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.

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...

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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It is proved that the potentials of the form β 2n (with n being integer) provide a "bridge" between the U(5) symmetry of the Bohr Hamiltonian with a harmonic oscillator potential (occuring for n = 1) and the E(5) model of Iachello (Bohr Hamiltonian with an infinite well potential, materialized for n → ∞). Parameter-free (up to overall scale factors) predictions for spectra and B(E2) transition rates are given for the potentials β 4 , β 6 , β 8 , corresponding to R 4 = E(4)/E(2) ratios of 2.093, 2.135, 2.157 respectively, compared to the R 4 ratios 2.000 of U(5) and 2.199 of E(5). Hints about nuclei showing this behaviour, as well as about potentials "bridging" the E(5) symmetry with O(6) are briefly discussed. A note about the appearance of Bessel functions in the framework of E(n) symmetries is given as a by-product.

An exactly separable version of the Bohr Hamiltonian is developed using a potential of the form u(β) + u(γ)/β 2 , with the Davidson potential u(β) = β 2 + β 4 0 /β 2 (where β 0 is the position of the minimum) and a stiff harmonic oscillator for u(γ) centered at γ = 0 • . In the resulting solution, called exactly separable Davidson (ES-D), the ground state band, γ band and 0 + 2 band are all treated on an equal footing. The bandheads, energy spacings within bands, and a number of interband and intraband B(E2) transition rates are well reproduced for almost all well-deformed rare earth and actinide nuclei using two parameters (β 0 , γ stiffness). Insights regarding the recently found correlation between γ stiffness and the γ-bandhead energy, as well as the long standing problem of producing a level scheme with Interacting Boson Approximation SU(3) degeneracies from the Bohr Hamiltonian, are also obtained.

A collective Hamiltonian for the rotation-vibration motion of nuclei is considered, in which the axial quadrupole and octupole degrees of freedom are coupled through the centrifugal interaction. The potential of the system depends on the two deformation variables β 2 and β 3 . The system is considered to oscillate between positive and negative β 3 -values, by rounding an infinite potential core in the (β 2 , β 3 )-plane with β 2 > 0. By assuming a coherent contribution of the quadrupole and octupole oscillation modes in the collective motion, the energy spectrum is derived in an explicit analytic form, providing specific parity shift effects. On this basis several possible ways in the evolution of quadrupole-octupole collectivity are outlined. A particular application of the model to the energy levels and electric transition probabilities in alternating parity spectra of the nuclei 150 Nd, 152 Sm, 154 Gd and 156 Dy is presented.

Starting from the original collective Hamiltonian of Bohr and separating the β and γ variables as in the X(5) model of Iachello, an exactly soluble model corresponding to a harmonic oscillator potential in the β-variable (to be called X(5)-β 2 ) is constructed. Furthermore, it is proved that the potentials of the form β 2n (with n being integer) provide a "bridge" between this new X(5)-β 2 model (occuring for n = 1) and the X(5) model (corresponding to an infinite well potential in the β-variable, materialized for n → ∞). Parameter-free (up to overall scale factors) predictions for spectra and B(E2) transition rates are given for the potentials β 2 , β 4 , β 6 , β 8 , corresponding to R 4 = E(4)/E(2) ratios of 2.646, 2.769, 2.824, and 2.852 respectively, compared to the R 4 ratios of 2.000 for U(5) and 2.904 for X(5). Hints about nuclei showing this behaviour, as well as about potentials "bridging" the X(5) symmetry with SU(3) are briefly discussed.PACS numbers: 21.60.Ev, 21.60.Fw, 21.10.Re 1. Introduction Models providing parameter-independent predictions for nuclear spectra and electromagnetic transition rates serve as useful benchmarks in nuclear theory. The recently introduced E(5) [1] and X(5) [2] models belong to this category, since their predictions for nuclear spectra (normalized to the excitation energy of the first excited state) and B(E2) transition rates (normalized to the B(E2) transition rate connecting the first excited state to the ground state) do not contain any free parameters. The E(5) model appears to be related to a phase transition from U(5) (vibrational) to O(6) (γ-unstable) nuclei [1], while X(5) is related to a phase transition from U(5) (vibrational) to SU(3) (prolate deformed) nuclei [2]. Both models originate (under certain simplifying assumptions) from the Bohr collective Hamiltonian [3], which is known to possess the U(5) symmetry of the five-dimensional (5-D) harmonic oscillator [4].In the present paper we study a sequence of potentials lying between the U(5) symmetry of the Bohr Hamiltonian and the X(5) model. The potentials, which are of the form 1