It is known that small and large numbers facilitate left/right respectively (the SNARC effect). Recently, it has been proposed that numerical magnitude is just one example of a range of quantities, which have a common cognitive/neural representation. To investigate this proposition, response congruency effects were explored for stimuli which differed according to their: (a) numerical size, (b) physical size, (c) luminance, (d) conceptual size and (e) auditory intensity. In a series of experiments, groups of undergraduate participants made two-alternative forced choice discriminations with their left or right hands. There were clear interactions between magnitude and responding hand whereby right hand responses were faster for stimuli with (a) large numbers, (b) large physical size, (c) low luminance, and (d) a reference to large objects. There was no congruency effect for the auditory stimuli. The data demonstrate that the response congruency effect observed for numbers also occurs for a variety of other non-numerical visual quantities. These results support models of general magnitude representation and suggest that the association between magnitude and the left/right sides of space may not be related to culture and/or directional reading habits.

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In this paper, we investigate optimal resource allocation in a power beacon-assisted wireless-powered communication network (PB-WPCN), which consists of a set of hybrid access point (AP)-source pairs and a power beacon (PB). Each source, which has no embedded power supply, first harvests energy from its associated AP and/or the PB in the downlink (DL) and then uses the harvested energy to transmit information to its AP in the uplink (UL). We consider both cooperative and noncooperative scenarios based on whether the PB is cooperative with the APs or not. For the cooperative scenario, we formulate a social welfare maximization problem to maximize the weighted sum-throughput of all AP-source pairs, which is subsequently solved by a water-filling based distributed algorithm. In the noncooperative scenario, all the APs and the PB are assumed to be rational and self-interested such that incentives from each AP are needed for the PB to provide wireless charging service. We then formulate an auction game and propose an auction based distributed algorithm by considering the PB as the auctioneer and the APs as the bidders. Finally, numerical results are performed to validate the convergence of both the proposed algorithms and demonstrate the impacts of various system parameters.Index Terms-Power beacon-assisted wireless-powered communication network (PB-WPCN), wireless energy transfer (WET), resource allocation, auction theory.0090-6778 (c) 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TCOMM.2015.2468215, IEEE Transactions on Communications 2 assisted WPCN (PB-WPCN)", in which each user can harvest wireless energy not only from the AP but also from the deployed PB. For this new model, a natural question that arises is "how to optimally allocate the resources of PB-WPCNs, including the PBs' energy, and the time for DL WET as well as the UL information transmission?". To the best of our knowledge, this is still an open question, which motivates this paper.In this paper, we consider a PB-WPCN consisting of one multi-antenna PB and multiple single-antenna AP-source pairs. In view of the state of art and trend of RF energy transfer [4], the considered network setup is very likely to find its applications in the practical scenario of small cells, such as picocells (range from 10 to 100 meters) and femtocells (WiFilike range), which has been regarded as one of the key enabling technologies of the upcoming 5G cellular networks [8]. It is also worth mentioning that although introducing the PB may result in some extra cost and complexity to the system, this could be beneficial as a whole based on the following considerations: (1) The PB could be dedicated designed for WET only and thus can achi...

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