The nested structure of urban business clusters

Although the cluster theory literature is bountiful in economics and regional science, there is still a lack of understanding of how the geographical scales of analysis (neighbourhood, city, region) relate to one another and impact the observed phenomenon, and to which extent the clusters are industrially bound or geographically consistent. In this paper, we cluster spatial economic activities through a multi-scalar approach following percolation theory. We consider both the industrial similarity and the geographical proximity of firms, through their joint probability function which is constructed as a copula. This gives rise to an emergent nested hierarchy of geoindustrial clusters, which enables us to analyse the relationships between the different scales, and specific industrial sectors. Using longitudinal business microdata from the Office for National Statistics, we look at the evolution of clusters which spans from very local groups of businesses to the metropolitan level, in 2007 and in 2014, so that the changes stemming from the financial crisis can be observed.Comment: 20 pages, 10 figure

Multi-Material Stereolithography: Spatially-Controlled Bioactive Poly(Ethylene Glycol) Scaffolds for Tissue Engineering

Challenges remain in tissue engineering to control the spatial and temporal mechanical and biochemical architectures of scaffolds. Unique capabilities of stereolithography (SL) for fabricating multi-material spatially-controlled bioactive scaffolds were explored in this work. To accomplish multi-material builds with implantable materials, a new mini-vat setup was designed, constructed and placed on top of the existing build platform to allow for accurate and selfaligning X-Y registration during fabrication. Precise quantities of photocrosslinkable solution were added to and removed from the mini-vat using micro-pipettes. The mini-vat setup allowed the part to be easily removed and rinsed and different photocrosslinkable solutions could be easily removed and added to the vat to aid in multi-material fabrication. Two photocrosslinkable hydrogel biopolymers, poly(ethylene glycol dimethacrylate) (PEG-dma, molecular wt 1,000) and poly(ethylene glycol)-diacrylate (PEG-da, molecular wt 3,400), were used as the primary scaffold materials, and controlled concentrations of fluorescently labeled dextran or bioactive PEG were prescribed and fabricated in different regions of the scaffold using SL. The equilibrium swelling behavior of the two biopolymers after SL fabrication was determined and used to design constructs with the specified dimensions at the swollen state. Two methods were used to measure the spatial gradients enabled by this process with multi-material spatial control successfully demonstrated down to 500-µm. First, the presence of the fluorescent component in specific regions of the scaffold was analyzed with fluorescent microscopy. Second, human dermal fibroblast cells were seeded on top of the fabricated scaffolds with selective bioactivity, and phase contrast microscopy images were used to show specific localization of cells in the regions patterned with bioactive PEG. The use of multi-material SL and the relative ease of conjugating different bioactive ligands or growth factors to PEG allows for the fabrication of tailored three-dimensional constructs with specified spatially-controlled bioactivity.Mechanical Engineerin

Hydrogels in Stereolithography

The use of stereolithography (SL) for fabricating complex three-dimensional (3D) tissue engineered scaffolds of aqueous poly(ethylene glycol) (PEG) hydrogel solutions is described. The primary polymer used in the study was PEG-dimethacrylate (PEG-dma) with an average molecular weight (MW) of 1000 in distilled water with the photoinitiator Irgacure 2959 (I-2959). Successful layered manufacturing (LM) with embedded channel architecture required investigation of the photopolymerization characteristics of the PEG solution (measured as hydrogel thickness or cure depth) as a function of photoinitiator concentration and laser energy dosage for a specific photoinitiator type and polymer concentration in solution. Hydrogel thickness was a strong function of PI concentration and energy dosage. Curves of hydrogel thickness were utilized to successfully plan, perform, and demonstrate layered manufacturing of highly complex hydrogel scaffold structures, including structures with internal channels of various orientations. Successful fabrication of 3D, multi-layered bioactive PEG scaffolds containing cells was accomplished using a slightly modified commercial SL system (with 325 nm wavelength laser) and procedure. Human dermal fibroblast (HDF) cells were encapsulated in PEG hydrogels using small concentrations (~ 5 mg/ml) of acryloyl-PEG-RGDS (MW 3400) added to the photopolymerizable PEG solution to promote cell attachment. HDF cells were combined with the PEG solution, photocrosslinked using SL, and successfully shown to survive the fabrication process. The combined use of SL and photocrosslinkable biomaterials such as PEG makes it possible to fabricate complex 3D scaffolds that provide site-specific and tailored mechanical properties (i.e., multiple polymer materials) with a polymer matrix that allows transport of nutrients and waste at the macroscale and facilitates cellular processes at the microscale through precisely placed bioactive agents.Mechanical Engineerin

Paradoxical Interpretations of Urban Scaling Laws

Scaling laws are powerful summaries of the variations of urban attributes with city size. However, the validity of their universal meaning for cities is hampered by the observation that different scaling regimes can be encountered for the same territory, time and attribute, depending on the criteria used to delineate cities. The aim of this paper is to present new insights concerning this variation, coupled with a sensitivity analysis of urban scaling in France, for several socio-economic and infrastructural attributes from data collected exhaustively at the local level. The sensitivity analysis considers different aggregations of local units for which data are given by the Population Census. We produce a large variety of definitions of cities (approximatively 5000) by aggregating local Census units corresponding to the systematic combination of three definitional criteria: density, commuting flows and population cutoffs. We then measure the magnitude of scaling estimations and their sensitivity to city definitions for several urban indicators, showing for example that simple population cutoffs impact dramatically on the results obtained for a given system and attribute. Variations are interpreted with respect to the meaning of the attributes (socio-economic descriptors as well as infrastructure) and the urban definitions used (understood as the combination of the three criteria). Because of the Modifiable Areal Unit Problem and of the heterogeneous morphologies and social landscapes in the cities internal space, scaling estimations are subject to large variations, distorting many of the conclusions on which generative models are based. We conclude that examining scaling variations might be an opportunity to understand better the inner composition of cities with regard to their size, i.e. to link the scales of the city-system with the system of cities

On the problem of boundaries and scaling for urban street networks

Urban morphology has presented significant intellectual challenges to mathematicians and physicists ever since the eighteenth century, when Euler first explored the famous Konigsberg bridges problem. Many important regularities and scaling laws have been observed in urban studies, including Zipf's law and Gibrat's law, rendering cities attractive systems for analysis within statistical physics. Nevertheless, a broad consensus on how cities and their boundaries are defined is still lacking. Applying an elementary clustering technique to the street intersection space, we show that growth curves for the maximum cluster size of the largest cities in the UK and in California collapse to a single curve, namely the logistic. Subsequently, by introducing the concept of the condensation threshold, we show that natural boundaries of cities can be well defined in a universal way. This allows us to study and discuss systematically some of the regularities that are present in cities. We show that some scaling laws present consistent behaviour in space and time, thus suggesting the presence of common principles at the basis of the evolution of urban systems