General Connectivity Distribution Functions for Growing Networks with Preferential Attachment of Fractional Power

We study the general connectivity distribution functions for growing networks with preferential attachment of fractional power, $\Pi_{i} \propto k^{\alpha}$, using the Simon's method. We first show that the heart of the previously known methods of the rate equations for the connectivity distribution functions is nothing but the Simon's method for word problem. Secondly, we show that the case of fractional $\alpha$ the $Z$-transformation of the rate equation provides a fractional differential equation of new type, which coincides with that for PA with linear power, when $\alpha = 1$. We show that to solve such a fractional differential equation we need define a transidental function $\Upsilon (a,s,c;z)$ that we call {\it upsilon function}. Most of all previously known results are obtained consistently in the frame work of a unified theory.Comment: 10 page

Isoscalar monopole excitations in 16^{16}O: α\alpha-cluster states at low energy and mean-field-type states at higher energy

Isoscalar monopole strength function in $^{16}$O up to $E_{x}\simeq40$ MeV is discussed. We found that the fine structures at the low energy region up to $E_{x} \simeq 16$ MeV in the experimental monopole strength function obtained by the $^{16}$O$(\alpha,\alpha^{\prime})$ reaction can be rather satisfactorily reproduced within the framework of the $4\alpha$ cluster model, while the gross three bump structures observed at the higher energy region ($16 \lesssim E_{x} \lesssim 40$ MeV) look likely to be approximately reconciled by the mean-field calculations such as RPA and QRPA. In this paper, it is emphasized that two different types of monopole excitations exist in $^{16}$O; one is the monopole excitation to cluster states which is dominant in the lower energy part ($E_{x} \lesssim 16$ MeV), and the other is the monopole excitation of the mean-field type such as one-particle one-hole ($1p1h$) which {is attributed} mainly to the higher energy part ($16 \lesssim E_{x} \lesssim 40$ MeV). It is found that this character of the monopole excitations originates from the fact that the ground state of $^{16}$O with the dominant doubly closed shell structure has a duality of the mean-field-type {as well as} $\alpha$-clustering {character}. This dual nature of the ground state seems to be a common feature in light nuclei.Comment: 35 pages, 5 figure

Evolution of deformations in medium-mass nuclei

Evolution of quadrupole deformations in $sd$ and $pf$ shell nuclei with mass A= 18$\sim$56 is studied by using deformed Skyrme Hartree-Fock (HF) model with pairing correlations. We point out that the quadrupole deformations of the nuclei with the isospin T=0 and T=1 show strong mass number dependence as a clear manifestation of dynamical evolution of deformation in nuclear many-body systems. The competition between the deformation driving particle-vibration coupling and the closed shell structure is shown in a systematic study of the ratios between the proton and neutron deformations in nuclei with T=$|$T$_z|$=1. Calculated quadrupole and hexadecapole deformations are compared with shell model results and available experimental data. A relation between the skin thickness and the intrinsic Q$_2$ moments is also discussed.Comment: 26 pages, 8figure

Nearly Instantaneous Alternatives in Quantum Mechanics

Usual quantum mechanics predicts probabilities for the outcomes of measurements carried out at definite moments of time. However, realistic measurements do not take place in an instant, but are extended over a period of time. The assumption of instantaneous alternatives in usual quantum mechanics is an approximation whose validity can be investigated in the generalized quantum mechanics of closed systems in which probabilities are predicted for spacetime alternatives that extend over time. In this paper we investigate how alternatives extended over time reduce to the usual instantaneous alternatives in a simple model in non-relativistic quantum mechanics. Specifically, we show how the decoherence of a particular set of spacetime alternatives becomes automatic as the time over which they extend approaches zero and estimate how large this time can be before the interference between the alternatives becomes non-negligible. These results suggest that the time scale over which coarse grainings of such quantities as the center of mass position of a massive body may be extended in time before producing significant interference is much longer than characteristic dynamical time scales.Comment: 12 pages, harvmac, no figure

Incommensurate spin correlations induced by magnetic Fe ions substituted into overdoped Bi1.75Pb0.35Sr1.90CuO6+z

Spin correlations in the overdoped region of Bi1.75Pb0.35Sr1.90CuO6+z have been explored with Fe-doped single crystals characterized by neutron scattering, muon-spin-rotation (muSR) spectroscopy, and magnetic susceptibility measurements. Static incommensurate spin correlations induced by the Fe spins are revealed by elastic neutron scattering. The resultant incommensurability delta is unexpectedly large (~0.2 r.l.u.), as compared with delta ~ 1/8 in overdoped superconductor La2-xSrxCuO4. Intriguingly, the large delta in this overdoped region is close to the hole concentration p. This result is reminiscent of the delta ~ p trend observed in underdoped La2-xSrxCuO4; however, it is inconsistent with the saturation of delta in the latter compound in the overdoped regime. While our findings in Fe-doped Bi1.75Pb0.35Sr1.90CuO6+z support the commonality of incommensurate spin correlations in high-Tc cuprate superconductors, they also suggest that the magnetic response might be dominated by a distinct mechanism in the overdoped region.Comment: 4 pages, 5 figures. Revision in introduction, discussion, and conclusion

In vivo microdialysis reveals age-dependent decrease of brain interstitial fluid tau levels in P301S human tau transgenic mice

Although tau is a cytoplasmic protein, it is also found in brain extracellular fluids, e.g., CSF. Recent findings suggest that aggregated tau can be transferred between cells and extracellular tau aggregates might mediate spread of tau pathology. Despite these data, details of whether tau is normally released into the brain interstitial fluid (ISF), its concentration in ISF in relation to CSF, and whether ISF tau is influenced by its aggregation are unknown. To address these issues, we developed a microdialysis technique to analyze monomeric ISF tau levels within the hippocampus of awake, freely moving mice. We detected tau in ISF of wild-type mice, suggesting that tau is released in the absence of neurodegeneration. ISF tau was significantly higher than CSF tau and their concentrations were not significantly correlated. Using P301S human tau transgenic mice (P301S tg mice), we found that ISF tau is fivefold higher than endogenous murine tau, consistent with its elevated levels of expression. However, following the onset of tau aggregation, monomeric ISF tau decreased markedly. Biochemical analysis demonstrated that soluble tau in brain homogenates decreased along with the deposition of insoluble tau. Tau fibrils injected into the hippocampus decreased ISF tau, suggesting that extracellular tau is in equilibrium with extracellular or intracellular tau aggregates. This technique should facilitate further studies of tau secretion, spread of tau pathology, the effects of different disease states on ISF tau, and the efficacy of experimental treatments

Direct relation between the low-energy spin excitations and superconductivity of overdoped high-TcT_c superconductors

The dynamic spin susceptibility, $\chi''(\omega)$, has been measured over the energy range of $2 \leq \omega \leq 10$ meV for overdoped La$_{2-x}$Sr$_{x}$CuO$_{4}$. Incommensurate (IC) spin excitations are observed at 8 K for all superconducting samples for $0.25 \leq x \leq 0.28$ with $\chi''$ peaking at $\sim 6$ meV. The IC peaks at 6 meV become smaller in intensity with increasing $x$ and, finally, become unobservable for a sample with $x=0.30$ which has no bulk superconductivity. The maximum $\chi''$ decreases linearly with $T_c$(onset) in the overdoped region, implying a direct cooperative relation between the spin fluctuations and the superconductivity.Comment: 4 pages, 4 figure