Conditional Reliability in Uncertain Graphs

Network reliability is a well-studied problem that requires to measure the probability that a target node is reachable from a source node in a probabilistic (or uncertain) graph, i.e., a graph where every edge is assigned a probability of existence. Many approaches and problem variants have been considered in the literature, all assuming that edge-existence probabilities are fixed. Nevertheless, in real-world graphs, edge probabilities typically depend on external conditions. In metabolic networks a protein can be converted into another protein with some probability depending on the presence of certain enzymes. In social influence networks the probability that a tweet of some user will be re-tweeted by her followers depends on whether the tweet contains specific hashtags. In transportation networks the probability that a network segment will work properly or not might depend on external conditions such as weather or time of the day. In this paper we overcome this limitation and focus on conditional reliability, that is assessing reliability when edge-existence probabilities depend on a set of conditions. In particular, we study the problem of determining the k conditions that maximize the reliability between two nodes. We deeply characterize our problem and show that, even employing polynomial-time reliability-estimation methods, it is NP-hard, does not admit any PTAS, and the underlying objective function is non-submodular. We then devise a practical method that targets both accuracy and efficiency. We also study natural generalizations of the problem with multiple source and target nodes. An extensive empirical evaluation on several large, real-life graphs demonstrates effectiveness and scalability of the proposed methods.Comment: 14 pages, 13 figure

Using Metrics Suites to Improve the Measurement of Privacy in Graphs

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.Social graphs are widely used in research (e.g., epidemiology) and business (e.g., recommender systems). However, sharing these graphs poses privacy risks because they contain sensitive information about individuals. Graph anonymization techniques aim to protect individual users in a graph, while graph de-anonymization aims to re-identify users. The effectiveness of anonymization and de-anonymization algorithms is usually evaluated with privacy metrics. However, it is unclear how strong existing privacy metrics are when they are used in graph privacy. In this paper, we study 26 privacy metrics for graph anonymization and de-anonymization and evaluate their strength in terms of three criteria: monotonicity indicates whether the metric indicates lower privacy for stronger adversaries; for within-scenario comparisons, evenness indicates whether metric values are spread evenly; and for between-scenario comparisons, shared value range indicates whether metrics use a consistent value range across scenarios. Our extensive experiments indicate that no single metric fulfills all three criteria perfectly. We therefore use methods from multi-criteria decision analysis to aggregate multiple metrics in a metrics suite, and we show that these metrics suites improve monotonicity compared to the best individual metric. This important result enables more monotonic, and thus more accurate, evaluations of new graph anonymization and de-anonymization algorithms

Diverse Structural Evolution at z > 1 in Cosmologically Simulated Galaxies

From mock Hubble Space Telescope images, we quantify non-parametric statistics of galaxy morphology, thereby predicting the emergence of relationships among stellar mass, star formation, and observed rest-frame optical structure at 1 < z < 3. We measure automated diagnostics of galaxy morphology in cosmological simulations of the formation of 22 central galaxies with 9.3 < log10 M_*/M_sun < 10.7. These high-spatial-resolution zoom-in calculations enable accurate modeling of the rest-frame UV and optical morphology. Even with small numbers of galaxies, we find that structural evolution is neither universal nor monotonic: galaxy interactions can trigger either bulge or disc formation, and optically bulge-dominated galaxies at this mass may not remain so forever. Simulated galaxies with M_* > 10^10 M_sun contain relatively more disc-dominated light profiles than those with lower mass, reflecting significant disc brightening in some haloes at 1 < z < 2. By this epoch, simulated galaxies with specific star formation rates below 10^-9.7 yr^-1 are more likely than normal star-formers to have a broader mix of structural types, especially at M_* > 10^10 M_sun. We analyze a cosmological major merger at z ~ 1.5 and find that the newly proposed MID morphology diagnostics trace later merger stages while G-M20 trace earlier ones. MID is sensitive also to clumpy star-forming discs. The observability time of typical MID-enhanced events in our simulation sample is less than 100 Myr. A larger sample of cosmological assembly histories may be required to calibrate such diagnostics in the face of their sensitivity to viewing angle, segmentation algorithm, and various phenomena such as clumpy star formation and minor mergers.Comment: 23 pages, 16 figures, MNRAS accepted versio

Diamonds on the Hat: Globular Clusters in The Sombrero Galaxy (M104)

Images from the HST ACS are used to carry out a new photometric study of the globular clusters (GCs) in M104, the Sombrero galaxy. The primary focus of our study is the characteristic distribution function of linear sizes (SDF) of the GCs. We measure the effective radii for 652 clusters with PSF-convolved King and Wilson dynamical model fits. The SDF is remarkably similar to those measured for other large galaxies of all types, adding strong support to the view that it is a "universal" feature of globular cluster systems. We develop a more general interpretation of the size distribution function for globular clusters, proposing that the shape of the SDF that we see today for GCs is strongly influenced by the early rapid mass loss during their star forming stage, coupled with stochastic differences from cluster to cluster in the star formation efficiency (SFE) and their initial sizes. We find that the observed SDF shape can be accurately predicted by a simple model in which the protocluster clouds had characteristic sizes of $0.9 \pm 0.1$ pc and SFEs of $0.3 \pm 0.07$. The colors and luminosities of the M104 clusters show the clearly defined classic bimodal form. The blue sequence exhibits a mass/metallicity relation (MMR), following a scaling of heavy-element abundance with luminosity of $Z \sim L^{0.3}$ very similar to what has been found in most giant elliptical galaxies. A quantitative self-enrichment model provides a good first-order match to the data for the same initial SFE and protocluster size that were required to explain the SDF. We also discuss various forms of the globular cluster Fundamental Plane (FP) of structural parameters, and show that useful tests of it can be extended to galaxies beyond the Local Group.Comment: In press for MNRA

Algorithmic Robot Design: Label Maps, Procrustean Graphs, and the Boundary of Non-Destructiveness

This dissertation is focused on the problem of algorithmic robot design. The process of designing a robot or a team of robots that can reliably accomplish a task in an environment requires several key elements. How the problem is formulated can play a big role in the design process. The ability of the model to correctly reflect the environment, the events, and different pieces of the problem is crucial. Another key element is the ability of the model to show the relationship between different designs of a single system. These two elements can enable design algorithms to navigate through the space of all possible designs, and find a set of solutions. In this dissertation, we introduce procrustean graphs, a model for encoding the robot-environment interactions. We also provide a model for navigating through the space of all possible designs, called label maps. Using these models, we focus on answering the following questions: What degradations to the set of sensors or actuators of a robotic system can be tolerated? How different degradations affect the cost of doing a given task? What sets of resources — that is, sensors and actuators — are minimal for accomplishing a specific given job? And how to find such a set? To this end, our general approach is to sample, using a variety of sampling methods, over the space of all maps for a given problem, and use different techniques for answering these questions. We use decision tree classifiers to determine the crucial sensors and actuators required for a robotic system to accomplish its job. We present an algorithm based on space bisection to find the boundary between the feasible and infeasible subspaces of possible designs. We present an algorithm to measure the cost of doing a given task, and another algorithm to find the relationship between different degradation of a robotic system and the cost of doing the task. In all these solutions, we use a variety of techniques to scale up each approach to enable it to solve real world problems. Our experiments show the efficiency of the presented approach

Dynamical Constraints on the Origin of Main Belt Comets

In an effort to understand the origin of the Main Belt Comets (MBCs) 7968 Elst-Pizzaro, 118401, and P/2005 U1, the dynamics of these three icy asteroids and a large number of hypothetical MBCs were studied. Results of extensive numerical integrations of these objects suggest that these MBCs were formed in-place through the collisional break up of a larger precursor body. Simulations point specifically to the Themis family of asteroids as the origin of these objects and rule out the possibility of a cometary origin (i.e. inward scattering of comets from outer solar system and their primordial capture in the asteroid belt). Results also indicate that while 7968 Elst-Pizzaro and 118401 maintain their orbits for 1 Gyr, P/2005 U1 diffuses chaotically in eccentricity and becomes unstable in ~20 Myr. The latter suggest that this MBC used to be a member of the Themis family and is now escaping away. Numerical integrations of the orbits of hypothetical MBCs in the vicinity of the Themis family show a clustering of stable orbits (with eccentricities smaller than 0.2 and inclinations less than 25 deg.) suggesting that many more MBCs may exist in the vicinity of this family (although they might have not been activated yet). The details of the results of simulations and the constraints on the models of the formation and origins of MBCs are presented, and their implications for the detection of more of these objects are discussed.Comment: 14 pages, 3 figures, to be published in the Nov 2009 issue of Meteoritics and Planetary Scienc