A collection of n anonymous mobile robots is deployed on a unit-perimeter ring or a unit-length line segment. Every robot starts moving at constant speed, and bounces each time it meets any other robot or segment endpoint, changing its walk direction. We study the problem of position discovery, in which the task of each robot is to detect the presence and the initial positions of all other robots. The robots cannot communicate or perceive information about the environment in any way other than by bouncing. Each robot has a clock allowing it to observe the times of its bounces. The robots have no control on their walks, which are determined by their initial positions and the starting directions. Each robot executes the same position detection algorithm, which receives input data in real-time about the times of the bounces, and terminates when the robot is assured about the existence and the positions of all the robots. Some initial configuration of robots are shown to be infeasible - no position detection algorithm exists for them. We give complete characterizations of all infeasible initial configurations for both the ring and the segment, and we design optimal position detection algorithms for all feasible configurations. For the case of the ring, we show that all robot configurations in which not all the robots have the same initial direction are feasible. We give a position detection algorithm working for all feasible configurations. The cost of our algorithm depends on the number of robots starting their movement in each direction. If the less frequently used initial direction is given to k ≤ n/2 robots, the time until completion of the algorithm by the last robot is 1/2 ⌈n/k⌉. We prove that this time is optimal. By contrast to the case of the ring, for the unit segment we show that the family of infeasible configurations is exactly the set of so-called symmetric configurations. We give a position detection algorithm which works for all feasible configurations on the segment in time 2, and this algorithm is also proven to be optimal.
We consider the rendezvous problem for identical mobile agents (i.e., running the same deterministic algorithm) with tokens in a synchronous torus with a sense of direction and show that there is a striking computational difference between one and more tokens. More specifically, we show that 1) two agents with a constant number of unmovable tokens, or with one movable token, each cannot rendezvous if they have o(log n) memory, while they can perform rendezvous with detection as long as they have one unmovable token and O(log n) memory; in contrast, 2) when two agents have two movable tokens each then rendezvous (respectively, rendezvous with detection) is possible with constant memory in an arbitrary n × m (respectively, n × n) torus; and finally, 3) two agents with three movable tokens each and constant memory can perform rendezvous with detection in a n × m torus. This is the first publication in the literature that studies tradeoffs between the number of tokens, memory and knowledge the agents need in order to meet in such a network.
We study the feasibility and time of communication in random geometric radio networks, where nodes fail randomly with positive correlation. We consider a set of radio stations with the same communication range, distributed in a random uniform way on a unit square region. In order to capture fault dependencies, we introduce the ranged spot model in which damaging events, called spots, occur randomly and independently on the region, causing faults in all nodes located within distance s from them. Node faults within distance 2s become dependent in this model and are positively correlated. We investigate the impact of the spot arrival rate on the feasibility and the time of communication in the fault-free part of the network. We provide an algorithm which broadcasts correctly with probability 1 - ε in faulty random geometric radio networks of diameter D in time O(D + log1/ε).
Current research depicts suburbs as becoming more heterogeneous in terms of socio-economic status. Providing a novel analysis, this paper engages with that research by operationalising suburban ways of living (homeownership, single-family dwelling occupancy and automobile use) and relating them to the geography of income across 26 Canadian metropolitan areas. We find that suburban ways of living exist in new areas and remain associated with higher incomes even as older suburbs, as places, have become more diverse. In the largest cities the relationship between income and suburban ways of living is weaker due to the growth of condominiums in downtowns that allow higher income earners to live urban lifestyles. Homeownership is overwhelmingly more important than other variables in explaining the geography of income across 26 metropolitan areas.
We present two results for path traversal in trees, where the traversal is performed in an asymptotically optimal number of I/Os and the tree structure is represented succinctly. Our first result is for bottom-up traversal that starts with a node in the tree T and traverses a path to the root. For blocks of size B, a tree on N nodes, and for a path of length K, we design data structures that permit traversal of the bottom-up path in O(K/B) I/Os using only bits, for an arbitrarily selected constant, ε, where 0∈<∈ε<∈1. Our second result is for top-down traversal in binary trees. We store T using (3∈+∈q)N∈+∈o(N) bits, where q is the number of bits required to store a key, while top-down traversal can still be performed in an asymptotically optimal number of I/Os.
A correspondence between database tuples as causes for query answers in databases and tuple-based repairs of inconsistent databases with respect to denial constraints has already been established. In this work, answer-set programs that specify repairs of databases are used as a basis for solving computational and reasoning problems about causes. Here, causes are also introduced at the attribute level by appealing to a both null-based and attribute-based repair semantics. The corresponding repair programs are presented, and they are used as a basis for computation and reasoning about attribute-level causes.
We consider online routing strategies for routing between the vertices of embedded planar straight line graphs. Our results include (1) two deterministic memoryless routing strategies, one that works for all Delaunay triangulations and the other that works for all regular triangulations, (2) a randomized memoryless strategy that works for all triangulations, (3) an O(1) memory strategy that works for all convex subdivisions, (4) an O(1) memory strategy that approximates the shortest path in Delaunay triangulations, and (5) theoretical and experimental results on the competitiveness of these strategies.
Social defeat in mice is a potent stressor that promotes the development of depressive- and anxiety-like behaviours, as well as variations of neuroendocrine and brain neurotransmitter activity. Although environmental enrichment may protect against some of the adverse behavioural and biological effects of social defeat, it seems that, among male group-housed mice maintained in an enriched environment (EE), aggressive behaviours may be more readily instigated, thus promoting distress and exacerbating psychopathological features. Thus, although an EE can potentially have numerous beneficial effects, these may depend on the general conditions in which mice were raised. It was observed in the current investigations that EE group-housed BALB/cByJ mice displayed increased anxiety-like behaviours compared to their counterparts maintained in a standard environment (SE). Furthermore, in response to social defeat, EE group-housed male mice exhibited decreased weight gain, exaggerated corticosterone elevations and altered hippocampal norepinephrine utilization compared to their SE counterparts. These effects were not apparent in the individually housed EE mice and, in fact, enrichment among these mice appeared to buffer against serotonin changes induced by social defeat. It is possible that some potentially beneficial effects of enrichment were precluded among group-housed mice, possibly owing to social disturbances that might occur in these conditions. In fact, even if social interaction is an essential feature of enrichment, it seems that some of the positive effects of this housing condition might be optimal when mice are housed individually, particularly with regard to buffering the effects of social defeat.
The electrical resistivity distribution at the base of La Soufrière of Guadeloupe lava dome is reconstructed by using transmission electrical resistivity data obtained by injecting an electrical current between two electrodes located on opposite sides of the volcano. Several pairs of injection electrodes are used in order to constitute a data set spanning the whole range of azimuths, and the electrical potential is measured along a cable covering an angular sector of ≈120? along the basis of the dome. The data are inverted to performa slice electrical resistivity tomography (SERT) with specific functions implemented in the EIDORS open source package dedicated to electrical impedance tomography applied to medicine and geophysics. The resulting image shows the presence of highly conductive regions separated by resistive ridges. The conductive regions correspond to unconsolidated material saturated by hydrothermal fluids. Two of them are associated with partial flank collapses and may represent large reservoirs that could have played an important role during past eruptive events. The resistive ridges may represent massive andesite and are expected to constitute hydraulic barriers.
Let (S,d) be a finite metric space, where each element p S has a non-negative weight w(p). We study spanners for the set S with respect to weighted distance function d w , where d w (p,q) is w(p)+d(p,q)+wq if p≠q and 0 otherwise. We present a general method for turning spanners with respect to the d-metric into spanners with respect to the d w -metric. For any given ε>0, we can apply our method to obtain (5+ε)-spanners with a linear number of edges for three cases: points in Euclidean space ℝ d , points in spaces of bounded doubling dimension, and points on the boundary of a convex body in ℝ d where d is the geodesic distance function. We also describe an alternative method that leads to (2+ε)-spanners for points in ℝ d and for points on the boundary of a convex body in ℝ d . The number of edges in these spanners is O(nlogn). This bound on the stretch factor is nearly optimal: in any finite metric space and for any ε>0, it is possible to assign weights to the elements such that any non-complete graph has stretch factor larger than 2-ε.