On the Metric Dimension of Cartesian Products of Graphs

A set S of vertices in a graph G resolves G if every vertex is uniquely determined by its vector of distances to the vertices in S. The metric dimension of G is the minimum cardinality of a resolving set of G. This paper studies the metric dimension of cartesian products G*H. We prove that the metric dimension of G*G is tied in a strong sense to the minimum order of a so-called doubly resolving set in G. Using bounds on the order of doubly resolving sets, we establish bounds on G*H for many examples of G and H. One of our main results is a family of graphs G with bounded metric dimension for which the metric dimension of G*G is unbounded

First order shape transition and critical point nuclei in Sm isotopes from relativistic mean field approach

The critical point nuclei in Sm isotopes, which marks the first order phase transition between spherical U(5) and axially deformed shapes SU(3), have been investigated in the microscopic quadrupole constrained relativistic mean field (RMF) model plus BCS method with all the most used interactions, i.e., NL1, NL3, NLSH and TM1. The calculated potential energy surfaces show a clear shape transition for the even-even Sm isotopes with $N = 82\sim 96$ and the critical point nuclei are found to be $^{148}$Sm, $^{150}$Sm and $^{152}$Sm. Similar conclusions can also be drawn from the microscopic neutron and proton single particle spectra.Comment: 6 figure

Observation of isotonic symmetry for enhanced quadrupole collectivity in neutron-rich 62,64,66Fe isotopes at N=40

The transition rates for the 2_{1}^{+} states in 62,64,66Fe were studied using the Recoil Distance Doppler-Shift technique applied to projectile Coulomb excitation reactions. The deduced E2 strengths illustrate the enhanced collectivity of the neutron-rich Fe isotopes up to N=40. The results are interpreted by the generalized concept of valence proton symmetry which describes the evolution of nuclear structure around N=40 as governed by the number of valence protons with respect to Z~30. The deformation suggested by the experimental data is reproduced by state-of-the-art shell calculations with a new effective interaction developed for the fpgd valence space.Comment: 4 pages, 2 figure

Role of the Laboratory in Ensuring Global Access to ARV Treatment for HIV-Infected Children: Consensus Statement on the Performance of Laboratory Assays for Early Infant Diagnosis

A two day meeting hosted by the World Health Organization (WHO) and the U.S. Centers for Disease Control and Prevention (CDC) was held in May 2006 in Entebbe, Uganda to review the laboratory performance of virologic molecular methods, particularly the Roche Amplicor DNA PCR version 1.5 assay, in the diagnosis of HIV-1 infection in infants. The meeting was attended by approximately 60 participants from 17 countries. Data on the performance and limitations of the HIV-1 DNA PCR assay from 9 African countries with high-burdens of HIV/AIDS were shared with respect to different settings and HIV- subtypes. A consensus statement on the use of the assay for early infant diagnosis was developed and areas of needed operational research were identified. In addition, consensus was reached on the usefulness of dried blood spot (DBS) specimens in childhood as a means for ensuring greater accessibility to serologic and virologic HIV testing for the paediatric population

Lifetime determination of excited states in Cd-106

Two separate experiments using the Differential Decay Curve Method have been performed to extract mean lifetimes of excited states in 106 Cd. The inedium-spin states of interest were populated by the Mo-98(C-12, 4n) Cd-106 reaction performed at the Wright Nuclear Structure Lab., Yale University. From this experiment, two isomeric state mean lifetimes have been deduced. The low-lying states were populated by the Mo-96(C-13, 3n)Cd-106 reaction performed at the Institut fur Kernphysik, Universitat zu Koln. The mean lifetime of the I-pi = 2(1)(+) state was deduced, tentatively, as 16.4(9) ps. This value differs from the previously accepted literature value from Coulomb excitation of 10.43(9) ps

Synchronized turbo apoptosis induced by cold-shock

In our research on the role of apoptosis in the pathogenesis of the autoimmune disease systemic lupus erythematosus (SLE), we aim to evaluate the effects of early and late apoptotic cells and blebs on antigen presenting cells. This requires the in vitro generation of sufficiently large and homogeneous populations of early and late apoptotic cells. Here, we present a quick method encountered by serendipity that results in highly reproducible synchronized homogeneous apoptotic cell populations. In brief, granulocytic 32Dcl3 cells are incubated on ice for 2 h and subsequently rewarmed at 37°C. After 30–90 min at 37°C more than 80–90% of the cells become early apoptotic (Annexin V positive/propidium iodide negative). After 24 h of rewarming at 37°C 98% of the cells were late apoptotic (secondary necrotic; Annexin V positive/propidium iodide positive). Cells already formed apoptotic blebs at their cell surface after approximately 20 min at 37°C. Inter-nucleosomal chromatin cleavage and caspase activation were other characteristics of this cold-shock-induced process of apoptosis. Consequently, apoptosis could be inhibited by a caspase inhibitor. Finally, SLE-derived anti-chromatin autoantibodies showed a high affinity for apoptotic blebs generated by cold-shock. Overall, cold-shock induced apoptosis is achieved without the addition of toxic compounds or antibodies, and quickly leads to synchronized homogeneous apoptotic cell populations, which can be applied for various research questions addressing apoptosis

Multi-particle effects in non-equilibrium electron tunnelling and field emission

We investigate energy resolved electric current from various correlated host materials under out-of-equilibrium conditions. We find that, due to a combined effect of electron-electron interactions, non-equilibrium and multi-particle tunnelling, the energy resolved current is finite even above the Fermi edge of the host material. In most cases, the current density possesses a singularity at the Fermi level revealing novel manifestations of correlation effects in electron tunnelling. By means of the Keldysh non-equilibrium technique, the current density is calculated for one-dimensional interacting electron systems and for two-dimensional systems, both in the pure limit and in the presence of disorder. We then specialise to the field emission and provide a comprehensive theoretical study of this effect in carbon nanotubes.Comment: 22 pages, 8 figures (eps files

Search for the electric dipole excitations to the 3s1/2⊗[21+⊗31−]3s_{1/2} \otimes [2^{+}_{1} \otimes 3^{-}_{1}] multiplet in 117^{117}Sn

The odd-mass $^{117}$Sn nucleus was investigated in nuclear resonance fluorescence experiments up to an endpoint energy of the incident photon spectrum of 4.1 MeV at the bremsstrahlung facility of the Stuttgart University. More than 50 mainly hitherto unknown levels were found. From the measurement of the scattering cross sections model independent absolute electric dipole excitation strengths were extracted. The measured angular distributions suggested the spins of 11 excited levels. Quasi-particle phonon model calculations including a complete configuration space were performed for the first time for a heavy odd-mass spherical nucleus. These calculations give a clear insight in the fragmentation and distribution of the $E1$, $M1$, and $E2$ excitation strength in the low energy region. It is proven that the $1^{-}$ component of the two-phonon $[2^{+}_{1} \otimes 3^{-}_{1}]$ quintuplet built on top of the $1/2^{+}$ ground state is strongly fragmented. The theoretical calculations are consistent with the experimental data.Comment: 10 pages, 5 figure

Strong fragmentation of low-energy electromagnetic excitation strength in 117^{117}Sn

Results of nuclear resonance fluorescence experiments on $^{117}$Sn are reported. More than 50 $\gamma$ transitions with $E_{\gamma} < 4$ MeV were detected indicating a strong fragmentation of the electromagnetic excitation strength. For the first time microscopic calculations making use of a complete configuration space for low-lying states are performed in heavy odd-mass spherical nuclei. The theoretical predictions are in good agreement with the data. It is concluded that although the E1 transitions are the strongest ones also M1 and E2 decays contribute substantially to the observed spectra. In contrast to the neighboring even $^{116-124}$Sn, in $^{117}$Sn the $1^-$ component of the two-phonon $[2^+_1 \otimes 3^-_1]$ quintuplet built on top of the 1/2$^+$ ground state is proved to be strongly fragmented.Comment: 4 pages, 3 figure