336 research outputs found
Emergence of product differentiation from consumer heterogeneity and asymmetric information
We introduce a fully probabilistic framework of consumer product choice based
on quality assessment. It allows us to capture many aspects of marketing such
as partial information asymmetry, quality differentiation, and product
placement in a supermarket.Comment: 12 pages, 12 figure
Zipf's Law Leads to Heaps' Law: Analyzing Their Relation in Finite-Size Systems
Background: Zipf's law and Heaps' law are observed in disparate complex
systems. Of particular interests, these two laws often appear together. Many
theoretical models and analyses are performed to understand their co-occurrence
in real systems, but it still lacks a clear picture about their relation.
Methodology/Principal Findings: We show that the Heaps' law can be considered
as a derivative phenomenon if the system obeys the Zipf's law. Furthermore, we
refine the known approximate solution of the Heaps' exponent provided the
Zipf's exponent. We show that the approximate solution is indeed an asymptotic
solution for infinite systems, while in the finite-size system the Heaps'
exponent is sensitive to the system size. Extensive empirical analysis on tens
of disparate systems demonstrates that our refined results can better capture
the relation between the Zipf's and Heaps' exponents. Conclusions/Significance:
The present analysis provides a clear picture about the relation between the
Zipf's law and Heaps' law without the help of any specific stochastic model,
namely the Heaps' law is indeed a derivative phenomenon from Zipf's law. The
presented numerical method gives considerably better estimation of the Heaps'
exponent given the Zipf's exponent and the system size. Our analysis provides
some insights and implications of real complex systems, for example, one can
naturally obtained a better explanation of the accelerated growth of scale-free
networks.Comment: 15 pages, 6 figures, 1 Tabl
The H-index of a network node and its relation to degree and coreness
Identifying influential nodes in dynamical processes is crucial in understanding network structure and function. Degree, H-index and coreness are widely used metrics, but previously treated as unrelated. Here we show their relation by constructing an operator , in terms of which degree, H-index and coreness are the initial, intermediate and steady states of the sequences, respectively. We obtain a family of H-indices that can be used to measure a node’s importance. We also prove that the convergence to coreness can be guaranteed even under an asynchronous updating process, allowing a decentralized local method of calculating a node’s coreness in large-scale evolving networks. Numerical analyses of the susceptible-infected-removed spreading dynamics on disparate real networks suggest that the H-index is a good tradeoff that in many cases can better quantify node influence than either degree or coreness.This work was partially supported by the National Natural Science Foundation of China (Grant Nos. 11205042, 11222543, 11075031, 61433014). L.L. acknowledges the research start-up fund of Hangzhou Normal University under Grant No. PE13002004039 and the EU FP7 Grant 611272 (project GROWTHCOM). The Boston University work was supported by NSF Grants CMMI 1125290, CHE 1213217 and PHY 1505000. (11205042 - National Natural Science Foundation of China; 11222543 - National Natural Science Foundation of China; 11075031 - National Natural Science Foundation of China; 61433014 - National Natural Science Foundation of China; PE13002004039 - research start-up fund of Hangzhou Normal University; 611272 - EU FP7 Grant (project GROWTHCOM); CMMI 1125290 - NSF; CHE 1213217 - NSF; PHY 1505000 - NSF)Published versio
Byzantine Attack and Defense in Cognitive Radio Networks: A Survey
The Byzantine attack in cooperative spectrum sensing (CSS), also known as the
spectrum sensing data falsification (SSDF) attack in the literature, is one of
the key adversaries to the success of cognitive radio networks (CRNs). In the
past couple of years, the research on the Byzantine attack and defense
strategies has gained worldwide increasing attention. In this paper, we provide
a comprehensive survey and tutorial on the recent advances in the Byzantine
attack and defense for CSS in CRNs. Specifically, we first briefly present the
preliminaries of CSS for general readers, including signal detection
techniques, hypothesis testing, and data fusion. Second, we analyze the spear
and shield relation between Byzantine attack and defense from three aspects:
the vulnerability of CSS to attack, the obstacles in CSS to defense, and the
games between attack and defense. Then, we propose a taxonomy of the existing
Byzantine attack behaviors and elaborate on the corresponding attack
parameters, which determine where, who, how, and when to launch attacks. Next,
from the perspectives of homogeneous or heterogeneous scenarios, we classify
the existing defense algorithms, and provide an in-depth tutorial on the
state-of-the-art Byzantine defense schemes, commonly known as robust or secure
CSS in the literature. Furthermore, we highlight the unsolved research
challenges and depict the future research directions.Comment: Accepted by IEEE Communications Surveys and Tutoiral
The role of a matchmaker in buyer-vendor interactions
We consider a simple market where a vendor offers multiple variants of a certain product and preferences of both the vendor and potential buyers are heterogeneous and possibly even antagonistic. Optimization of the joint benefit of the vendor and the buyers turns the toy market into a combinatorial matching problem. We compare the optimal solutions found with and without a matchmaker, examine the resulting inequality between the market participants, and study the impact of correlations on the syste
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