A critical point symmetry for the prolate to oblate shape phase transition is introduced, starting from the Bohr Hamiltonian and approximately separating variables for γ = 30 o . Parameter-free (up to overall scale factors) predictions for spectra and B(E2) transition rates are found to be in good agreement with experimental data for 194 Pt, which is supposed to be located very close to the prolate to oblate critical point, as well as for its neighbours ( 192 Pt, 196 (5) [3], related to the transition from axial to triaxial shapes. All these critical point symmetries have been constructed by considering the original Bohr equation [8], separating the collective β and γ variables, and making different assumpions about the u(β) and u(γ) potentials involved.Furthermore, it has been demonstrated [9] that experimental data in the Hf-Hg mass region indicate the presence of a prolate to oblate shape phase transition, the nucleus 194 Pt being the closest one to the critical point. No critical point symmetry for the prolate to oblate shape phase transition originating from the Bohr equation has been given so far, although it has been suggested [10,11] that the (parameter-dependent) O(6) limit of the Interacting Boson Model (IBM) [12] can serve as the critical point of this transition, since various physical quantities exhibit a drastic change of behaviour at O(6), as they should [13].In the present work a parameter-free (up to overall scale factors) critical point symmetry, to be called Z(5), is introduced for the prolate to oblate shape phase transition, leading to parameter-free predictions which compare very well with the experimental data for 194 Pt. The path followed for constructing the Z(5) critical point symmetry is described here: 1) Separation of variables in the Bohr equation [8] is achieved by assuming γ = 30 o . When considering the transition from γ = 0 o (prolate) to γ = 60 o (oblate), it is reasonable to expect that the triaxial region (0 o < γ < 60 o ) will be crossed, γ = 30 o lying in its middle. Indeed, there is experimental evidence supporting this assumption [14].2) For γ = 30 o the K quantum number (angular momentum projection on the bodyfixedẑ ′ -axis) is not a good quantum number any more, but α, the angular momentum projection on the body-fixedx ′ -axis is, as found [15] in the study of the triaxial rotator [16,17].3) Assuming an infinite well potential in the β-variable and a harmonic oscillator potential having a minimum at γ = 30 o in the γ-variable, the Z(5) model is obtained.On these choices, the following comments apply: 1) Taking γ = 30 o does not mean that rigid triaxial shapes are prefered. In fact, it has been pointed out [18] that a nucleus in a γ-flat potential [19] (as it should be expected for a prolate to oblate shape phase transition) oscillates uniformly over γ from γ = 0 o to γ = 60 o , having an average value of γ av = 30 o , and, therefore, the triaxial case to which it should be compared is the one with γ = 30 o . Furthermore, it is known [20] that many prediction...

Analytical expressions for spectra and wave functions are derived for a Bohr Hamiltonian, describing the collective motion of deformed nuclei, in which the mass is allowed to depend on the nuclear deformation. Solutions are obtained for separable potentials consisting of a Davidson potential in the β variable, in the cases of γ-unstable nuclei, axially symmetric prolate deformed nuclei, and triaxial nuclei, implementing the usual approximations in each case. The solution, called the Deformation Dependent Mass (DDM) Davidson model, is achieved by using techniques of supersymmetric quantum mechanics (SUSYQM), involving a deformed shape invariance condition. Spectra and B(E2) transition rates are compared to experimental data. The dependence of the mass on the deformation, dictated by SUSYQM for the potential used, reduces the rate of increase of the moment of inertia with deformation, removing a main drawback of the model.

The success of deep convolutional neural networks (NNs) on image classification and recognition tasks has led to new applications in very diversified contexts, including the field of medical imaging. In this paper, we investigate and propose NN architectures for automated multiclass segmentation of anatomical organs in chest radiographs (CXRs), namely for lungs, clavicles, and heart. We address several open challenges including model overfitting, reducing number of parameters, and handling of severely imbalanced data in CXR by fusing recent concepts in convolutional networks and adapting them to the segmentation problem task in CXR. We demonstrate that our architecture combining delayed subsampling, exponential linear units, highly restrictive regularization, and a large number of high-resolution low-level abstract features outperforms state-of-the-art methods on all considered organs, as well as the human observer on lungs and heart. The models use a multiclass configuration with three target classes and are trained and tested on the publicly available Japanese Society of Radiological Technology database, consisting of 247 X-ray images the ground-truth masks for which are available in the segmentation in CXR database. Our best performing model, trained with the loss function based on the Dice coefficient, reached mean Jaccard overlap scores of 95% for lungs, 86.8% for clavicles, and 88.2% for heart. This architecture outperformed the human observer results for lungs and heart.

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