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Nominal set plays a central role in a group-theoretic extension of finite automata to those over an infinite set of data values. Moerman et al. proposed an active learning algorithm for nominal word automata with the equality symmetry. In this paper, we introduce deterministic bottom-up nominal tree automata (DBNTA), which operate on trees whose nodes are labelled with elements of an orbit finite nominal set. We then prove a Myhill-Nerode theorem for the class of languages recognized by DBNTA and propose an active learning algorithm for DBNTA. The algorithm can deal with any data symmetry that admits least support, not restricted to the equality symmetry and/or the total order symmetry. To prove the termination of the algorithm, we define a partial order on nominal sets and show that there is no infinite chain of orbit finite nominal sets with respect to this partial order between any two orbit finite sets.

We have studied the electronic structure of bulk single crystals and epitaxial films of magnetite Fe$_3$O$_4$. Fe $2p$ core-level spectra show clear differences between hard x-ray (HAX-) and soft x-ray (SX-) photoemission spectroscopy (PES), indicative of surface effects. The bulk-sensitive spectra exhibit temperature ($T$)-dependent charge excitations across the Verwey transition at $T_V$=122 K, which is missing in the surface-sensitive spectra. An extended impurity Anderson model full-multiplet analysis reveals roles of the three distinct Fe-species (A-Fe$^{3+}$, B-Fe$^{2+}$, B-Fe$^{3+}$) below $T_V$ for the Fe $2p$ spectra, and its $T-$dependent evolution. The Fe $2p$ HAXPES spectra show a clear magnetic circular dichroism (MCD) in the metallic phase of magnetized 100-nm-thick films. The model calculations also reproduce the MCD and identify the magnetically distinct sites associated with the charge excitations. Valence band HAXPES shows finite density of states at $E_F$ for the polaronic metal with remnant order above $T_V$, and a clear gap formation below $T_V$. The results indicate that the Verwey transition is driven by changes in the strongly correlated and magnetically active B-Fe$^{2+}$ and B-Fe$^{3+}$ electronic states, consistent with resistivity and bulk-sensitive optical spectra., Comment: 5 pages, 4 figures Accepted in Physical Review Letters

We use hard x-ray photoemission spectroscopy (HAXPES) to investigate the electronic structure of YbAl2, for which the Yb valence has not been consistently reported to date. The bulk sensitivity and the analytical simplicity provided by the Yb 3d core-level HAXPES allow a reliable determination of the mean valence of Yb ions. For YbAl2, it is evaluated to be +2.20, which remains nearly unchanged below 300 K. The Kondo resonance peak with an extremely high Kondo temperature (above 2000 K) is clearly identified in the valence-band spectra. The results indicate that a coherent Kondo state can be robust even in a nearly divalent system.

In layered polar semiconductor BiTeI, giant Rashba-type spin-split band dispersions show up due to the crystal structure asymmetry and the strong spin-orbit interaction. Here we investigate the 3-dimensional (3D) bulk band structures of BiTeI using the bulk-sensitive $h\nu$-dependent soft x-ray angle resolved photoemission spectroscopy (SX-ARPES). The obtained band structure is shown to be well reproducible by the first-principles calculations, with huge spin splittings of ${\sim}300$ meV at the conduction-band-minimum and valence-band-maximum located in the $k_z=\pi/c$ plane. It provides the first direct experimental evidence of the 3D Rashba-type spin splitting in a bulk compound., Comment: 9 pages, 4 figures

The three-dimensional Fermi surface structure of hole-doped metallic layered nickelate Eu2-xSrxNiO4 (x=1.1), an important counterpart to the isostructural superconducting cuprate La2-xSrxCuO4, is investigated by energy-dependent soft-x-ray angle-resolved photoemission spectroscopy. In addition to a large cylindrical hole Fermi surface analogous to the cuprates, we observe a Gamma-centered 3z2-r2-derived small electron pocket. This finding demonstrates that in the layered nickelate the 3z2-r2 band resides close to the x2-y2 one in energy. The resultant multi-band feature with varying orbital character as revealed may strongly work against the emergence of the high-temperature superconductivity., Comment: 5 pages, 4 figures. Accepted in Physical Review B (Rapid Communication)

We performed temperature dependent X-ray linear dichroism (XLD) experiments on an iron pnictide system, Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$ with $x$=0.00 and 0.05, to experimentally verify existence of orbital ordering (OO). We observed clear XLD in polarization dependent X-ray absorption spectra of Fe $L$ edges. By exploiting the difference in the temperature dependent behaviors, we were able to separate OO and structure contributions to XLD. The observed OO signal indicates different occupation numbers for $d_{yz}$ and $d_{zx}$ orbitals and supports existence of a ferro-OO. The results are also consistent with the theoretical prediction. Moreover, we find substantial OO signal above the transition temperature, which suggests that OO fluctuation exists well above the transition temperature.

We study the surface and bulk electronic structure of the room-temperature ferromagnet Co:TiO2 anatase films using soft and hard x-ray photoemission spectroscopy with probe sensitivities of ~1 nm and ~10 nm, respectively. We obtain direct evidence of metallic Ti$^{3+}$ states in the bulk, which get suppressed to give a surface semiconductor, thus indicating a surface-bulk dichotomy. X-ray absorption and high-sensitivity resonant photoemission spectroscopy reveal Ti$^{3+}$ electrons at the Fermi level (E$_F$) and high-spin Co$^{2+}$ electrons occurring away from E$_F$. The results show the importance of the charge neutrality condition: Co$^{2+}$ + V$_{O}$$^{2-}$ + 2Ti$^{4+}$ $\leftrightarrow$ Co$^{2+}$ + 2Ti$^{3+}$ (V$_O$ is oxygen vacancy), which gives rise to the elusive Ti 3d carriers mediating ferromagnetism via the Co 3d-O 2p-Ti 3d exchange interaction pathway of the occupied orbitals., Comment: 4 pages, 4 figures

We investigate the electronic structure of Chromium Nitride (CrN) across the first-order magneto-structural transition at T_N ~ 286 K. Resonant photoemission spectroscopy shows a gap in the 3d partial density of states at the Fermi level and an On-site Coulomb energy U ~ 4.5 eV, indicating strong electron-electron correlations. Bulk-sensitive high resolution (6 meV) laser photoemission reveals a clear Fermi edge indicating an antiferromagnetic metal below T_N. Hard x-ray Cr 2p core-level spectra show T-dependent changes across T_N which originate from screening due to coherent states as substantiated by cluster model calculations using the experimentally observed U. The electrical resistivity confirms an insulator above T_N (E_g ~ 70 meV) which becomes a disordered metal below T_N. The results indicate CrN transforms from a correlated insulator to an antiferromagnetic metal, coupled to the magneto-structural transition., Comment: Submitted to Physical Review Letters (February 2010) 11 pages, 3 figures in the main text, 1 Supplementary Information

Epitaxial ultrathin Fe films on fcc Cu(001) exhibit a spin spiral (SS), in contrast to the ferromagnetism of bulk bcc Fe. We study the in-plane and out-of-plane Fermi surfaces (FSs) of the SS in 8 monolayer Fe/Cu(001) films using energy dependent soft x-ray momentum-resolved photoemission spectroscopy. We show that the SS originates in nested regions confined to out-of-plane FSs, which are drastically modified compared to in-plane FSs. From precise reciprocal space maps in successive zones, we obtain the associated real space compressive strain of 1.5+-0.5% along c-axis. An autocorrelation analysis quantifies the incommensurate ordering vector q=(2pi/a)(0,0,~0.86), favoring a SS and consistent with magneto-optic Kerr effect experiments. The results reveal the importance of in-plane and out-of-plane FS mapping for ultrathin films., Comment: 4 pages, 3 figures

Electronic structures of the quantum critical superconductor beta-YbAlB4 and its polymorph alpha-YbAlB4 are investigated by using bulk-sensitive hard x-ray photoemission spectroscopy. From the Yb 3d core level spectra, the values of the Yb valence are estimated to be ~2.73 and ~2.75 for alpha- and beta-YbAlB4, respectively, thus providing clear evidence for valence fluctuations. The valence band spectra of these compounds also show Yb2+ peaks at the Fermi level. These observations establish an unambiguous case of a strong mixed valence at quantum criticality for the first time among heavy fermion systems, calling for a novel scheme for a quantum critical model beyond the conventional Doniach picture in beta-YbAlB4., Comment: 4 pages, 3 figures, revised version accepted for publication in PRL

The Magneli phase Ti4O7 exhibits two sharp jumps in resistivity with coupled structural transitions as a function of temperature at Tc1=142 K and Tc2=154 K. We have studied electronic structure changes across the two transitions using 7 eV laser, soft x-ray and hard x-ray (HX) photoemission spectroscopy (PES). Ti 2p-3d resonant PES and HX-PES show a clear metallic Fermi-edge and mixed valency above Tc2. The low temperature phase below Tc1 shows a clear insulating gap of 100 meV. The intermediate phase between Tc1 and Tc2 indicates a pseudogap coexisting with remnant coherent states. HX-PES and complementary calculations have confirmed the coherent screening in the strongly correlated intermediate phase. The results suggest existence of a highly anomalous state sandwiched between the mixed-valent Fermi liquid and charge ordered Mott-insulating phase in Ti4O7., Comment: 4 pages, 3 figures

Hard x-ray photoemission and optical spectroscopies have been performed on YbS and Yb metal to determine the precise $f$-electron occupation. A comparison of the photoemission spectra with the energy loss functions in bulk and surface, obtained from optical reflectivity, enables us to distinguish between the energy loss satellite of Yb$^{2+}$ peak and Yb$^{3+}$ multiplet. The results clearly indicate a purely divalent Yb state except for the surface of YbS. We demonstrate that the present method is highly reliable in identifying the electronic structure and the mean valence in $f$-electron systems.

High energy resolution photoelectron spectroscopy of conduction electrons in the vicinity of the Fermi-edge in Al and Au at the excitation energy of 880 and 7940 eV was carried out using synchrotron radiation. For the excitation energy of 7940 eV, the observed Fermi energy of Al shows a remarkable shift to higher binding energy as compared with that of Au, with accompanying broadening. This is due to the recoil effect of the emitted photoelectrons. The observed spectra are well reproduced by a simple model of Bloch electrons based on the isotropic Debye model., Comment: 5 pages, 2 figures

At interfaces between polar and nonpolar perovskite oxides, an unusual electron-doping has been previously observed, due to electronic reconstructions. We report on remote hole-doping at an interface composed of only polar layers, revealed by high-resolution hard x-ray core-level photoemission spectroscopy. In LaAlO3/LaVO3/LaAlO3 trilayers, the vanadium valence systematically evolves from the bulk value of V3+ to higher oxidation states with decreasing LaAlO3 cap layer thickness. These results provide a synthetic approach to hole-doping transition metal oxide heterointerfaces without invoking a polar discontinuity.

We have re-examined the valence-band (VB) and core-level electronic structure of NiO by means of hard and soft x-ray photoemission spectroscopy (PES). The spectral weight of the lowest energy state found to be enhanced in the bulk sensitive Ni 2p core-level PES. A configuration-interaction model including the bound state screening has shown significant agreement with the core-level spectra, and the off and on-resonance VB spectra. These results identify the lowest energy state in core-level and VB-PES as the Zhang-Rice doublet bound state, consistent with the spin-fermion model and recent ab initio calculation with dynamical mean-field theory (LDA + DMFT)., Comment: 4 pages, 3 figures

We have studied the electronic structure of multilayers composed of a band insulator LaAlO$_3$ (LAO) and a Mott insulator LaVO$_3$ (LVO) by means of hard x-ray photoemission spectroscopy, which has a probing depth as large as $\sim 60 {\AA}$. The Mott-Hubbard gap of LVO remained open at the interface, indicating that the interface is insulating unlike the LaTiO$_3$/SrTiO$_3$ multilayers. We found that the valence of V in LVO were partially converted from V$^{3+}$ to V$^{4+}$ only at the interface on the top side of the LVO layer and that the amount of V$^{4+}$ increased with LVO layer thickness. We suggest that the electronic reconstruction to eliminate the polarity catastrophe inherent in the polar heterostructure is the origin of the highly asymmetric valence change at the LVO/LAO interfaces., Comment: 5 pages, 7 figures

We have performed a detailed study of Cu $2p$ core-level spectra in single layer La$_{2-x}$Sr$_{x}$CuO$_{4}$, La doped Bi$_2$Sr$_{1.6}$La$_{0.4}$CuO$_{6+\delta}$ (Bi2201) and bilayer Bi$_2$Sr$_{2}$CaCu$_{2}$O$_{8+\delta}$ (Bi2212) high-temperature superconductors by using hard x-ray photoemission (HX-PES). We identify the Cu$^{2+}$ derived (i) the Zhang-Rice singlet (ZRS) feature, (ii) the $d^{n+1}\underline{L}$ (ligand screened) feature, (iii) the $d^{n}$ satellite feature, as well as the hole-doping derived high binding energy feature in the main peak. In Bi-based cuprates, intensities of the $d^{n}$ satellite features seem to be strongly enhanced compared to La$_{2-x}$Sr$_{x}$CuO$_{4}$. From x-ray photon energy dependent measurements, it is shown that the increased intensity in the satellite region is associated with Bi $4s$ core-level spectral intensity. The corrected $d^{n}$ satellite intensity is independent of the doping content or number of Cu-O layers. Our results suggest a correlation of the relative intensity of ZRS feature and hole-doping induced high binding energy spectral changes in the main peak with superconductivity., Comment: 6 pages, 3 figures

The temperature ($T$) dependent metal-insulator transition (MIT) in VO$_2$ is investigated using bulk sensitive hard x-ray ($\sim$ 8 keV) valence band, core level, and V 2$p-3d$ resonant photoemission spectroscopy (PES). The valence band and core level spectra are compared with full-multiplet cluster model calculations including a coherent screening channel. Across the MIT, V 3$d$ spectral weight transfer from the coherent ($d^1\underbar{\it {C}}$ final) states at Fermi level to the incoherent ($d^{0}+d^1\underbar{\it {L}}$ final) states, corresponding to the lower Hubbard band, lead to gap-formation. The spectral shape changes in V 1$s$ and V 2$p$ core levels as well as the valence band are nicely reproduced from a cluster model calculations, providing electronic structure parameters. Resonant-PES finds that the $d^1\underbar{\it{L}}$ states resonate across the V 2$p-3d$ threshold in addition to the $d^{0}$ and $d^1\underbar{\it {C}}$ states. The results support a Mott-Hubbard transition picture for the first order MIT in VO$_2$., Comment: 6 pages, 3 figures. to be published in Phys. Rev. B

Semiconducting skutterudite CeFe$_4$P$_{12}$ is investigated by synchrotron x-ray photoemission spectroscopy (PES) and x-ray absorption spectroscopy (XAS). Ce 3$d$ core-level PES and 3$d-4f$ XAS, in combination with single impurity Anderson model (SIAM) calculations, confirm features due to $f^0$, $f^1$ and $f^2$ configurations. The Ce 4$f$ density of states (DOS) indicates absence of a Kondo resonance at Fermi level, but can still be explained by SIAM with a small gap in non-$f$ DOS. While Ce 4$f$ partial DOS from band structure calculations are also consistent with the main Ce 4$f$ DOS, the importance of SIAM for core and valence spectra indicates Kondo semiconducting mixed valence for CeFe$_4$P$_{12}$, derived from strong hybridization between non-$f$ conduction and Ce 4$f$ DOS., Comment: 4pages, 4figures

We study the mixed valence transition ($T$$_{v}$ $\sim$80 K) in EuNi$_{2}$(Si$_{0.2}$Ge$_{0.8}$)$_{2}$ using Eu 3$d-4f$ X-ray absorption spectroscopy (XAS) and resonant photoemission spectroscopy (RESPES). The Eu$^{2+}$ and Eu$^{3+}$ main peaks show a giant resonance and the spectral features match very well with atomic multiplet calculations. The spectra show dramatic temperature ($T$)-dependent changes over large energies ($\sim$10 eV) in RESPES and XAS. The observed non-integral mean valencies of $\sim$2.35 $\pm$ 0.03 ($T$ = 120 K) and $\sim$2.70 $\pm$ 0.03 ($T$ = 40 K) indicate homogeneous mixed valence above and below $T$$_{v}$. The redistribution between Eu$^{2+}$$4f^7$+$[spd]^0$ and Eu$^{3+}$$4f^6$+$[spd]^1$ states is attributed to a hybridization change coupled to a Kondo-like volume collapse., Comment: 4 pages, 3 figures

Hard X-ray Photoemission spectroscopy (PES) of copper core electronic states, with a probing depth of $\sim$60 \AA, is used to show that the Zhang-Rice singlet feature is present in La$_2$CuO$_4$ but is absent in Nd$_2$CuO$_4$. Hole- and electron doping in La$_{2-x}$Sr$_x$CuO$_4$ (LSCO) and Nd$_{2-x}$Ce$_x$CuO$_4$ (NCCO) result in new well-screened features which are missing in soft X-ray PES. Impurity Anderson model calculations establish metallic screening as its origin, which is strongly suppressed within 15 $\text{\AA}$ of the surface. Complemented with X-ray absorption spectroscopy, the small chemical-potential shift in core levels ($\sim0.2$ eV) are shown to be consistent with modifications of valence and conduction band states spanning the band gap ($\sim1$ eV) upon hole- and electron-doping in LSCO and NCCO., Comment: 4 pages, 4 figures

We study the electronic structure of the recently discovered diluted magnetic semiconductor Ga$_{1-x}$Cr$_{x}$N ($x$ = 0.01-0.10). A systematic study of the changes in the $occupied$ and $unoccupied$ ligand (N) partial density of states (DOS) of the host lattice is carried out using N 1$s$ soft x-ray emission and absorption spectroscopy, respectively. X-ray absorption measurements confirm the wurtzite N 2$p$ DOS and substitutional doping of Cr into Ga-sites. Coupled changes in the $occupied$ and $unoccupied$ N 2$p$ character DOS of Ga$_{1-x}$Cr$_{x}$N identify states responsible for ferromagnetism consistent with band structure calculations., Comment: 5 pages, 4 figures, submitted to Phys. Rev. B

Using hard x-ray (HX ; $h\nu$ = 5.95 keV) synchrotron photoemission spectroscopy (PES), we study the intrinsic electronic structure of La$_{1-x}$Sr$_x$MnO$_3$ (LSMO) thin films. Comparison of Mn 2$p$ core-levels with Soft x-ray (SX ; $h\nu$ $\sim$ 1000 eV) -PES shows a clear additional well-screened feature only in HX-PES. Take-off-angle dependent data indicate its bulk ($\ge$ 20 {\AA}) character. The doping and temperature dependence track the ferromagnetism and metallicity of the LSMO series. Cluster model calculations including charge transfer from doping induced states show good agreement, confirming this picture of bulk properties reflected in Mn 2$p$ core-levels using HX-PES., Comment: 4 pages, 4 figures; accepted for publication in Phys. Rev. Lett

We report bulk-sensitive hard X-ray ($h\nu$ = 5.95 KeV) core level photoemission spectroscopy (PES) of single crystal V$_{1.98}$Cr$_{0.02}$O$_{3}$ and the high-$T_c$ cuprate Bi$_2$Sr$_{2}$CaCu$_{2}$O$_{8+\delta}$ (Bi2212). V$_{1.98}$Cr$_{0.02}$O$_{3}$ exhibits low binding energy "satellites" to the V $2p$ "main lines" in the metallic phase, which are suppressed in the antiferromagnetic insulator phase. In contrast, the Cu $2p$ spectra of Bi2212 do not show temperature dependent features, but a comparison with soft X-ray PES indicates a large increase in the $2p^5 3d^9$ "satellites" or $3d^9$ weight in the bulk. Cluster model calculations, including full multiplet structure and a screening channel derived from the coherent band at the Fermi energy, give very satisfactory agreement with experiments.

High-energy (h$\nu$ = 5.95 keV) synchrotron Photoemission spectroscopy (PES) is used to study bulk electronic structure of Na$_{0.35}$CoO$_{2}$.1.3H$_{2}$O, the layered superconductor. In contrast to 3-dimensional doped Co oxides, Co $\it{2p}$ core level spectra show well-separated Co$^{3+}$ and Co$^{4+}$ ions. Cluster calculations suggest low spin Co$^{3+}$ and Co$^{4+}$ character, and a moderate on-site Coulomb correlation energy U$_{dd}\sim$3-5.5 eV. Photon dependent valence band PES identifies Co $\it{3d}$ and O $\it{2p}$ derived states, in near agreement with band structure calculations., Comment: 4 pages 4 figures Revised text added reference

A recombination emission spectrum is applied to study the local lattice distortion due to core excitation in graphite. The recombination emission spectrum reveals a long low-energy tail when the C $1s$ electron is excited to the $\sigma^*$ core exciton state. This indicates a large local lattice distortion around the excited carbon atom within a core hole lifetime ($\sim$10fs). Theoretical calculation based upon an ionic cluster model well reproduces the experiments. The strong polarization correlation between incident and emitted X-rays is conclusive evidence of symmetry breaking in the core exciton state due to coupling with asymmetric vibrational modes., Comment: 9 pages, 4 figures

Soft X-ray Angle-Resolved Photoemission Spectroscopy is applied to study in-plane band dispersions of Nickel as a function of probing depth. Photon energies between 190 and 780 eV were used to effectively probe up to 3-7 layers. The results show layer dependent band dispersion of the Delta_2 minority-spin band which crosses the Fermi level in 3 or more layers, in contrast to known top 1-2 layers dispersion obtained using ultra-violet rays. The layer dependence corresponds to an increased value of exchange splitting and suggests reduced correlation effects in the bulk compared to the surface., Comment: 7 pages, 3 figures Revised text and figure

We describe a start-timing detector for the PHENIX experiment at the relativistic heavy-ion collider RHIC. The role of the detector is to detect a nuclear collision, provide precise time information with an accuracy of 50ps, and determine the collision point along the beam direction with a resolution of a few cm. Technical challenges are that the detector must be operational in a wide particle-multiplicity range in a high radiation environment and a strong magnetic field. We present the performance of the prototype and discuss the final design of the detector., Comment: 12 pages, LaTeX, 9 gif and 4 ps figures. Submitted to NIM A