equalization algorithm based on Coordinate Transformation and CMA (T/2-FSE-MCTCMA) was proposed by analyzing the character of 16QAM signal constellations. In the proposed algorithm, real and imaginary parts of input signal of T/2 fractionally spaced blind equalizer are equalized, respectively, and output signals of equalizer are transformed to the same unit circle by coordinate transformation method, a new error function is defined after making coordinate transformation and used to adjust weight vector of T/2 fractionally spaced blind equalizer. The proposed algorithm can overcome large misjudgments of T/2 fractionally spaced blind equalization algorithm for equalizing multi-modulus higher order QAM. Simulation results with underwater acoustic channel models demonstrate that the proposed T/2-FSE-MCTCMA algorithm outperforms T/2 Fractionally Spaced blind Equalization algorithm bas-ed on Coordinate Transformation and CMA (T/2-FSE-CTCMA) and the T/2-FSE-CMA in convergence rate and MSE.

Structural Characteristics and Ferroelectric Properties of Bismuth-Based Compound Thin Films Crystallized by Hot Isostatic Pressing

After depositing amorphous (Bi0.5La0.5)(Ni0.5Ti0.5)O3 (BLNT) films on BLNT seed layer/Pt(100)/ MgO(100) substrates by room-temperature sputtering, the crystallization of the perovskite-struc- tured films has been tried by hot isostatic pressing (HIP). The samples with a single-phase perovskite structure HIP-treated at 800°C for 1 h under gas pressures of 0.51.0 MPa showed good crystallinity of  = 0.960.98 without accompanying the precipitation of the secondary phase. It was confirmed that a large root mean square roughness value of 44.2 nm for the sample HIP-treated at 800°C for 1 h under gas pressure of 0.1 MPa is due to innumerable Bi4Ti3O12-like rod-shaped grains precipitated in the film surface, based on atomic force microscopy. It is shown that the BLNT sample HIP-treated at 800°C for 1 h under gas pressure of 1.0 MPa exhibits the best hysteresis loop shape with a remanent polarization of Pr = 5 C/cm2 and a coercive field of Ec = 150 kV/cm of the six.

Water and energy budgets simulation over the AMMA-Niger super-site spatially constrained with remote sensing data

The SEtHyS_Savannah model [Saux-Picart et al., submitted for publication. SEtHyS_Savannah: a multiple source land surface model applied to sahelian landscapes. Agricultural and Forest Meteorology] was developed as an extension of the SEtHyS land surface model to simulate the water and energy fluxes over dry savannah landscapes. The vegetation cover is represented by a two layer model and a mulch approach is used for the soil description. The SEtHyS_Savannah model was regionalized over the AMMA-Niger super-site (about 50 km by 40 km), with the help of remote sensing data. The model uses a regular 1km grid and each cell is divided in sub-grid patches in order to represent land cover and soil heterogeneities (tile approach). The vegetation cover parameters were prescribed according to the land cover map and the seasonal evolution of the Leaf Area Index (LAI), both derived from SPOT-HRV (Satellite Pour l’Observation de la Terre – High Resolution Visible) data imagery. The atmospheric forcing was assumed homogeneous over the area and provided by a meteorological station installed at the Fakara experimental site. The surface water and energy budgets were simulated over a one-year period (2005) at a 5-min time step and validated against MSG-SEVIRI (Meteosat Second Generation – Spinning Enhanced Visible and Infra-red Imager) land surface temperature and ENVISAT-ASAR (ENVIronnement SATellite – Advanced Synthetic Aperture Radar) soil humidity products. The results show realistic surface fluxes and good agreement with the MSG-SEVIRI temperature observations. The soil moisture comparison presents significant correlation but large root mean square errors. These discrepancies are the consequence of both the use of a non-spatialized atmospheric forcing and to residual vegetation effects on the radar signal. Despite these uncertainties, the results increase confidence in the model representation of Sahelian soil–vegetation processes and open new perspectives to quantify the effects of vegetation changes on evapotranspiration and runoff over the region.

KPP fronts in a one-dimensional random drift

We establish the variational principle ofKolmogorov-Petrovsky-Piskunov (KPP) front speedsin a one dimensional random drift which is a mean zero stationaryergodic process with mixing property and local Lipschitz continuity.To prove the variational principle, we use the pathintegral representation of solutions,hitting time and large deviation estimates of theassociated stochastic flows.The variational principle allows us to derive upper and lower bounds of thefront speeds which decay according to a power law in the limit of large root meansquare amplitude of the drift. This scaling law is different fromthat of the effective diffusion (homogenization) approximationwhich is valid for front speeds in incompressible periodic advection.

UV inactivation and model of UV inactivation of foot-and-mouth disease viruses in suspension

Foot-and-mouth disease virus (FMDV) causes one of the most contagious diseases affecting cloven-hoofed animals (e.g., cattle and swine) and causes severe economic loss for many countries. The resistance to UV irradiation of FMDV strains isolated from outbreaks in Thailand was investigated in phosphate-buffered saline at 25 °C. Since the regression coefficients of linear regression were large and root mean square errors were small, UV inactivation could be appropriately summarized and fitted well by a linear equation. The first-order kinetics then could describe UV inactivation, which was experimentally and mathematically shown in this study to be an effective means to inactivate FMDV in suspension. The decimal inactivation dose (DID) was modified from D value in traditional thermal-inactivation kinetics. The DID was the amount of UV irradiation required to reduce the number of microorganisms by a factor of 10, or by 90%. DIDs of FMDV serotypes O189, A132, A-Sakol, and AS1 ranged from 19.66 to 31.31 mWs/cm 2. FMDV serotype AS1 was the most UV-resistant, and FMDV serotype A132 was the least UV-resistant. UV resistance of FMDV did not vary significantly among strains and serotypes ( P value > 0.05). DID raw data were used to determine the fitted probability distributions by simulation software @Risk. The fitted distributions suggested were Exponential, Logistic, Normal, and LogNormal. Exponential distribution was the best fit by Chi-square test, Kolmogorov–Smirnov test, and Anderson–Darling test ( P value > 0.10). The parameter β of the Exponential distribution, equivalent to the mean DID, was 24.173 mWs/cm 2 as a first-order model. Poisson probability distribution described the uncertainty of parameter β for the second-order model. After running simulations of both first-order and second-order models, the curves of both first-order and second-order models were overlaid on the same graph, which indicated that both models were only slightly different. This study concluded that FMDV in suspension was effectively inactivated by UV irradiation, the fitted probability distribution for UV inactivation was Exponential, and source of total uncertainty of this UV-inactivation model was not the uncertainty component.

Inferring Selection in Partially Sequenced Regions

A common approach for identifying loci influenced by positive selection involves scanning large portions of the genome for regions that are inconsistent with the neutral equilibrium model or represent outliers relative to the empirical distribution of some aspect of the data. Once identified, partial sequence is generated spanning this more localized region in order to quantify the site-frequency spectrum and evaluate the data with tests of neutrality and selection. This method is widely used as partial sequencing is less expensive with regard to both time and money. Here, we demonstrate that this approach can lead to biased maximum likelihood estimates of selection parameters and reduced rejection rates, with some parameter combinations resulting in clearly misleading results. Most significantly, for a commonly used sample size in Drosophila population genetics (i.e., n = 12), the estimate of the target of selection has a large mean square error and the strength of selection is severely under estimated when the true selected site has not been sampled. We propose sequencing approaches that are much more likely to accurately localize the target and estimate the strength of selection. Additionally, we examine the performance of a commonly used test of selection under a variety of recurrent and single sweep models.

Development and evaluation of a model for prediction of fecal and urinary nitrogen excretions in cattle

Abstract The reduction of nitrogen (N) excretion in animal production is crucial in intensive farming systems particularly in the developed countries. In this study, a model to predict N excretion in cattle was developed based on existing feeding standards and evaluated using independent N balance experiments for Holstein steers and lactating cows and Japanese Black (JB) steers. Although model predictions for fecal and urinary N excretions appeared to be close to observed values in plot figures, statistical analysis showed that the model tended to over-predict both fecal and urinary N excretions, especially in Holstein lactating cows. This was because body weight changes of cows during lactation period were not considered in the model due to the lack of information (i.e., body weight gain or loss) available in the experimental data for evaluation. There were large mean bias and small line bias for urinary N prediction, but reverse results were obtained for fecal N prediction. The largest mean square prediction errors for both N excretions were due to random variation in all cases. When all data were pooled (combined), the accuracy for predictions for fecal N excretion was considerably high ( r 2 = 0.94), indicating that the model may predict fecal N excretion beyond breeds, sexes and physiological states (growing and lactating). More information and accumulated data will be required to predict urinary N excretion under a wide range of genotype and environmental situation.

Deformation change in light iridium nuclei from laser spectroscopy

Laser spectroscopy measurements have been performed on neutron-deficient and stable Ir isotopes using the COMPLIS experimental setup installed at ISOLDE-CERN. The radioactive Ir atoms were obtained from successive decays of a mass-separated Hg beam deposited onto a carbon substrate after deceleration to 1kV and subsequently laser desorbed. A three-color, two-step resonant scheme was used to selectively ionize the desorbed Ir atoms. The hyperfine structure (HFS) and isotope shift (IS) of the first transition of the ionization path 5d76s24F9/2 → 5d76s6p6F11/2 at 351.5nm were measured for 182-189Ir, 186Irm and the stable 191, 193Ir. The nuclear magnetic moments μI and the spectroscopic quadrupole moments Qs were obtained from the HFS spectra and the change of the mean square charge radii from the IS measurements. The sign of μI was experimentally determined for the first time for the masses 182≤A≤189 and the isomeric state 186Irm. The spectroscopic quadrupole moments of 182Ir and 183Ir were measured also for the first time. A large mean square charge radius change between 187Ir and 186Irg and between 186Irm and 186Irg was observed corresponding to a sudden increase in deformation: from β2 ≃ + 0.16 for the heavier group A = 193, 191, 189, 187 and 186m to β2≥ + 0.2 for the lighter group A = 186g, 185, 184, 183 and 182. These results were analyzed in the framework of a microscopic treatment of an axial rotor plus one or two quasiparticle(s). This sudden deformation change is associated with a change in the proton state that describes the odd-nuclei ground state or that participates in the coupling with the neutron in the odd-odd nuclei. This state is identified with the π3/2+[402] orbital for the heavier group and with the π1/2-[541] orbital stemming from the 1h9/2 spherical subshell for the lighter group. That last state seems to affect strongly the observed values of the nuclear moments.