Multi-objective engineering shape optimization using differential evolution interfaced to the Nimrod/O tool

This paper presents an enhancement of the Nimrod/O optimization tool by interfacing DEMO, an external multiobjective optimization algorithm. DEMO is a variant of differential evolution – an algorithm that has attained much popularity in the research community, and this work represents the first time that true multiobjective optimizations have been performed with Nimrod/O. A modification to the DEMO code enables multiple objectives to be evaluated concurrently. With Nimrod/O’s support for parallelism, this can reduce the wall-clock time significantly for compute intensive objective function evaluations. We describe the usage and implementation of the interface and present two optimizations. The first is a two objective mathematical function in which the Pareto front is successfully found after only 30 generations. The second test case is the three-objective shape optimization of a rib-reinforced wall bracket using the Finite Element software, Code_Aster. The interfacing of the already successful packages of Nimrod/O and DEMO yields a solution that we believe can benefit a wide community, both industrial and academic

Dynamics-based centrality for general directed networks

Determining the relative importance of nodes in directed networks is important in, for example, ranking websites, publications, and sports teams, and for understanding signal flows in systems biology. A prevailing centrality measure in this respect is the PageRank. In this work, we focus on another class of centrality derived from the Laplacian of the network. We extend the Laplacian-based centrality, which has mainly been applied to strongly connected networks, to the case of general directed networks such that we can quantitatively compare arbitrary nodes. Toward this end, we adopt the idea used in the PageRank to introduce global connectivity between all the pairs of nodes with a certain strength. Numerical simulations are carried out on some networks. We also offer interpretations of the Laplacian-based centrality for general directed networks in terms of various dynamical and structural properties of networks. Importantly, the Laplacian-based centrality defined as the stationary density of the continuous-time random walk with random jumps is shown to be equivalent to the absorption probability of the random walk with sinks at each node but without random jumps. Similarly, the proposed centrality represents the importance of nodes in dynamics on the original network supplied with sinks but not with random jumps.Comment: 7 figure

The Grism Lens-Amplified Survey from Space (GLASS). XII. Spatially Resolved Galaxy Star Formation Histories and True Evolutionary Paths at z > 1

Modern data empower observers to describe galaxies as the spatially and biographically complex objects they are. We illustrate this through case studies of four, $z\sim1.3$ systems based on deep, spatially resolved, 17-band + G102 + G141 Hubble Space Telescope grism spectrophotometry. Using full spectrum rest-UV/-optical continuum fitting, we characterize these galaxies' observed $\sim$kpc-scale structures and star formation rates (SFRs) and reconstruct their history over the age of the universe. The sample's diversity---passive to vigorously starforming; stellar masses $\log M_*/M_\odot=10.5$ to $11.2$---enables us to draw spatio-temporal inferences relevant to key areas of parameter space (Milky Way- to super-Andromeda-mass progenitors). Specifically, we find signs that bulge mass-fractions ($B/T$) and SF history shapes/spatial uniformity are linked, such that higher $B/T$s correlate with "inside-out growth" and central specific SFRs that peaked above the global average for all starforming galaxies at that epoch. Conversely, the system with the lowest $B/T$ had a flat, spatially uniform SFH with normal peak activity. Both findings are consistent with models positing a feedback-driven connection between bulge formation and the switch from rising to falling SFRs ("quenching"). While sample size forces this conclusion to remain tentative, this work provides a proof-of-concept for future efforts to refine or refute it: JWST, WFIRST, and the 30-m class telescopes will routinely produce data amenable to this and more sophisticated analyses. These samples---spanning representative mass, redshift, SFR, and environmental regimes---will be ripe for converting into thousands of sub-galactic-scale empirical windows on what individual systems actually looked like in the past, ushering in a new dialog between observation and theory.Comment: 18 pp, 15 figs, 3 tables (main text); 5 pp, 5 figs, 1 table (appendix); Submitted to AAS Journals 1 October 201

Two-dimensional projections of an hypercube

We present a method to project a hypercube of arbitrary dimension on the plane, in such a way as to preserve, as well as possible, the distribution of distances between vertices. The method relies on a Montecarlo optimization procedure that minimizes the squared difference between distances in the plane and in the hypercube, appropriately weighted. The plane projections provide a convenient way of visualization for dynamical processes taking place on the hypercube.Comment: 4 pages, 3 figures, Revtex