Sparse Partitioning Around Medoids

Partitioning Around Medoids (PAM, k-Medoids) is a popular clustering technique to use with arbitrary distance functions or similarities, where each cluster is represented by its most central object, called the medoid or the discrete median. In operations research, this family of problems is also known as facility location problem (FLP). FastPAM recently introduced a speedup for large k to make it applicable for larger problems, but the method still has a runtime quadratic in N. In this chapter, we discuss a sparse and asymmetric variant of this problem, to be used for example on graph data such as road networks. By exploiting sparsity, we can avoid the quadratic runtime and memory requirements, and make this method scalable to even larger problems, as long as we are able to build a small enough graph of sufficient connectivity to perform local optimization. Furthermore, we consider asymmetric cases, where the set of medoids is not identical to the set of points to be covered (or in the interpretation of facility location, where the possible facility locations are not identical to the consumer locations). Because of sparsity, it may be impossible to cover all points with just k medoids for too small k, which would render the problem unsolvable, and this breaks common heuristics for finding a good starting condition. We, hence, consider determining k as a part of the optimization problem and propose to first construct a greedy initial solution with a larger k, then to optimize the problem by alternating between PAM-style "swap" operations where the result is improved by replacing medoids with better alternatives and "remove" operations to reduce the number of k until neither allows further improving the result quality. We demonstrate the usefulness of this method on a problem from electrical engineering, with the input graph derived from cartographic data

A Trope Theoretical Analysis of Relational Inherence

The trope bundle theories of objects are capable of analyzing monadic inherence (objects having tropes), which is one of their main advantage. However, the best current trope theoretical account of relational tropes, namely, the relata specific view leaves relational inherence (a relational trope relating two or more entities) primitive. This article presents the first trope theoretical analysis of relational inherence by generalizing the trope theoretical analysis of inherence to relational tropes. The analysis reduces the holding of relational inherence to the obtaining of certain other facts about entities of the trope theoretical category system. Moreover, I show that the analysis can deal with asymmetric and non-symmetric relations by assuming that all relation-like tropes are quantities. Finally, I provide an account of the spatial location of tropes in the difficult case in which tropes contribute to determining of the location of other entities

Dynamics of two planets in co-orbital motion

We study the stability regions and families of periodic orbits of two planets locked in a co-orbital configuration. We consider different ratios of planetary masses and orbital eccentricities, also we assume that both planets share the same orbital plane. Initially we perform numerical simulations over a grid of osculating initial conditions to map the regions of stable/chaotic motion and identify equilibrium solutions. These results are later analyzed in more detail using a semi-analytical model. Apart from the well known quasi-satellite (QS) orbits and the classical equilibrium Lagrangian points L4 and L5, we also find a new regime of asymmetric periodic solutions. For low eccentricities these are located at $(\sigma,\Delta\omega) = (\pm 60\deg, \mp 120\deg)$, where \sigma is the difference in mean longitudes and \Delta\omega is the difference in longitudes of pericenter. The position of these Anti-Lagrangian solutions changes with the mass ratio and the orbital eccentricities, and are found for eccentricities as high as ~ 0.7. Finally, we also applied a slow mass variation to one of the planets, and analyzed its effect on an initially asymmetric periodic orbit. We found that the resonant solution is preserved as long as the mass variation is adiabatic, with practically no change in the equilibrium values of the angles.Comment: 9 pages, 11 figure

Implications of Selfish Neighbor Selection in Overlay Networks

In a typical overlay network for routing or content sharing, each node must select a fixed number of immediate overlay neighbors for routing traffic or content queries. A selfish node entering such a network would select neighbors so as to minimize the weighted sum of expected access costs to all its destinations. Previous work on selfish neighbor selection has built intuition with simple models where edges are undirected, access costs are modeled by hop-counts, and nodes have potentially unbounded degrees. However, in practice, important constraints not captured by these models lead to richer games with substantively and fundamentally different outcomes. Our work models neighbor selection as a game involving directed links, constraints on the number of allowed neighbors, and costs reflecting both network latency and node preference. We express a node's "best response" wiring strategy as a k-median problem on asymmetric distance, and use this formulation to obtain pure Nash equilibria. We experimentally examine the properties of such stable wirings on synthetic topologies, as well as on real topologies and maps constructed from PlanetLab and AS-level Internet measurements. Our results indicate that selfish nodes can reap substantial performance benefits when connecting to overlay networks composed of non-selfish nodes. On the other hand, in overlays that are dominated by selfish nodes, the resulting stable wirings are optimized to such great extent that even non-selfish newcomers can extract near-optimal performance through naive wiring strategies.Marie Curie Outgoing International Fellowship of the EU (MOIF-CT-2005-007230); National Science Foundation (CNS Cybertrust 0524477, CNS NeTS 0520166, CNS ITR 0205294, EIA RI 020206

High Ratio of 44Ti/56Ni in Cas A and Axisymmetric Collapse-Driven Supernova Explosion

The large abundance ratio of $^{44}Ti/^{56}Ni$ in Cas A is puzzling. In fact, the ratio seems to be larger than the theoretical constraint derived by Woosley & Hoffman (1991). However, this constraint is obtained on the assumption that the explosion is spherically symmetric, whereas Cas A is famous for the asymmetric form of the remnant. Recently, Nagataki et al. (1997) calculated the explosive nucleosynthesis of axisymmetrically deformed collapse-driven supernova. They reported that the ratio of $^{44}Ti/^{56}Ni$ was enhanced by the stronger alpha-rich freezeout in the polar region. In this paper, we apply these results to Cas A and examine whether this effect can explain the large amount of $^{44}Ti$ and the large ratio of $^{44}Ti/^{56}Ni$. We demonstrate that the conventional spherically symmetric explosion model can not explain the $^{44}$Ti mass produced in Cas A if its lifetime is shorter than $\sim$ 80 years and the intervening space is transparent to the gamma-ray line from the decay of $^{44}$Ti. On the other hand, we show the axisymmetric explosion models can solve the problem. We expect the same effect from a three dimensionally asymmetric explosion, since the stronger alpha-rich freezeout will also occur in that case in the region where the larger energy is deposited.Comment: 10 pages, LaTeX text and 3 postscript figure

Asymmetric Actor Critic for Image-Based Robot Learning

Deep reinforcement learning (RL) has proven a powerful technique in many sequential decision making domains. However, Robotics poses many challenges for RL, most notably training on a physical system can be expensive and dangerous, which has sparked significant interest in learning control policies using a physics simulator. While several recent works have shown promising results in transferring policies trained in simulation to the real world, they often do not fully utilize the advantage of working with a simulator. In this work, we exploit the full state observability in the simulator to train better policies which take as input only partial observations (RGBD images). We do this by employing an actor-critic training algorithm in which the critic is trained on full states while the actor (or policy) gets rendered images as input. We show experimentally on a range of simulated tasks that using these asymmetric inputs significantly improves performance. Finally, we combine this method with domain randomization and show real robot experiments for several tasks like picking, pushing, and moving a block. We achieve this simulation to real world transfer without training on any real world data.Comment: Videos of experiments can be found at http://www.goo.gl/b57WT

Codes for Asymmetric Limited-Magnitude Errors With Application to Multilevel Flash Memories

Several physical effects that limit the reliability and performance of multilevel flash memories induce errors that have low magnitudes and are dominantly asymmetric. This paper studies block codes for asymmetric limited-magnitude errors over q-ary channels. We propose code constructions and bounds for such channels when the number of errors is bounded by t and the error magnitudes are bounded by ℓ. The constructions utilize known codes for symmetric errors, over small alphabets, to protect large-alphabet symbols from asymmetric limited-magnitude errors. The encoding and decoding of these codes are performed over the small alphabet whose size depends only on the maximum error magnitude and is independent of the alphabet size of the outer code. Moreover, the size of the codes is shown to exceed the sizes of known codes (for related error models), and asymptotic rate-optimality results are proved. Extensions of the construction are proposed to accommodate variations on the error model and to include systematic codes as a benefit to practical implementation