To examine the utility and performance of 50mer oligonucleotide (oligonucleotide probe) microarrays, gene-specific oligonucleotide probes were spotted along with PCR probes onto glass microarrays and the performance of each probe type was evaluated. The specificity of oligonucleotide probes was studied using target RNAs that shared various degrees of sequence similarity. Sensitivity was defined as the ability to detect a 3-fold change in mRNA. No significant difference in sensitivity between oligonucleotide probes and PCR probes was observed and both had a minimum reproducible detection limit of approximately 10 mRNA copies/cell. Specificity studies showed that for a given oligonucleotide probe any 'non-target' transcripts (cDNAs) >75% similar over the 50 base target may show cross-hybridization. Thus non-target sequences which have >75-80% sequence similarity with target sequences (within the oligonucleotide probe 50 base target region) will contribute to the overall signal intensity. In addition, if the 50 base target region is marginally similar, it must not include a stretch of complementary sequence >15 contiguous bases. Therefore, knowledge about the target sequence, as well as its similarity to other mRNAs in the target tissue or RNA sample, is required to design successful oligonucleotide probes for quality microarray results. Together these results validate the utility of oligonucleotide probe (50mer) glass microarrays.

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A microscopic theory for nuclear pairing is proposed through the generalized density matrix formalism. The analytical equations are as simple as that of the BCS theory, and could be solved within a similar computer time. The current theory conserves the exact particle number, and is valid at arbitrary pairing strength (including those below the BCS critical strength). These are the two main advantages over the conventional BCS theory. The theory is also of interests to other mesoscopic systems.

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Recently a procedure by generalized density matrix (GDM) is proposed [1] for calculating a collective/bosonic Hamiltonian microscopically from the shell-model Hamiltonian. In this work we examine the validity of the method by comparing the GDM results with that of the exact shellmodel diagonalization in a number of models. It is shown that the GDM method reproduces the low-lying collective states quite well, both for energies and transition rates, across the whole region going from vibrational to γ-unstable and deformed nuclei. It is a long-standing problem in nuclear physics to understand how macroscopic collective motion arises from microscopic single-particle motion. The shell-model (configuration interaction) successfully reproduces various collective behaviors by diagonalizing the nucleon Hamiltonian in a huge Slater-determinant basis. However, the dimension of the basis makes it impractical except for the cases with only a few valence nucleons. On the other hand, phenomenological bosonic approaches are often successful in fitting the experimental data (first of all the geometric Bohr Hamiltonian [2,3] and the interacting boson model [4]). This shows that, out of the huge Slater-determinant space, there exists a few degrees of freedom with a bosonic nature, which are usually enough in describing the collective states. Serious efforts were devoted to deriving those parameters of the bosonic Hamiltonian from the underlying shell-model Hamiltonian. However, the complete theory is still missing.Recently we proposed [1] a procedure based on the generalized density matrix (GDM) that was originally formulated in Refs. [5][6][7][8]. This procedure is rather simple, clean, and consistent. In compact form, there are only two equations, (14) and (23) in Ref. [1]. Results from the lowest orders give the well-known Hatree-Fock (HF) equations and random phase approximation (RPA). Higher orders fix the anharmonic terms in the collective/bosonic Hamiltonian. The aim of this work is to demonstrate the validity of the GDM method, by comparing its results with that of the exact shell-model diagonalization.In this work for simplicity we restrict ourselves to systems without rotational symmetry. The GDM formulation with angular-momentum vector coupling has been considered in Ref [9]. The single particle (s.p.) space in this work is drawn schematically in Fig. 1. There are two degenerate s.p. levels with energies e = ±1/2. The Fermi surface is in between, thus the lower levels are completely * Electronic address: jial@nscl.msu.edu filled and upper levels are empty. Each s.p. level has a quantum number m that is a half integer. Degenerate time-reversal pair has m with different sign, m1 = −m 1 . For fermions, |1 = −|1 , and we choose the phases such thatWe assume a two-body Hamiltonian,where f 12 = δ 12 e 1 , e 1 are the HF s.p. energies shown in Fig. 1. The density matrix ρ 12 = δ 12 n 1 , where the occupation number n 1 = 1(0) for the lower(upper) s.p. levels. N [a † 1 a † 2 a 3 a 4 ] is the normal-ordering form of operators. T...

We propose a scheme or procedure for doing practical calculations with generalized seniority. It reduces the total computing time by calculating and storing in advance a set of intermediate quantities, taking advantage of the memory capability of modern computers. The requirements and performance of the algorithm are analyzed in detail.

The collective bosonic Hamiltonian is derived from the microscopic nucleonic Hamiltonian by the generalized density matrix method. Independent parameters in the collective Hamiltonian are fixed completely, solutions are given in detail. The random phase approximation corresponds to the harmonic potential of the current approach. The full solution (very close to the exact diagonalization) is obtained over the whole region of parameters including and beyond the instability point of the random phase approximation. The method is tested in the simple model.

Large-scale shell-model calculations are carried out in the model space including neutron-hole orbitals 2p 1/2 , 1f 5/2 , 2p 3/2 , 0i 13/2 , 1f 7/2 and 0h 9/2 to study the structure and electromagnetic properties of neutron deficient Pb isotopes. An optimized effective interaction is used. Good agreement between full shell-model calculations and experimental data is obtained for the spherical states in isotopes 194−206 Pb. The lighter isotopes are calculated with an importance-truncation approach constructed based on the monopole Hamiltonian. The full shell-model results also agree well with our generalized seniority and nucleon-pair-approximation truncation calculations. The deviations between theory and experiment concerning the excitation energies and electromagnetic properties of low-lying 0 + and 2 + excited states and isomeric states may provide a constraint on our understanding of nuclear deformation and intruder configuration in this region.