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There are many numerical methods for solving partial different equations (PDEs) on manifolds such as classical implicit, finite difference, finite element, and isogeometric analysis methods which aim at improving the interoperability between finite element method and computer aided design (CAD) software. However, these approaches have difficulty when the domain has singularities since the solution at the singularity may be multivalued. This paper develops a novel numerical approach to solve elliptic PDEs on real, closed, connected, orientable, and almost smooth algebraic curves and surfaces. Our method integrates numerical algebraic geometry, differential geometry, and a finite difference scheme which is demonstrated on several examples.

\noindent \textbf{Background:} Detailed spectroscopy of neutron-rich, heavy, deformed nuclei is of broad interest for nuclear astrophysics and nuclear structure. Nuclei in the r-process path and following freeze-out region impact the resulting r-process abundance distribution, and the structure of nuclei midshell in both proton and neutron number helps to understand the evolution of subshell gaps and large deformation in these nuclei. \noindent \textbf{Purpose:} To improve the understanding of the nuclear structure of $^{160}$Gd, specifically the $K^\pi$=$4^+$ bands, as well as study the $\beta$-decay of $^{160}$Eu into $^{160}$Gd. \noindent \textbf{Methods:} High-statistics decay spectroscopy of $^{160}$Gd resulting from the $\beta$-decay of $^{160}$Eu was collected using the GRIFFIN spectrometer at the TRIUMF-ISAC facility. \noindent \textbf{Results:} Two new excited states and ten new transitions were observed in $^{160}$Gd. The $\beta$-decaying half-lives of the low- and high-spin isomer in $^{160}$Eu were determined, and the low-spin state's half-life was measured to be $t_{1/2}=26.0(8)$~s, $\sim$16\% shorter than previous measurements. Lifetimes of the two $K^\pi$=$4^+$ band-heads in $^{160}$Gd were measured for the first time, as well as $\gamma$-$\gamma$ angular correlations and mixing ratios of intense transitions out of those band-heads. \noindent \textbf{Conclusions:} Lifetimes and mixing ratios suggest that the hexadecapole phonon model of the $K^\pi$=$4^+$ band-heads in $^{160}$Gd is preferred over a simple two-state strong mixing scenario, although further theoretical calculations are needed to fully understand these states. Additionally, the 1999.0 keV state in $^{160}$Gd heavily populated in $\beta$-decay is shown to have positive parity, which raises questions regarding the structure of the high-spin $\beta$-decaying state in $^{160}$Eu.

We consider Galois/monodromy groups arising in computer vision applications, with a view towards building more efficient polynomial solvers. The Galois/monodromy group allows us to decide when a given problem decomposes into algebraic subproblems, and whether or not it has any symmetries. Tools from numerical algebraic geometry and computational group theory allow us to apply this framework to classical and novel reconstruction problems. We consider three classical cases--3-point absolute pose, 5-point relative pose, and 4-point homography estimation for calibrated cameras--where the decomposition and symmetries may be naturally understood in terms of the Galois/monodromy group. We then show how our framework can be applied to novel problems from absolute and relative pose estimation. For instance, we discover new symmetries for absolute pose problems involving mixtures of point and line features. We also describe a problem of estimating a pair of calibrated homographies between three images. For this problem of degree 64, we can reduce the degree to 16; the latter better reflecting the intrinsic difficulty of algebraically solving the problem. As a byproduct, we obtain new constraints on compatible homographies, which may be of independent interest.

The neutron-rich $^{213}$Pb isotope was produced in the fragmentation of a primary 1 GeV $A$ $^{238}$U beam, separated in FRS in mass and atomic number, and then implanted for isomer decay $\gamma$-ray spectroscopy with the RISING setup at GSI. A newly observed isomer and its measured decay properties indicate that states in $^{213}$Pb are characterized by the seniority quantum number that counts the nucleons not in pairs coupled to angular momentum $J=0$. The conservation of seniority is a consequence of the Berry phase associated with particle-hole conjugation, which becomes gauge invariant and therefore observable in semi-magic nuclei where nucleons half-fill the valence shell. The $\gamma$-ray spectroscopic observables in $^{213}$Pb are thus found to be driven by two mechanisms, particle-hole conjugation and seniority conservation, which are intertwined through the Berry phase.

Parameterized systems of polynomial equations arise in many applications in science and engineering with the real solutions describing, for example, equilibria of a dynamical system, linkages satisfying design constraints, and scene reconstruction in computer vision. Since different parameter values can have a different number of real solutions, the parameter space is decomposed into regions whose boundary forms the real discriminant locus. This article views locating the real discriminant locus as a supervised classification problem in machine learning where the goal is to determine classification boundaries over the parameter space, with the classes being the number of real solutions. For multidimensional parameter spaces, this article presents a novel sampling method which carefully samples the parameter space. At each sample point, homotopy continuation is used to obtain the number of real solutions to the corresponding polynomial system. Machine learning techniques including nearest neighbor and deep learning are used to efficiently approximate the real discriminant locus. One application of having learned the real discriminant locus is to develop a real homotopy method that only tracks the real solution paths unlike traditional methods which track all~complex~solution~paths. Examples show that the proposed approach can efficiently approximate complicated solution boundaries such as those arising from the equilibria of the Kuramoto model., Comment: 22 pages, 14 figures

The monodromy group is an invariant for parameterized systems of polynomial equations that encodes structure of the solutions over the parameter space. Since the structure of real solutions over real parameter spaces are of interest in many applications, real monodromy action is investigated here. A naive extension of monodromy action from the complex numbers to the real numbers is shown to be very restrictive. Therefore, we define a real monodromy structure which need not be a group but contains tiered characteristics about the real solutions. This real monodromy structure is applied to an example in kinematics which summarizes all the ways performing loops parameterized by leg lengths can cause a mechanism to change poses.

The STELLA (STELlar LAboratory) experimental station for the measurement of deep sub-barrier light heavy-ion fusion cross sections has been installed at the Androm\`{e}de accelerator at the Institut de Physique Nucl\'{e}aire, Orsay (France). The setup is designed for the direct experimental determination of heavy-ion fusion cross sections as low as tens of picobarn. The detection concept is based on the coincident measurement of emitted gamma rays with the UK FATIMA (FAst TIMing Array) and evaporated charged particles using a silicon detector array. Key developments relevant to reaching the extreme sub-barrier fusion region are a rotating target mechanism to sustain beam intensities above 10$\mu$A, an ultra-high vacuum to prevent carbon built-up and gamma charged-particle timing in the order of nanoseconds sufficient to separate proton and alpha particles., Comment: 18 pages, 11 figures

The low-lying structures of the midshell $\nu g_{9/2}$ Ni isotopes $^{72}$Ni and $^{74}$Ni have been investigated at the RIBF facility in RIKEN within the EURICA collaboration. Previously unobserved low-lying states were accessed for the first time following $\beta$ decay of the mother nuclei $^{72}$Co and $^{74}$Co. As a result, we provide a complete picture in terms of the seniority scheme up to the first $(8^+)$ levels for both nuclei. The experimental results are compared to shell-model calculations in order to define to what extent the seniority quantum number is preserved in the first neutron $g_{9/2}$ shell. We find that the disappearance of the seniority isomerism in the $(8^+_1)$ states can be explained by a lowering of the seniority-four $(6^+)$ levels as predicted years ago. For $^{74}$Ni, the internal de-excitation pattern of the newly observed $(6^+_2)$ state supports a restoration of the normal seniority ordering up to spin $J=4$. This property, unexplained by the shell-model calculations, is in agreement with a dominance of the single-particle spherical regime near $^{78}$Ni.

Three aspects of applying homotopy continuation, which is commonly used to solve parameterized systems of polynomial equations, are investigated. First, for parameterized systems which are homogeneous, we investigate options for performing computations on an adaptively chosen affine coordinate patch. Second, for parameterized systems which are overdetermined, we investigate options for adaptively selecting a well-constrained subsystem to restore numerical stability. Finally, since one is typically interested in only computing real solutions for parameterized problems which arise from applications, we investigate a scheme for heuristically identifying solution paths which appear to be ending at nonreal solutions and truncating them. We demonstrate these three aspects on two problems arising in computer vision.

The beta decays of $^{86}$Br and $^{91}$Rb have been studied using the total absorption spectroscopy technique. The radioactive nuclei were produced at the IGISOL facility in Jyv\"askyl\"a and further purified using the JYFLTRAP. $^{86}$Br and $^{91}$Rb are considered to be major contributors to the decay heat in reactors. In addition $^{91}$Rb was used as a normalization point in direct measurements of mean gamma energies released in the beta decay of fission products by Rudstam {\it et al.} assuming that this decay was well known from high-resolution measurements. Our results show that both decays were suffering from the {\it Pandemonium} effect and that the results of Rudstam {\it et al.} should be renormalized. The relative impact of the studied decays in the prediction of the decay heat and antineutrino spectrum from reactors has been evaluated., Comment: 11 pages, 13 figures

The antineutrino spectra measured in recent experiments at reactors are inconsistent with calculations based on the conversion of integral beta spectra recorded at the ILL reactor. $^{92}$Rb makes the dominant contribution to the reactor spectrum in the 5-8 MeV range but its decay properties are in question. We have studied $^{92}$Rb decay with total absorption spectroscopy. Previously unobserved beta feeding was seen in the 4.5-5.5 region and the GS to GS feeding was found to be 87.5(25)%. The impact on the reactor antineutrino spectra calculated with the summation method is shown and discussed., Comment: 6 pages, 3 figures

Neutron-rich silver isotopes were populated in the fragmentation of a 136Xe beam and the relativistic fission of 238U. The fragments were mass analyzed with the GSI Fragment separator and subsequently implanted into a passive stopper. Isomeric transitions were detected by 105 HPGe detectors. Eight isomeric states were observed in 122-126Ag nuclei. The level schemes of 122,123,125Ag were revised and extended with isomeric transitions being observed for the first time. The excited states in the odd-mass silver isotopes are interpreted as core-coupled states. The isomeric states in the even-mass silver isotopes are discussed in the framework of the proton-neutron split multiplets. The results of shell-model calculations, performed for the most neutron-rich silver nuclei are compared to the experimental data.

High-spin states of $^{40}$K have been populated in the fusion-evaporation reaction $^{12}$C($^{30}$Si,np)$^{40}$K and studied by means of $\gamma$-ray spectroscopy techniques using one AGATA triple cluster detector, at INFN - Laboratori Nazionali di Legnaro. Several new states with excitation energy up to 8 MeV and spin up to $10^-$ have been discovered. These new states are discussed in terms of J=3 and T=0 neutron-proton hole pairs. Shell-model calculations in a large model space have shown a good agreement with the experimental data for most of the energy levels. The evolution of the structure of this nucleus is here studied as a function of excitation energy and angular momentum., Comment: 23 pages, 5 figures, submitted to Phys. Rev. C

Neutron-rich nuclei were populated in a relativistic fission of 238U. Gamma-rays with energies of 135 keV and 184 keV were associated with two isomeric states in 121Pd and 117Ru. Half-lives of 0.63(5) microseconds and 2.0(3) micrisecondss were deduced and the isomeric states were interpreted in terms of deformed single-particle states.

With a new detector setup and the high-resolution performance of the fragment separator FRS at GSI we discovered 57 new isotopes in the atomic number range of 60$\leq Z \leq 78$: \nuc{159-161}{Nb}, \nuc{160-163}{Pm}, \nuc{163-166}Sm, \nuc{167-168}{Eu}, \nuc{167-171}{Gd}, \nuc{169-171}{Tb}, \nuc{171-174}{Dy}, \nuc{173-176}{Ho}, \nuc{176-178}{Er}, \nuc{178-181}{Tm}, \nuc{183-185}{Yb}, \nuc{187-188}{Lu}, \nuc{191}{Hf}, \nuc{193-194}{Ta}, \nuc{196-197}{W}, \nuc{199-200}{Re}, \nuc{201-203}{Os}, \nuc{204-205}{Ir} and \nuc{206-209}{Pt}. The new isotopes have been unambiguously identified in reactions with a $^{238}$U beam impinging on a Be target at 1 GeV/u. The isotopic production cross-section for the new isotopes have been measured and compared with predictions of different model calculations. In general, the ABRABLA and COFRA models agree better than a factor of two with the new data, whereas the semiempirical EPAX model deviates much more. Projectile fragmentation is the dominant reaction creating the new isotopes, whereas fission contributes significantly only up to about the element holmium., Comment: 9 pages, 4 figures

The Advanced GAmma Tracking Array (AGATA) is a European project to develop and operate the next generation gamma-ray spectrometer. AGATA is based on the technique of gamma-ray energy tracking in electrically segmented high-purity germanium crystals. This technique requires the accurate determination of the energy, time and position of every interaction as a gamma ray deposits its energy within the detector volume. Reconstruction of the full interaction path results in a detector with very high efficiency and excellent spectral response. The realization of gamma-ray tracking and AGATA is a result of many technical advances. These include the development of encapsulated highly-segmented germanium detectors assembled in a triple cluster detector cryostat, an electronics system with fast digital sampling and a data acquisition system to process the data at a high rate. The full characterization of the crystals was measured and compared with detector-response simulations. This enabled pulse-shape analysis algorithms, to extract energy, time and position, to be employed. In addition, tracking algorithms for event reconstruction were developed. The first phase of AGATA is now complete and operational in its first physics campaign. In the future AGATA will be moved between laboratories in Europe and operated in a series of campaigns to take advantage of the different beams and facilities available to maximize its science output. The paper reviews all the achievements made in the AGATA project including all the necessary infrastructure to operate and support the spectrometer., Comment: This version contains a correction of a typing error in the caption of Fig. 2. The DOI to the article published in Nucl. Instr. Meth A was also added

Structural evolution in neutron-rich Os and W isotopes is investigated in terms of the Interacting Boson Model (IBM) Hamiltonian determined by (constrained) Hartree-Fock-Bogoliubov (HFB) calculations with the Gogny-D1S Energy Density Functional (EDF). The interaction strengths of the IBM Hamiltonian are produced by mapping the potential energy surface (PES) of the Gogny-EDF with quadrupole degrees of freedom onto the corresponding PES of the IBM system. We examine the prolate-to-oblate shape/phase transition which is predicted to take place in this region as a function of neutron number $N$ within the considered Os and W isotopic chains. The onset of this transition is found to be more rapid compared to the neighboring Pt isotopes. The calculations also allow prediction of spectroscopic variables (excited state energies and reduced transition probabilities) which are presented for the neutron-rich $^{192,194,196}$W nuclei, for which there is only very limited experimental data available to date., Comment: 7 pages, 5 figures; accepted for publication in Phys. Rev. C

The yrast sequence of the neutron-rich dysprosium isotope 168Dy has been studied using multi-nucleon transfer reactions following collisions between a 460-MeV 82Se beam and a 170Er target. The reaction products were identified using the PRISMA magnetic spectrometer and the gamma rays detected using the CLARA HPGe-detector array. The 2+ and 4+ members of the previously measured ground state rotational band of 168Dy have been confirmed and the yrast band extended up to 10+. A tentative candidate for the 4+ to 2+ transition in 170Dy was also identified. The data on these nuclei and on the lighter even-even dysprosium isotopes are interpreted in terms of Total Routhian Surface calculations and the evolution of collectivity in the vicinity of the proton-neutron valence product maximum is discussed., Comment: 15 pages, 7 figures, submitted to Phys. Rev. C

Preliminary results from an experiment aiming at Dy-170. Submitted to the LNL Annual Report 2008., Comment: 2 pages, 4 figures, Submitted to the LNL Annual Report 2008

Recent theoretical calculations predict a possible existence of nuclei with tetrahedral symmetry: more precisely, the mean-field hamiltonians of such nuclei are symmetric with respect to double point-group Td. In this paper, we focus on the neutron-rich Zirconium isotopes as an example and present realistic mean-field calculations which predict tetrahedral ground-state configurations in 108,110Zr and low-lying excited states of tetrahedral symmetry in a number of N > 66 isotopes. The motivations for focusing on these nuclei, as well as a discussion of the possible experimental signatures of tetrahedral symmetry are also presented., Comment: Accepted in Phys. Rev. C - Rapid Communications

The RF system for the SNS superconducting linac consists of a superconducting cavity, a klystron, and a low-level RF (LLRF) control system. For a proton linac like SNS, the field in each individual cavity needs to be controlled to meet the overall system requirements. The purpose of the LLRF control system is to maintain the RF cavity field to a desired magnitude and phase by controlling the klystron driver signal. The Lorentz force detuning causes the shift of the resonant frequency during the normal operation in the order of a few hundreds hertz. In order to compensate the Lorentz force detuning effects, the cavity is pre-tuned into the middle of the expected frequency shift caused by the Lorentz force detuning. Meanwhile, to reduce the overshoot in the transient response, a feed-forward algorithm, a linear parameter varying gain scheduling (LPV-GS) controller, is proposed to get away a repetitive noised caused by the pulsed operation as well as the Lorentz force detuning effects., Comment: LINAC2000, TUC16