A greedy algorithm for computing eigenvalues of a symmetric matrix

We present a greedy algorithm for computing selected eigenpairs of a large sparse matrix $H$ that can exploit localization features of the eigenvector. When the eigenvector to be computed is localized, meaning only a small number of its components have large magnitudes, the proposed algorithm identifies the location of these components in a greedy manner, and obtains approximations to the desired eigenpairs of $H$ by computing eigenpairs of a submatrix extracted from the corresponding rows and columns of $H$. Even when the eigenvector is not completely localized, the approximate eigenvectors obtained by the greedy algorithm can be used as good starting guesses to accelerate the convergence of an iterative eigensolver applied to $H$. We discuss a few possibilities for selecting important rows and columns of $H$ and techniques for constructing good initial guesses for an iterative eigensolver using the approximate eigenvectors returned from the greedy algorithm. We demonstrate the effectiveness of this approach with examples from nuclear quantum many-body calculations, many-body localization studies of quantum spin chains and road network analysis.Comment: 19 pages, 9 figures, 1 tabl

Intruder band mixing in an ab initio description of 12Be

The spectrum of 12Be exhibits exotic features, e.g., an intruder ground state and shape coexistence, normally associated with the breakdown of a shell closure. While previous phenomenological treatments indicated the ground state has substantial contributions from intruder configurations, it is only with advances in computational abilities and improved interactions that this intruder mixing is observed in ab initio no-core shell model (NCSM) predictions. In this work, we extract electromagnetic observables and symmetry decompositions from the NCSM wave functions to demonstrate that the low-lying positive parity spectrum can be explained in terms of mixing of rotational bands with very different intrinsic structure coexisting within the low-lying spectrum. These observed bands exhibit an approximate SU(3) symmetry and are qualitatively consistent with Elliott model predictions.Comment: 10 pages, 7 figure

Natural orbitals for the ab initio no-core configuration interaction approach

Ab initio no-core configuration interaction (NCCI) calculations for the nuclear many-body problem have traditionally relied upon an antisymmetrized product (Slater determinant) basis built from harmonic oscillator orbitals. The accuracy of such calculations is limited by the finite dimensions which are computationally feasible for the truncated many-body space. We therefore seek to improve the accuracy obtained for a given basis size by optimizing the choice of single-particle orbitals. Natural orbitals, which diagonalize the one-body density matrix, provide a basis which maximizes the occupation of low-lying orbitals, thus accelerating convergence in a configuration-interaction basis, while also possibly providing physical insight into the single-particle structure of the many-body wave function. We describe the implementation of natural orbitals in the NCCI framework, and examine the nature of the natural orbitals thus obtained, the properties of the resulting many-body wave functions, and the convergence of observables. After taking $^3\mathrm{He}$ as an illustrative testbed, we explore aspects of NCCI calculations with natural orbitals for the ground state of the $p$-shell neutron halo nucleus $^6\mathrm{He}$.Comment: 26 pages, 17 figure

Magnetic moments of A=3A = 3 nuclei with chiral effective field theory operators

Chiral effective field theory ($\chi$EFT) provides a framework for obtaining internucleon interactions in a systematically improvable fashion from first principles, while also providing for the derivation of consistent electroweak current operators. In this work, we apply consistently derived interactions and currents towards calculating the magnetic dipole moments of the $A=3$ systems Triton and Helium-3. We focus here on LENPIC interactions obtained using semilocal coordinate-space (SCS) regularization. Starting from the momentum-space representation of the LENPIC $\chi$EFT vector current, we derive the SCS-regularized magnetic dipole operator up through N2LO. We then carry out no-core shell model calculations for Triton and Helium-3 systems, using the SCS LENPIC interaction at N2LO in $\chi$EFT, and evaluate the magnetic dipole moments obtained using the consistently derived one-nucleon and two-nucleon electromagnetic currents. As anticipated by prior results with $\chi$EFT currents, the current corrections through N2LO provide improved, but not yet complete, agreement with experiment for the Triton and Helium-3 magnetic dipole moments.Comment: 30 pages, 2 figure

Ab Initio No Core Shell Model - Recent Results and Further Prospects

There has been significant recent progress in solving the long-standing problems of how nuclear shell structure and collective motion emerge from underlying microscopic inter-nucleon interactions. We review a selection of recent significant results within the ab initio No Core Shell Model (NCSM) closely tied to three major factors enabling this progress: (1) improved nuclear interactions that accurately describe the experimental two-nucleon and three-nucleon interaction data; (2) advances in algorithms to simulate the quantum many-body problem with strong interactions; and (3) continued rapid development of high-performance computers now capable of performing $20 \times 10^{15}$ floating point operations per second. We also comment on prospects for further developments.Comment: Invited paper presented at NTSE-2014 and published online in the proceedings (see footnote on p.1

Minor intron splicing is critical for survival of lethal prostate cancer.

The evolutionarily conserved minor spliceosome (MiS) is required for protein expression of ∼714 minor intron-containing genes (MIGs) crucial for cell-cycle regulation, DNA repair, and MAP-kinase signaling. We explored the role of MIGs and MiS in cancer, taking prostate cancer (PCa) as an exemplar. Both androgen receptor signaling and elevated levels of U6atac, a MiS small nuclear RNA, regulate MiS activity, which is highest in advanced metastatic PCa. siU6atac-mediated MiS inhibition in PCa in vitro model systems resulted in aberrant minor intron splicing leading to cell-cycle G1 arrest. Small interfering RNA knocking down U6atac was ∼50% more efficient in lowering tumor burden in models of advanced therapy-resistant PCa compared with standard antiandrogen therapy. In lethal PCa, siU6atac disrupted the splicing of a crucial lineage dependency factor, the RE1-silencing factor (REST). Taken together, we have nominated MiS as a vulnerability for lethal PCa and potentially other cancers

Resolving Troubled Systemically Important Cross-Border Financial Institutions: Is a New Corporate Organizational Form Required?

This paper explores the advantages of a new financial charter for large, complex, internationally active financial institutions that would address the corporate governance challenges of such organizations, including incentive problems in risk decisions and the complicated corporate and regulatory structures that impede cross-border resolutions. The charter envisions a single entity with broad powers in which the extent and timing of compensation are tied to financial results, senior managers and risk takers form a new risk-bearing stakeholder class, and a home-country-based resolution regime operates for the benefit of all creditors. The proposal is offered 1) to highlight the point that even in the face of a more efficient and effective resolution process, incentives for excessive risk taking will continue unless the costs of risk decisions are internalized by institutions, 2) to suggest another avenue for moving toward a streamlined organizational structure and single global resolution process, and 3) to complement other proposals aimed at preserving a large role for market discipline and firm incentives in a post-reform financial system