Diversification and Intensification in Hybrid Metaheuristics for Constraint Satisfaction Problems

Metaheuristics are used to find feasible solutions to hard Combinatorial Optimization Problems (COPs). Constraint Satisfaction Problems (CSPs) may be formulated as COPs, where the objective is to reduce the number of violated constraints to zero. The popular puzzle Sudoku is an NP-complete problem that has been used to study the effectiveness of metaheuristics in solving CSPs. Applying the Simulated Annealing (SA) metaheuristic to Sudoku has been shown to be a successful method to solve CSPs. However, the ‘easy-hard-easy’ phase-transition behavior frequently attributed to a certain class of CSPs makes finding a solution extremely difficult in the hard phase because of the vast search space, the small number of solutions and a fitness landscape marked by many plateaus and local minima. Two key mechanisms that metaheuristics employ for searching are diversification and intensification. Diversification is the method of identifying diverse promising regions of the search space and is achieved through the process of heating/reheating. Intensification is the method of finding a solution in one of these promising regions and is achieved through the process of cooling. The hard phase area of the search terrain makes traversal without becoming trapped very challenging. Running the best available method - a Constraint Propagation/Depth-First Search algorithm - against 30,000 benchmark problem-instances, 20,240 remain unsolved after ten runs at one minute per run which we classify as very hard. This dissertation studies the delicate balance between diversification and intensification in the search process and offers a hybrid SA algorithm to solve very hard instances. The algorithm presents (a) a heating/reheating strategy that incorporates the lowest solution cost for diversification; (b) a more complex two-stage cooling schedule for faster intensification; (c) Constraint Programming (CP) hybridization to reduce the search space and to escape a local minimum; (d) a three-way swap, secondary neighborhood operator for a low expense method of diversification. These techniques are tested individually and in hybrid combinations for a total of 11 strategies, and the effectiveness of each is evaluated by percentage solved and average best run-time to solution. In the final analysis, all strategies are an improvement on current methods, but the most remarkable results come from the application of the “Quick Reset” technique between cooling stages

Modeling the Large Scale Structures of Astrophysical Jets in the Magnetically Dominated Limit

We suggest a new approach that could be used for modeling both the large scale behavior of astrophysical jets and the magnetically dominated explosions in astrophysics. We describe a method for modeling the injection of magnetic fields and their subsequent evolution in a regime where the free energy is magnetically dominated. The injected magnetic fields, along with their associated currents, have both poloidal and toroidal components, and they are not force free. The dynamic expansion driven by the Lorentz force of the injected fields is studied using 3-dimensional ideal magnetohydrodynamic simulations. The generic behavior of magnetic field expansion, the interactions with the background medium, and the dependence on various parameters are investigated.Comment: Accepted to ApJ, May 10, 2006 issue, 12 figures total (3 color figures

Pseudobulges in the Disk Galaxies NGC 7690 and NGC 4593

We present Ks-band surface photometry of NGC 7690 (Hubble type Sab) and NGC 4593 (SBb). We find that, in both galaxies, a major part of the "bulge" is as flat as the disk and has approximately the same color as the inner disk. In other words, the "bulges" of these galaxies have disk-like properties. We conclude that these are examples of "pseudobulges" -- that is, products of secular dynamical evolution. Nonaxisymmetries such as bars and oval disks transport disk gas toward the center. There, star formation builds dense stellar components that look like -- and often are mistaken for -- merger-built bulges but that were constructed slowly out of disk material. These pseudobulges can most easily be recognized when, as in the present galaxies, they retain disk-like properties. NGC 7690 and NGC 4593 therefore contribute to the growing evidence that secular processes help to shape galaxies. NGC 4593 contains a nuclear ring of dust that is morphologically similar to nuclear rings of star formation that are seen in many barred and oval galaxies. The nuclear dust ring is connected to nearly radial dust lanes in the galaxy's bar. Such dust lanes are a signature of gas inflow. We suggest that gas is currently accumulating in the dust ring and hypothesize that the gas ring will starburst in the future. The observations of NGC 4593 therefore suggest that major starburst events that contribute to pseudobulge growth can be episodic.Comment: 10 pages, 3 Postscript figures; requires emulateapj.cls, apjfonts.sty, and psfig.sty; accepted for publication in ApJ; for a version with full resolution figures, see http://chandra.as.utexas.edu/~kormendy/n7690.pd

Accretion disc-stellar magnetosphere interaction: field line inflation and the effect on the spin-down torque

We calculate the structure of a force-free magnetosphere which is assumed to corotate with a central star and which interacts with an embedded differentially rotating accretion disc. The magnetic and rotation axes are aligned and the stellar field is assumed to be a dipole. We concentrate on the case when the amount of field line twisting through the disc-magnetosphere interaction is large and consider different outer boundary conditions. In general the field line twisting produces field line inflation (eg. Bardou & Heyvaerts 1996) and in some cases with large twisting many field lines can become open. We calculate the spin-down torque acting between the star and the disc and we find that it decreases significantly for cases with large field line twisting. This suggests that the oscillating torques observed for some accreting neutron stars could be due to the magnetosphere varying between states with low and high field line inflation. Calculations of the spin evolution of T Tauri stars may also have to be revised in light of the significant effect that field line twisting has on the magnetic torque resulting from star-disc interactions.Comment: Accepted by MNRAS. 21 pages, 15 figures. LaTeX2e in the MN style. PostScript files are also available from http://www-star.qmw.ac.uk/~va/ or by e-mail: [email protected]

Halo Star Streams in the Solar Neighborhood

We have assembled a sample of halo stars in the solar neighborhood to look for halo substructure in velocity and angular momentum space. Our sample includes red giants, RR Lyrae, and red horizontal branch stars within 2.5 kpc of the Sun with [Fe/H] less than -1.0. It was chosen to include stars with accurate distances, space velocities, and metallicities as well as well-quantified errors. We confirm the existence of the streams found by Helmi and coworkers, which we refer to as the H99 streams. These streams have a double-peaked velocity distribution in the z direction. We use the results of modeling of the H99 streams by Helmi and collaborators to test how one might use v_z velocity information and radial velocity information to detect kinematic substructure in the halo. We find that detecting the H99 streams with radial velocities alone would require a large sample. We use the velocity distribution of the H99 streams to estimate their age. From our model of the progenitor of the H99 streams, we determine that it was accreted between 6 and 9 Gyr ago. The H99 streams have [alpha/Fe] abundances similar to other halo stars in the solar neighborhood, suggesting that the gas that formed these stars were enriched mostly by Type II SNe. We have also discovered in angular momentum space two other possible substructures, which we refer to as the retrograde and prograde outliers. The retrograde outliers are likely to be halo substructure, but the prograde outliers are most likely part of the smooth halo. The retrograde outliers have significant structure in the v_phi direction and show a range of [alpha/Fe]. The methods presented in this paper can be used to exploit the kinematic information present in future large databases like RAVE, SDSSII/SEGUE, and Gaia.Comment: 46 pages, 13 figures, and 9 tables. Minor changes to text to match proofed version of the paper. Low resolution figures. High resolution version at http://www.astro.wisc.edu/~kepley/solar_streams.p

Resolving the Formation of Protogalaxies. I. Virialization

(Abridged) Galaxies form in hierarchically assembling dark matter halos. With cosmological three dimensional adaptive mesh refinement simulations, we explore in detail the virialization of baryons in the concordance cosmology, including optically thin primordial gas cooling. We focus on early protogalaxies with virial temperatures of 10^4 K and their progenitors. Without cooling, virial heating occurs in shocks close to the virial radius for material falling in from voids. Material in dense filaments penetrates deeper to about half that radius. With cooling the virial shock position shrinks and also the filaments reach scales as small as a third the virial radius. The temperatures in protogalaxies found in adiabatic simulations decrease by a factor of two from the center and show flat entropy cores. In cooling halos the gas reaches virial equilibrium with the dark matter potential through its turbulent velocities. We observe turbulent Mach numbers ranging from one to three in the cooling cases. This turbulence is driven by the large scale merging and interestingly remains supersonic in the centers of these early galaxies even in the absence of any feedback processes. The virial theorem is shown to approximately hold over 3 orders of magnitude in length scale with the turbulent pressure prevailing over the thermal energy. The turbulent velocity distributions are Maxwellian and by far dominate the small rotation velocities associated with the total angular momentum of the galaxies. Decomposing the velocity field using the Cauchy-Stokes theorem, we show that ample amounts of vorticity are present around shocks even at the very centers of these objects.Comment: 13 pages, 6 figures. Submitted to ApJ on 8 March 2007. Revised manuscript. Comments welcom

Resolving the Formation of Protogalaxies. II. Central Gravitational Collapse

Numerous cosmological hydrodynamic studies have addressed the formation of galaxies. Here we choose to study the first stages of galaxy formation, including non-equilibrium atomic primordial gas cooling, gravity and hydrodynamics. Using initial conditions appropriate for the concordance cosmological model of structure formation, we perform two adaptive mesh refinement simulations of ~10^8 M_sun galaxies at high redshift. The calculations resolve the Jeans length at all times with more than 16 cells and capture over 14 orders of magnitude in length scales. In both cases, the dense, 10^5 solar mass, one parsec central regions are found to contract rapidly and have turbulent Mach numbers up to 4. Despite the ever decreasing Jeans length of the isothermal gas, we only find one site of fragmentation during the collapse. However, rotational secular bar instabilities transport angular momentum outwards in the central parsec as the gas continues to collapse and lead to multiple nested unstable fragments with decreasing masses down to sub-Jupiter mass scales. Although these numerical experiments neglect star formation and feedback, they clearly highlight the physics of turbulence in gravitationally collapsing gas. The angular momentum segregation seen in our calculations plays an important role in theories that form supermassive black holes from gaseous collapse.Comment: Replaced with accepted version. To appear in ApJ v681 (July 1

Physical Conditions of Accreting Gas in T Tauri Star Systems

We present results from a low resolution (R~300) near-infrared spectroscopic variability survey of actively accreting T Tauri stars (TTS) in the Taurus-Auriga star forming region. Paschen and Brackett series H I recombination lines were detected in 73 spectra of 15 classical T Tauri systems. The values of the Pan/PaB, Brn/BrG, and BrG/Pan H I line ratios for all observations exhibit a scatter of < 20% about the weighted mean, not only from source to source, but also for epoch-to-epoch variations in the same source. A representative or `global' value was determined for each ratio in both the Paschen and Brackett series as well as the BrG/Pan line ratios. A comparison of observed line ratio values was made to those predicted by the temperature and electron density dependent models of Case B hydrogen recombination line theory. The measured line ratios are statistically well-fit by a tightly constrained range of temperatures (T < 2000 K) and electron densities 1e9 < n_e < 1e10 cm^-3. A comparison of the observed line ratio values to the values predicted by the optically thick and thin local thermodynamic equilibrium cases rules out these conditions for the emitting H I gas. Therefore, the emission is consistent with having an origin in a non-LTE recombining gas. While the range of electron densities is consistent with the gas densities predicted by existing magnetospheric accretion models, the temperature range constrained by the Case B comparison is considerably lower than that expected for accreting gas. The cooler gas temperatures will require a non-thermal excitation process (e.g., coronal/accretion-related X-rays and UV photons) to power the observed line emission.Comment: 12 pages, emulateapj format, Accepted for publication in Ap

Radio Continuum Emission at 1.4 GHz from KISS Emission-Line Galaxies

We have searched the Faint Images of the Radio Sky at Twenty centimeters (FIRST) and the NRAO VLA Sky Survey (NVSS) 1.4 GHz radio surveys for sources that are coincident with emission-line galaxy (ELG) candidates from the KPNO International Spectroscopic Survey (KISS). A total of 207 of the 2157 KISS ELGs (~10%) in the first two H-alpha-selected survey lists were found to possess radio detections in FIRST and/or NVSS. Follow-up spectra exist for all of the radio detections, allowing us to determine the activity type (star-forming vs. AGN) for the entire sample. We explore the properties of the radio-detected KISS galaxies in order to gain a better insight into the nature of radio-emitting galaxies in the local universe (z < 0.1). No dwarf galaxies were detected, despite the large numbers of low-luminosity galaxies present in KISS, suggesting that lower mass, lower luminosity objects do not possess strong galaxian-scale magnetic fields. Due to the selection technique used for KISS, our radio ELGs represent a quasi-volume-limited sample, which allows us to develop a clearer picture of the radio galaxy population at low redshift. Nearly 2/3rds of the KISS radio galaxies are starburst/star-forming galaxies, which is in stark contrast to the results of flux-limited radio surveys that are dominated by AGNs and elliptical galaxies (i.e., classic radio galaxies). While there are many AGNs among the KISS radio galaxies, there are no objects with large radio powers in our local volume. We derive a radio luminosity function (RLF) for the KISS ELGs that agrees very well with previous RLFs that adequately sample the lower-luminosity radio population.Comment: Accepted for publication in the Astronomical Journal (April 2004); 23 pages, 16 figure

Investigating planet formation in circumstellar disks: CARMA observations of RY Tau and DG Tau

(Abridged) We present CARMA observations of the thermal dust emission from the circumstellar disks around the young stars RYTau and DGTau at wavelengths of 1.3mm and 2.8mm. The angular resolution of the maps is as high as 0.15arcsec, or 20AU at the distance of the Taurus cloud, which is a factor of 2 higher than has been achieved to date at these wavelengths. The unprecedented detail of the resulting disk images enables us to address three important questions related to the formation of planets. (1) What is the radial distribution of the circumstellar dust? (2) Does the dust emission show any indication of gaps that might signify the presence of (proto-)planets? (3) Do the dust properties depend on the orbital radius? We find that modeling the disk surface density in terms of either a classical power law or the similarity solution for viscous disk evolution, reproduces the observations well. The 1.3mm image from RYTau shows two peaks separated by 0.2arcsec with a decline in the dust emission toward the stellar position, which is significant at about 2-4sigma. For both RYTau and DGTau, the dust emission at radii larger than 15 AU displays no significant deviation from an unperturbed viscous disk model. In particular, no radial gaps in the dust distribution are detected. Under reasonable assumptions, we exclude the presence of planets more massive than 5 Jupiter masses orbiting either star at distances between about 10 and 60 AU. The radial variation of the dust opacity slope, beta, was investigated by comparing the 1.3mm and 2.8mm observations. We find mean values of beta of 0.5 and 0.7 for DGTau and RYTau respectively. Variations in beta are smaller than 0.7 between 20 and 70 AU. These results confirm that the circumstellar dust throughout these disks differs significantly from dust in the interstellar medium.Comment: ApJ in press