Understanding the truth about subjectivity

Results of two experiments show children’s understanding of diversity in personal preference is incomplete. Despite acknowledging diversity, in Experiment 1(N=108), 6- and 8-year-old children were less likely than adults to see preference as a legitimate basis for personal tastes and more likely to say a single truth could be found about a matter of taste. In Experiment 2 (N=96), 7- and 9-year-olds were less likely than 11- and 13-yearolds to say a dispute about a matter of preference might not be resolved. These data suggest that acceptance of the possibility of diversity does not indicate an adult-like understanding of subjectivity. An understanding of the relative emphasis placed on objective and subjective factors in different contexts continues to develop into adolescence

SQPR: Stream Query Planning with Reuse

When users submit new queries to a distributed stream processing system (DSPS), a query planner must allocate physical resources, such as CPU cores, memory and network bandwidth, from a set of hosts to queries. Allocation decisions must provide the correct mix of resources required by queries, while achieving an efficient overall allocation to scale in the number of admitted queries. By exploiting overlap between queries and reusing partial results, a query planner can conserve resources but has to carry out more complex planning decisions. In this paper, we describe SQPR, a query planner that targets DSPSs in data centre environments with heterogeneous resources. SQPR models query admission, allocation and reuse as a single constrained optimisation problem and solves an approximate version to achieve scalability. It prevents individual resources from becoming bottlenecks by re-planning past allocation decisions and supports different allocation objectives. As our experimental evaluation in comparison with a state-of-the-art planner shows SQPR makes efficient resource allocation decisions, even with a high utilisation of resources, with acceptable overheads

Gaia Stellar Kinematics in the Head of the Orion A Cloud: Runaway Stellar Groups and Gravitational Infall

This work extends previous kinematic studies of young stars in the Head of the Orion A cloud (OMC-1/2/3/4/5). It is based on large samples of infrared, optical, and X-ray selected pre-main sequence stars with reliable radial velocities and Gaia-derived parallaxes and proper motions. Stellar kinematic groups are identified assuming they mimic the motion of their parental gas. Several groups are found to have peculiar kinematics: the NGC 1977 cluster and two stellar groups in the Extended Orion Nebula (EON) cavity are caught in the act of departing their birthplaces. The abnormal motion of NGC 1977 may have been caused by a global hierarchical cloud collapse, feedback by massive Ori OB1ab stars, supersonic turbulence, cloud-cloud collision, and/or slingshot effect; the former two models are favored by us. EON groups might have inherited anomalous motions of their parental cloudlets due to small-scale `rocket effects' from nearby OB stars. We also identify sparse stellar groups to the east and west of Orion A that are drifting from the central region, possibly a slowly expanding halo of the Orion Nebula Cluster. We confirm previously reported findings of varying line-of-sight distances to different parts of the cloud's Head with associated differences in gas velocity. Three-dimensional movies of star kinematics show contraction of the groups of stars in OMC-1 and global contraction of OMC-123 stars. Overall, the Head of Orion A region exhibits complex motions consistent with theoretical models involving hierarchical gravitational collapse in (possibly turbulent) clouds with OB stellar feedback.Comment: Accepted for publication in MNRAS. 26 pages, 13 figures. The two 3-D stellar kinematic movies, aimed as Supplementary Materials, can be found on YouTube at: https://youtu.be/B4GHCVvCYfo (`restricted' sample) and https://youtu.be/6fUu8sP0QFI (`full' sample

Approximation Algorithms for the Max-Buying Problem with Limited Supply

We consider the Max-Buying Problem with Limited Supply, in which there are $n$ items, with $C_i$ copies of each item $i$, and $m$ bidders such that every bidder $b$ has valuation $v_{ib}$ for item $i$. The goal is to find a pricing $p$ and an allocation of items to bidders that maximizes the profit, where every item is allocated to at most $C_i$ bidders, every bidder receives at most one item and if a bidder $b$ receives item $i$ then $p_i \leq v_{ib}$. Briest and Krysta presented a 2-approximation for this problem and Aggarwal et al. presented a 4-approximation for the Price Ladder variant where the pricing must be non-increasing (that is, $p_1 \geq p_2 \geq \cdots \geq p_n$). We present an $e/(e-1)$-approximation for the Max-Buying Problem with Limited Supply and, for every $\varepsilon > 0$, a $(2+\varepsilon)$-approximation for the Price Ladder variant

Tight local approximation results for max-min linear programs

In a bipartite max-min LP, we are given a bipartite graph \myG = (V \cup I \cup K, E), where each agent $v \in V$ is adjacent to exactly one constraint $i \in I$ and exactly one objective $k \in K$. Each agent $v$ controls a variable $x_v$. For each $i \in I$ we have a nonnegative linear constraint on the variables of adjacent agents. For each $k \in K$ we have a nonnegative linear objective function of the variables of adjacent agents. The task is to maximise the minimum of the objective functions. We study local algorithms where each agent $v$ must choose $x_v$ based on input within its constant-radius neighbourhood in \myG. We show that for every $\epsilon>0$ there exists a local algorithm achieving the approximation ratio ${\Delta_I (1 - 1/\Delta_K)} + \epsilon$. We also show that this result is the best possible -- no local algorithm can achieve the approximation ratio ${\Delta_I (1 - 1/\Delta_K)}$. Here $\Delta_I$ is the maximum degree of a vertex $i \in I$, and $\Delta_K$ is the maximum degree of a vertex $k \in K$. As a methodological contribution, we introduce the technique of graph unfolding for the design of local approximation algorithms.Comment: 16 page

Representations and KK-theory of Discrete Groups

Let $\Gamma$ be a discrete group of finite virtual cohomological dimension with certain finiteness conditions of the type satisfied by arithmetic groups. We define a representation ring for $\Gamma$, determined on its elements of finite order, which is of finite type. Then we determine the contribution of this ring to the topological $K$-theory $K^*(B\Gamma)$, obtaining an exact formula for the difference in terms of the cohomology of the centralizers of elements of finite order in $\Gamma$.Comment: 4 page