Eigenvector Synchronization, Graph Rigidity and the Molecule Problem

The graph realization problem has received a great deal of attention in recent years, due to its importance in applications such as wireless sensor networks and structural biology. In this paper, we extend on previous work and propose the 3D-ASAP algorithm, for the graph realization problem in $\mathbb{R}^3$, given a sparse and noisy set of distance measurements. 3D-ASAP is a divide and conquer, non-incremental and non-iterative algorithm, which integrates local distance information into a global structure determination. Our approach starts with identifying, for every node, a subgraph of its 1-hop neighborhood graph, which can be accurately embedded in its own coordinate system. In the noise-free case, the computed coordinates of the sensors in each patch must agree with their global positioning up to some unknown rigid motion, that is, up to translation, rotation and possibly reflection. In other words, to every patch there corresponds an element of the Euclidean group Euc(3) of rigid transformations in $\mathbb{R}^3$, and the goal is to estimate the group elements that will properly align all the patches in a globally consistent way. Furthermore, 3D-ASAP successfully incorporates information specific to the molecule problem in structural biology, in particular information on known substructures and their orientation. In addition, we also propose 3D-SP-ASAP, a faster version of 3D-ASAP, which uses a spectral partitioning algorithm as a preprocessing step for dividing the initial graph into smaller subgraphs. Our extensive numerical simulations show that 3D-ASAP and 3D-SP-ASAP are very robust to high levels of noise in the measured distances and to sparse connectivity in the measurement graph, and compare favorably to similar state-of-the art localization algorithms.Comment: 49 pages, 8 figure

Generalized decomposition and cross entropy methods for many-objective optimization

Decomposition-based algorithms for multi-objective optimization problems have increased in popularity in the past decade. Although their convergence to the Pareto optimal front (PF) is in several instances superior to that of Pareto-based algorithms, the problem of selecting a way to distribute or guide these solutions in a high-dimensional space has not been explored. In this work, we introduce a novel concept which we call generalized decomposition. Generalized decomposition provides a framework with which the decision maker (DM) can guide the underlying evolutionary algorithm toward specific regions of interest or the entire Pareto front with the desired distribution of Pareto optimal solutions. Additionally, it is shown that generalized decomposition simplifies many-objective problems by unifying the three performance objectives of multi-objective evolutionary algorithms – convergence to the PF, evenly distributed Pareto optimal solutions and coverage of the entire front – to only one, that of convergence. A framework, established on generalized decomposition, and an estimation of distribution algorithm (EDA) based on low-order statistics, namely the cross-entropy method (CE), is created to illustrate the benefits of the proposed concept for many objective problems. This choice of EDA also enables the test of the hypothesis that low-order statistics based EDAs can have comparable performance to more elaborate EDAs

Modeling Individual Cyclic Variation in Human Behavior

Cycles are fundamental to human health and behavior. However, modeling cycles in time series data is challenging because in most cases the cycles are not labeled or directly observed and need to be inferred from multidimensional measurements taken over time. Here, we present CyHMMs, a cyclic hidden Markov model method for detecting and modeling cycles in a collection of multidimensional heterogeneous time series data. In contrast to previous cycle modeling methods, CyHMMs deal with a number of challenges encountered in modeling real-world cycles: they can model multivariate data with discrete and continuous dimensions; they explicitly model and are robust to missing data; and they can share information across individuals to model variation both within and between individual time series. Experiments on synthetic and real-world health-tracking data demonstrate that CyHMMs infer cycle lengths more accurately than existing methods, with 58% lower error on simulated data and 63% lower error on real-world data compared to the best-performing baseline. CyHMMs can also perform functions which baselines cannot: they can model the progression of individual features/symptoms over the course of the cycle, identify the most variable features, and cluster individual time series into groups with distinct characteristics. Applying CyHMMs to two real-world health-tracking datasets -- of menstrual cycle symptoms and physical activity tracking data -- yields important insights including which symptoms to expect at each point during the cycle. We also find that people fall into several groups with distinct cycle patterns, and that these groups differ along dimensions not provided to the model. For example, by modeling missing data in the menstrual cycles dataset, we are able to discover a medically relevant group of birth control users even though information on birth control is not given to the model.Comment: Accepted at WWW 201

The temporal and spatial evolution of the starburst in ESO 338-IG04 as probed by its star clusters

In this paper we use ultra-violet (UV) and optical HST photometry in five bands, and an extensive set of spectral evolutionary synthesis scenarios to investigate the age and masses of 124 star clusters in the luminous blue compact galaxy ESO338-IG04 (Tololo 1924-416). The very small internal reddening makes ESO 338-IG04 an excellent laboratory for studying the formation of massive star clusters. We have used the star clusters to trace the temporal and spatial evolution of the starburst, and to put constraints on the star formation activity over a cosmological time-scale. The present starburst has been active for about 40 Myr. A standard Salpeter initial mass function (IMF) extending up to 120 solar masses provides the best fit to the data, although a flatter IMF cannot be excluded. The compact star clusters provide 30-40 percent of the UV luminosity and star formation activity. We find no evidence for dust obscuration even among the youngest (< 1 Myr) clusters. The fraction of stellar mass contained in compact star clusters is found to be several percent, which is an unusually high value. The intermediate age clusters show a flattened space distribution which agrees with the isophotal shape of the galaxy, whereas the oldest clusters seem to have a spherical distribution.(abridged)Comment: Accepted for publication in A&

The spatial distribution of galaxies of different spectral types in the massive intermediate-redshift cluster MACSJ0717.5+3745

We present the results of a wide-field spectroscopic analysis of the galaxy population of the massive cluster MACSJ0717.5+3745 and the surrounding filamentary structure (z=0.55), as part of our systematic study of the 12 most distant clusters in the MACS sample. Of 1368 galaxies spectroscopically observed in this field, 563 are identified as cluster members; of those, 203 are classified as emission-line galaxies, 260 as absorption-line galaxies, and 17 as E+A galaxies (defined by $\frac{H_{\delta}+H_{\gamma}}{2}>6$\AA and no detection of [OII] and $H_{\beta}$ in emission). The variation of the fraction of emission- and absorption-line galaxies as a function of local projected galaxy density confirms the well-known morphology-density relation, and becomes flat at projected galaxy densities less than $\sim 20Mpc^{-2}. Interestingly, 16 out of 17 E+A galaxies lie (in projection) within the ram-pressure stripping radius around the cluster core, which we take to be direct evidence of ram-pressure stripping being the primary mechanism that terminates star-formation in the E+A population of galaxy clusters. This conclusion is supported by the rarity of E+A galaxies in the filament which rules out galaxy mergers as the dominant driver of evolution for E+A galaxies in clusters. In addition, we find the 42 e(a) and 27 e(b) member galaxies, i.e., the dusty-starburst and starburst galaxies respectively, to be spread out across almost the entire study area. Their spatial distribution, which shows a strong preference for the filament region, suggests that starbursts are triggered in relatively low-density environments as galaxies are accreted from the field population.Comment: 16 pages, 15 figures, accepted by Ap