10,334 research outputs found
Common adversaries form alliances: modelling complex networks via anti-transitivity
Anti-transitivity captures the notion that enemies of enemies are friends,
and arises naturally in the study of adversaries in social networks and in the
study of conflicting nation states or organizations. We present a simplified,
evolutionary model for anti-transitivity influencing link formation in complex
networks, and analyze the model's network dynamics. The Iterated Local
Anti-Transitivity (or ILAT) model creates anti-clone nodes in each time-step,
and joins anti-clones to the parent node's non-neighbor set. The graphs
generated by ILAT exhibit familiar properties of complex networks such as
densification, short distances (bounded by absolute constants), and bad
spectral expansion. We determine the cop and domination number for graphs
generated by ILAT, and finish with an analysis of their clustering
coefficients. We interpret these results within the context of real-world
complex networks and present open problems
Unveiling residual, spontaneous recovery from subtle hemispatial neglect three years after stroke
A common and disabling consequence of stroke is the difficulty in processing contralesional space (i.e., hemispatial neglect). According to paper-and-pencil tests, neglect remits or stabilizes in severity within a few months after a brain injury. This arbitrary temporal limit, however, is at odds with neglect's well-known dependency on task-sensitivity. The present study tested the hypothesis that the putative early resolution of neglect might be due to the insensitivity of testing methods rather than to the lack of spontaneous recovery at later stages. A right hemisphere stroke patient was studied longitudinally for 3 years. According to paper-and-pencil tests the patient showed no symptom of hemispatial neglect 1 month post stroke. Awareness of spatially lateralized visual targets was then assessed by means of computer based single-and dual tasks requiring an additional top-down deployment of attention for the parallel processing of visual or auditory stimuli. Errorless performance at computer-based tasks was reached at month 12 and maintained until month 29 after stroke. A bottom-up manipulation was then implemented by reducing target diameter. Following this change, more than 50% of contralesional targets were omitted, mostly under dual-tasking. At months 40 and 41 the same task revealed a significant (but not complete) reduction in the number of contralesional omissions. lpsilesional targets were, in contrast, still errorless detected. The coupling of a bottom-up (target change) and a top-down (dual-tasking) manipulation revealed the presence of a long-lasting spontaneous recovery from contralesional spatial awareness deficits. In contrast, neither manipulation was effective when implemented separately. After having excluded the potential confound of practice effects, it was concluded that not only the presence but also the time course of hemispatial neglect strongly depends on the degree of attentional engagement required by the task
Characterizations and algorithms for generalized Cops and Robbers games
We propose a definition of generalized Cops and Robbers games where there are
two players, the Pursuer and the Evader, who each move via prescribed rules. If
the Pursuer can ensure that the game enters into a fixed set of final
positions, then the Pursuer wins; otherwise, the Evader wins. A relational
characterization of the games where the Pursuer wins is provided. A precise
formula is given for the length of the game, along with an algorithm for
computing if the Pursuer has a winning strategy whose complexity is a function
of the parameters of the game. For games where the position of one player does
not affect the available moves of he other, a vertex elimination ordering
characterization, analogous to a cop-win ordering, is given for when the
Pursuer has a winning strategy
Distinguishing homomorphisms of infinite graphs
We supply an upper bound on the distinguishing chromatic number of certain
infinite graphs satisfying an adjacency property. Distinguishing proper
-colourings are generalized to the new notion of distinguishing
homomorphisms. We prove that if a graph satisfies the connected
existentially closed property and admits a homomorphism to , then it admits
continuum-many distinguishing homomorphisms from to join
Applications are given to a family universal -colourable graphs, for a
finite core
Adaptive tracking of a time-varying field with a quantum sensor
Sensors based on single spins can enable magnetic field detection with very
high sensitivity and spatial resolution. Previous work has concentrated on
sensing of a constant magnetic field or a periodic signal. Here, we instead
investigate the problem of estimating a field with non-periodic variation
described by a Wiener process. We propose and study, by numerical simulations,
an adaptive tracking protocol based on Bayesian estimation. The tracking
protocol updates the probability distribution for the magnetic field, based on
measurement outcomes, and adapts the choice of sensing time and phase in real
time. By taking the statistical properties of the signal into account, our
protocol strongly reduces the required measurement time. This leads to a
reduction of the error in the estimation of a time-varying signal by up to a
factor 4 compared to protocols that do not take this information into account.Comment: 10 pages, 6 figure
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