It suggests an interesting aspect differentiating these two urban metrics’ dynamics. With the approach presented above, it is possible to write a relation between the transversal and the longitudinal scaling exponent. We are deeply saddened to share with the urban science community the unexpected passing of our coauthor and dearest friend Joao Meirelles. Fig 2 also presents the time evolution of the transversal scaling exponent βT for the water supply network length (in blue). Neto CR, In short, does an individual city growing in time follow the same scaling pattern observed for a snapshot of a group of cities? Meirelles J, Some works in the recent literature suggest this methodology, as for instance [31, 52, 53]., of the Eq (1) for different years. Wichtige Resonatortypen sind der konzentrische, der konfokale und der hemisphärische Resonator. Interpreting our concept of the external vector through Pumain et al.’s theory, one could argue that some technologies required for water networks were initially deployed in bigger cities and then progressively diffused throughout the urban system. Section Empirical Evidence brings results from our data analysis for both transversal and longitudinal scaling for our studied variables, namely GDP and water network length as a function of population size in different periods of time (from 1998 to 2014) for all Brazilian cities. [14], provided a hypothesis about the temporal dynamics of water network length in a developing economy like Brazil. To sum up, the transversal and longitudinal scaling exponent will only be the same when: This conclusion is in agreement with [47]. However, the universality proposition has been challenged, either by counter-evidence [10, 28, 35–37], or by methodological arguments [38–42]. For example, in the case of GDP, which has a relatively constant transversal scaling exponent in the analyzed period, the removal (decomposition) of external factors leads us to a distribution of longitudinal exponents around the expected value of the transversal exponent. Magnitude of the external vector as a function of population size for every single Brazilian municipality in our subset. One way to deal with this is to decompose the longitudinal trajectory, graphing not ln Yi(t) in the ordinate, but instead, ln Yi(t) − ln Y0(t), that is ln(Yi(t)/Y0(t)), in order to eliminate global effects, as suggested by [50]. However, we also saw that decomposition alone is not sufficient to establish a general relation between transversal and longitudinal scaling. Physical implications of the longitudinal dynamics are also … The available data (see spreadsheet in the supplementary material (SM)) cover all 5570 Brazilian municipalities. Thus, a more feasible situation for future analyses consists of finding a way to normalize the longitudinal scaling exponent to the city’s growth rate. One can see that cities experience different slopes, and in all cases, the exponent is greater than the transversal one (given by βT and represented by the dark red line in Fig 3-b). These advances were also enabled by the work of many theorists from different areas, such as physicists, urbanists and complex systems scientists, among others, who brought new insights and theories to the field, resulting in a significant step towards a new science of cities [5]. The first condition can be understood as an ideal situation since in practice it would be impossible to find a city completely isolated from the rest of the system. When βT(t) is constant, as it is approximately the case for GDP dynamics, then ϵ = 0. … In any case, in order to have a better understanding of that process, further research is necessary, which can be achieved by following the evolution of more urban variables. For more information about PLOS Subject Areas, click These results suggest that, in order for the urban metric to depend only on the population size (under the form ), it is necessary for βT to be constant (ϵ → 0) and Fext → 0, which means absence of global growth. SS/D6/04: De reïntegratie van langdurig werklozen: een longitudinale analyse. Bei einem Spiegelabstand von 0.5 m und Spiegelreflektivitäten von 0.9 beträgt die spektrale Breite einer Resonatormode Δνc = 4.9 MHz, was einer Photonenlebensdauer von 32 ns im Resonator entspricht. The mechanism to explain this was linked to properties of networks at the heart of urban density and diversity, triggering increasing returns to scale in the economy and scale economies in infrastructure. This may be the case since the transversal scaling exponent βT for water network length is not stable across the studied years. In the vertical direction of this plane, we have vectors acting on the increment of the urban metric (GDP or water supply network length, for instance). Is the Subject Area "Cities" applicable to this article? Beim Anschwingen der Moden kann unter den Moden eine Konkurrenz um die größte Verstärkung auftreten. Similarly, we can compute the individual decomposed scaling exponent, say , with the decomposed longitudinal trajectory described in Fig 3c and 3d. All other wavelengths are suppressed by destructive interference. However, in the case of water supply network length, bigger cities show external vectors smaller than the average. Data curation, The dashed line is Fext = 0. Investigation, Each dot represents the data of a single Brazilian city and the red curve is the theoretical prediction given by Eq (10) using: ϵ = 0 for both cases; βT = 1.15 for GDP; and βT = 0.9 for water network length. To be sure, ‘municipality’ is a political and territorial definition used for administrative purposes in Brazil, and it includes both urban and rural areas within those borders. Das Retinaculum patellae ist ein Halteband der Kniescheibe und gehört zur äußeren Schicht der Gelenkkapsel des Kniegelenks.. 2 Anatomie. Quantum-like approach to the transversal and longitudinal beam dynamics. One can find attached the spreadsheet generated by data mining of the website of the Brazilian Institute of Geography and Statistics (IBGE) and the water-sewage-waste companies national survey (SNIS). Quantenmechanisch folgt die Linienbreite auch aus der Energie-Zeit-Unschärferelation. Nous discutons le caractère transverse et longitudinal d'une onde.Réalisation, simulations et enregistrement par Christophe FINOT. That seems to make sense, since urban scaling in both longitudinal and transversal contexts are intrinsically related phenomena tied by their statistical nature. Each set aggregates the information of all municipalities that belong to it. In the previous section, when we decomposed each city’s evolution into a relative change, we removed external factors acting on each city and considering only internal factors (the ones that come from agglomeration/scaling effects). De knopen, d.w.z. We now focus on the individual evolution of Brazilian cities. sufficiently close to each other to form a single, continuous urban unit or formation. Software, In the first scenario, the external vector is approximately the same for all cities of the system, regardless of their size; it implies that the slope of the fit line (in ln Y-x-ln N plane) remains constant. No, Is the Subject Area "Brazil" applicable to this article? The numeric time evolution of the transversal scaling exponent and the intercept parameter are shown in Fig 2. https://doi.org/10.1371/journal.pone.0233003.g001. The two parallel lines are given by the global system (transversal) power law (Eq (1)) in t and t + Δt. In einem konfokalen Resonator ist der freie Spektralbereich übrigens c/(4L), weil der Strahl erst nach vier Durchläufen wieder auf sich … Department of Civil and Environmental Engineering, Swiss Federal Institute of Technology Lausanne, Lausanne, VD, Switzerland, Roles een plaats waar de … Many translated example sentences containing "analyse longitudinale et transversale" – English-French dictionary and search engine for English translations. Yes Fig 3-a presents the raw longitudinal trajectories, while Fig 3-b presents them re-scaled as Yi(t)/Yi(t0), as a function of Ni(t)/Ni(t0), following the idea proposed in [49]. Investigation, e0233003. Funding: This work was supported by École polytechnique fédérale de Lausanne (Joao Meirelles), Conselho Nacional de Desenvolvimento Científico e Tecnológico (Fabiano Lemes Ribeiro, process number: 405921/2016-0), Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (Fabiano Lemes Ribeiro, process number: 88881.119533/2016-01). The dots represent computed from the expression (11) while the red line represents the average magnitude of this vector over the system, computed by the expression (7). Thus, the universality proposition is still an open question both from the methodological and the theoretical point of views. Data Availability: All relevant data are within the paper and its Supporting Information files. Pour cela, diverses approches méthodologiques sont possibles.Selon une première approche « transversale », les groupes d’âge à comparer sont constitués par des échantillons d’enfants différents : autant d’échantillons que … If this equation is a law, then any theory that is formulated to describe scaling properties in cities must be constrained to follow it. Quantum-like approach to the transversal and longitudinal beam dynamics. Bei einer Laserleistung von P = 1 W ergibt sich eine Schawlow-Townes Laser-Linienbreite von ΔνST = 1.4 x 10-5 Hz. Empirical evidence has shown that an urban variable, Y, scales with the population size N of a city, obeying a power law of the kind Y ∝ Nβ, where β is the scaling exponent quantifying how the urban metric reacts to the population increase [6–12]. The increment in the intercept implies a more accentuated slope of the city trajectory in the plane ln Y-x-ln N (that is, bigger βi) in relation to the transversal trajectory (related to βT), in accordance with empirical observations brought by our study as well as other evidences available in recent literature [49–51]. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. https://doi.org/10.1371/journal.pone.0233003.g009. spektralen Lochbrennen kommen, wenn eine schmalbandige Resonatormode ein Ensemble von Atomen anregt und dort die Verstärkung sättigt. Baronchelli A It reveals a superlinear scaling property, compatible with the fact that the GDP is a socio-economic urban variable. [43] have proposed a new index based on scaling laws instead of per-capita analysis to classify levels of economic efficiency of cities; Youn et al. Avec l'analyse de socialisation longitudinale, pas besoin. Lasertypen - Gaslaser Image : Sciage d'une planche de 2 cm d'épaisseur et de 80 cm de long avec une Ryoba. This is a direct consequence of the fact that urban scaling laws, in both longitudinal and transversal contexts, are phenomena of an intrinsically statistical nature. (siehe auch Vorlesungsstunde zu Gaußschen Strahlen). The halo problem . Assez souvent brus'ja lancent sur longitudinal razrezku, avec la peinture ou la corrosion des planches. Den Frequenzabstand longitudinaler Moden eines Lasers kann man mit einem Scanning-Fabry-Perot-Interferometer messen. Beschreiben lässt sich der optische Übergang mit dem Modell eines gedämpften harmonischen Oszillators. In einem (leeren) plan-parallelen Resonator beträgt der Abstand der Frequenzmaxima c/(2L) und hängt damit nur von der Resonatorlänge L ab. La mesure transversale se rapporte à la mesure d'un phénomène sur une période de temps donnée assez courte, souvent l'année civile. Our results add complexity to the idea that the longitudinal dynamics is a micro-scaling version of the transversal dynamics of the entire urban system. Hieraus folgt eine Linienbreite von Î”ω = 1/τ=4348 Hz. Eq (7) represents the average magnitude of the external vector, i.e. Approche transversale et longitudinale - Volume 35 Issue 4 - Michèle van Houte-Minet. By far, most of these sets are formed by a single municipality, but some of the biggest Brazilian urban agglomerations are formed by more than one municipality, aggregated in metropolitan conurbations. Das Wort transversal (von lat. The parameter bc delimits the cities that will be used to compute the average. In kartesischen Koordinaten erhält man Hermite-Gauß-Moden und die Variablen x und y bei TEMxy geben die Anzahl der Nullstellen in x- und y-Richtung der Feldverteilung an. Il s'agit de la mesure la plus courante en démographie obtenue par analyse transversale.Elle s'oppose à la mesure longitudinale, cette dernière se déroulant sur une longue période d'études, parfois plusieurs dizaines d'années : elle a ainsi sur … For instance, we can use the result given by Eq (10) to infer the external vector relative to the i-th city. We would like to acknowledge all colleagues from the Mathematical Department of City, University of London, where most of the analytical work for this article was done. This vector has to do with the agglomeration effect stemming from the interaction between individuals or agencies located in this single city. This vectorial approach can be seen as a technical possibility to separate in two parts the forces acting in an urban metric: one that is pure scaling (internal factors); and the other that is the result of public policies or other external factors. Their theory proposes that urban scaling is a result of an interplay between urban density and diversity, which are related to economic competition and knowledge exchange, respectively. Do they behave similarly even for different urban metrics? Some recent works addressed this issue, reaching no unanimous conclusion. As a result, we found signs of a relationship between the longitudinal and transversal exponents, provided that certain conditions are met. Project administration, Fig 3 presents different ways of observing the longitudinal dynamics of the GDP and city population size. Les ondes transversales Les ondes longitudinales -Crée les crêtes et les creux -Crée les compression et les rarefactions -évident dans les solides et les surfaces des liquides -évident dans les trois types de la matière. The data presented in the previous section suggest that we have an empirical law that governs cities, which can be described by the expression (1). Lasertypen - Farbstofflaser (Anwendungen): In this sense, the value given by (7) is an average value of the external vector. In fact, large values of scaling exponents are related to cities with a very low growth rate (according to Eq (9)), so the raw value of βi is not useful if the purpose is to see how productivity or scaling economies emerge. (5). This result (10) was also obtained by Bettencourt et al. (6) Data curation, For example, Depersin and Barthelemy analyzed the scaling exponent in time for delays in traffic congestion in 101 US cities, and found longitudinal scaling to be path-dependent on the individual evolution of cities and unrelated to the transversal scaling, challenging the universality proposition [49]. It suggests an equilibrium situation, or at least that this urban variable is in a mature state inside the system. Another work has found that the power-law scaling of 32 major cities in China could adequately be characterized for both transversal and longitudinal scaling [51]. In order to analyze the conditions of compatibility between longitudinal and transversal scaling exponents, we introduced a theoretical formulation based on vector fields, first to separate internal from external factors active in the urban metrics, and then to yield a quantitative relationship between βT and βi. Transversale Moden ergeben sich als Lösungen der paraxialen Helmholtzgleichung. One possible explanation is that the system is still out of equilibrium. Individual cities are being pushed by the growth of the global intercept parameter Yi(t) and will rise in the ln Y−x−ln N plane, having higher slopes than the global one. Different ways to see the longitudinal dynamics of GDP and population size for all Brazilian cities. We analyzed scaling dynamics of 5507 Brazilian cities and conurbations, aggregated as contiguous urban agglomerations from the totality of 5570 municipalities. Moreover, we also introduced as the average value of the transversal exponent during the time interval Δt, and the parameter ϵ, which is a quantity proportional to the difference βT(t + Δt) − βT(t). Der Laserübergang findet bei 1064 nm statt. De transversale en longitudinale gegevens worden vanaf 2004 jaarlijks geproduceerd. The action of these vector fields (in the horizontal and vertical directions) during a time interval Δt conducts to a “displacement” Δr(t) of this city (or particle) in the two-dimensional plane ln Y-x-ln N. Now let us try to identify these vectors with the empirical variables available. For GDP (plot A) and water network length (plot B).