Diophantine networks

We introduce a new class of deterministic networks by associating networks with Diophantine equations, thus relating network topology to algebraic properties. The network is formed by rep- resenting integers as vertices and by drawing cliques between M vertices every time that M dis- tinct integers satisfy the equation. We analyse the network generated by the Pythagorean equation x2+y2 = z2 showing that its degree distribution is well approximated by a power law with exponen- tial cut-o®. We also show that the properties of this network di®er considerably from the features of scale-free networks generated through preferential attachment. Remarkably we also recover a power law for the clustering coe±cient. We then study the network associated with the equation x2 + y2 = z showing that the degree distribution is consistent with a power-law for several decades of values of k and that, after having reached a minimum, the distribution begins rising again. The power law exponent, in this case, is given by ° » 4:5 We then analyse clustering and ageing and compare our results to the ones obtained in the Pythagorean case

Random planar graphs and the London street network

In this paper we analyse the street network of London both in its primary and dual representation. To understand its properties, we consider three idealised models based on a grid, a static random planar graph and a growing random planar graph. Comparing the models and the street network, we find that the streets of London form a self-organising system whose growth is characterised by a strict interaction between the metrical and informational space. In particular, a principle of least effort appears to create a balance between the physical and the mental effort required to navigate the city

Wikipedia Information Flow Analysis Reveals the Scale-Free Architecture of the Semantic Space

In this paper we extract the topology of the semantic space in its encyclopedic acception, measuring the semantic flow between the different entries of the largest modern encyclopedia, Wikipedia, and thus creating a directed complex network of semantic flows. Notably at the percolation threshold the semantic space is characterised by scale-free behaviour at different levels of complexity and this relates the semantic space to a wide range of biological, social and linguistics phenomena. In particular we find that the cluster size distribution, representing the size of different semantic areas, is scale-free. Moreover the topology of the resulting semantic space is scale-free in the connectivity distribution and displays small-world properties. However its statistical properties do not allow a classical interpretation via a generative model based on a simple multiplicative process. After giving a detailed description and interpretation of the topological properties of the semantic space, we introduce a stochastic model of content-based network, based on a copy and mutation algorithm and on the Heaps' law, that is able to capture the main statistical properties of the analysed semantic space, including the Zipf's law for the word frequency distribution

Computational fact checking from knowledge networks

Traditional fact checking by expert journalists cannot keep up with the enormous volume of information that is now generated online. Computational fact checking may significantly enhance our ability to evaluate the veracity of dubious information. Here we show that the complexities of human fact checking can be approximated quite well by finding the shortest path between concept nodes under properly defined semantic proximity metrics on knowledge graphs. Framed as a network problem this approach is feasible with efficient computational techniques. We evaluate this approach by examining tens of thousands of claims related to history, entertainment, geography, and biographical information using a public knowledge graph extracted from Wikipedia. Statements independently known to be true consistently receive higher support via our method than do false ones. These findings represent a significant step toward scalable computational fact-checking methods that may one day mitigate the spread of harmful misinformation

Unveiling relationships between crime and property in England and Wales via density scale-adjusted metrics and network tools

Scale-adjusted metrics (SAMs) are a significant achievement of the urban scaling hypothesis. SAMs remove the inherent biases of per capita measures computed in the absence of isometric allometries. However, this approach is limited to urban areas, while a large portion of the world’s population still lives outside cities and rural areas dominate land use worldwide. Here, we extend the concept of SAMs to population density scale-adjusted metrics (DSAMs) to reveal relationships among different types of crime and property metrics. Our approach allows all human environments to be considered, avoids problems in the definition of urban areas, and accounts for the heterogeneity of population distributions within urban regions. By combining DSAMs, cross-correlation, and complex network analysis, we find that crime and property types have intricate and hierarchically organized relationships leading to some striking conclusions. Drugs and burglary had uncorrelated DSAMs and, to the extent property transaction values are indicators of affluence, twelve out of fourteen crime metrics showed no evidence of specifically targeting affluence. Burglary and robbery were the most connected in our network analysis and the modular structures suggest an alternative to "zero-tolerance" policies by unveiling the crime and/or property types most likely to affect each other

Limited Urban Growth: London's Street Network Dynamics since the 18th Century

We investigate the growth dynamics of Greater London defined by the administrative boundary of the Greater London Authority, based on the evolution of its street network during the last two centuries. This is done by employing a unique dataset, consisting of the planar graph representation of nine time slices of Greater London's road network spanning 224 years, from 1786 to 2010. Within this time-frame, we address the concept of the metropolitan area or city in physical terms, in that urban evolution reveals observable transitions in the distribution of relevant geometrical properties. Given that London has a hard boundary enforced by its long-standing green belt, we show that its street network dynamics can be described as a fractal space-filling phenomena up to a capacitated limit, whence its growth can be predicted with a striking level of accuracy. This observation is confirmed by the analytical calculation of key topological properties of the planar graph, such as the topological growth of the network and its average connectivity. This study thus represents an example of a strong violation of Gibrat's law. In particular, we are able to show analytically how London evolves from a more loop-like structure, typical of planned cities, toward a more tree-like structure, typical of self-organized cities. These observations are relevant to the discourse on sustainable urban planning with respect to the control of urban sprawl in many large cities, which have developed under the conditions of spatial constraints imposed by green belts and hard urban boundaries.Comment: PlosOne, in publicatio

Soluble urokinase receptor released from human carcinoma cells: a plasma parameter for xenograft tumour studies

The urokinase plasminogen activator receptor (uPAR) plays a critical role in urokinase-mediated plasminogen activation and thereby in the process leading to invasion and metastasis. Soluble urokinase receptor (suPAR) is released from tumours, and in cancer patients the blood level of soluble receptor is increased. Using an enzyme-linked, immunosorbent assay (ELISA)-specific for the human urokinase receptor, release of soluble receptor was measured in cultures of human breast carcinoma cells, in tumour extracts and in plasma from mice with xenografted human tumours. Soluble human urokinase receptor (shuPAR) was released into culture supernatant during the growth of the human breast cancer cell line MDA-MB-231 BAG, and the level of shuPAR in conditioned medium determined by ELISA was a linear function of both viable cell number and time of incubation. Western blotting showed that the form of shuPAR measured by ELISA in conditioned medium consisted virtually exclusively of the three-domain full-length protein, while uPAR in cell lysates consisted of full-length uPAR as well as the domains (2+3) cleavage product. shuPAR was also released into the plasma of nude mice during growth of MDA-MB-231 BAG, MDA-MB-435 BAG and HCT 116 cells as subcutaneously xenografted tumours. Western blotting demonstrated that the shuPAR released from the xenografted human tumours into plasma consisted of the three-domain full-length protein, despite the finding of some cleaved uPAR in detergent extracts of tumour tissue. The levels of shuPAR determined by ELISA in the plasma of host mice during the growth of xenografted cell lines were highly correlated with tumour volume. © 1999 Cancer Research Campaig

DETORQUEO, QUIRKY, and ZERZAUST Represent Novel Components Involved in Organ Development Mediated by the Receptor-Like Kinase STRUBBELIG in Arabidopsis thaliana

Intercellular signaling plays an important role in controlling cellular behavior in apical meristems and developing organs in plants. One prominent example in Arabidopsis is the regulation of floral organ shape, ovule integument morphogenesis, the cell division plane, and root hair patterning by the leucine-rich repeat receptor-like kinase STRUBBELIG (SUB). Interestingly, kinase activity of SUB is not essential for its in vivo function, indicating that SUB may be an atypical or inactive receptor-like kinase. Since little is known about signaling by atypical receptor-like kinases, we used forward genetics to identify genes that potentially function in SUB-dependent processes and found recessive mutations in three genes that result in a sub-like phenotype. Plants with a defect in DETORQEO (DOQ), QUIRKY (QKY), and ZERZAUST (ZET) show corresponding defects in outer integument development, floral organ shape, and stem twisting. The mutants also show sub-like cellular defects in the floral meristem and in root hair patterning. Thus, SUB, DOQ, QKY, and ZET define the STRUBBELIG-LIKE MUTANT (SLM) class of genes. Molecular cloning of QKY identified a putative transmembrane protein carrying four C2 domains, suggesting that QKY may function in membrane trafficking in a Ca2+-dependent fashion. Morphological analysis of single and all pair-wise double-mutant combinations indicated that SLM genes have overlapping, but also distinct, functions in plant organogenesis. This notion was supported by a systematic comparison of whole-genome transcript profiles during floral development, which molecularly defined common and distinct sets of affected processes in slm mutants. Further analysis indicated that many SLM-responsive genes have functions in cell wall biology, hormone signaling, and various stress responses. Taken together, our data suggest that DOQ, QKY, and ZET contribute to SUB-dependent organogenesis and shed light on the mechanisms, which are dependent on signaling through the atypical receptor-like kinase SUB