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The Dynamic Characterization of Cities ROBERT HERMAN, SIAMAK A. ARDEKANI, SHEKHAR GOVIND, AND EDGAR DONA The unprecedented rate of urban development over the last few gen- erations has led to a wide variety of human problems, many of which stem from the nature and growth of a city's infrastructure. Blumenfeld (1971) has studied the consequences of urban sprawl, the process by which a metropolis (Greek for mother city defined as the largest center of activity in a region) develops satellite cities or suburbs and evolves into a megalopolis (also Greek, meaning great city originally a town in the Peloponnesus that the ancient Greeks unsuccessfully tried to develop into a large city). Gottman (1961) recognized this phenomenon taking place along the Boston-Washington corridor and saw in it new patterns in the use of space. He argued that this reorganization of space was inevitable because of the gregarious nature of opportunity-seeking people and leads to a high concentration of white-collar and service-oriented workers. Geographers have also looked at the growth of the metropolitan frame- work. Adams (Chapter 6 in this volume) has used modes of transportation to classify urban development into four eras or epochs: sail-wagon, iron horse, steel rail, and auto-air-amenity. Each epoch sees unique metro- politan growth patterns being molded by the transportation available. Ad- ams has also speculated about the epoch yet to come, one in which telecommunications and not transportation is the prime mover. Dantzig and Saaty (1973) have looked at some of the problems that have been identified in today's urban environment and have proposed new ideas in space and time use. Their "compact city," which was designed using a mathematically and architecturally elegant approach, makes full ~2

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THE DYNAMIC CHARACTERI7ATION OF CITIES ~3 - use of time and the third dimension in space in reorganizing urban activ . . tles. Studies in urban planning have not been confined to printed words and designs alone. The incorporation of Le Corbusier's ideas into the building of the metropolises of Chandigarh (India), Brasilia (Brazil), and the more recent example of Islamabad (Pakistan) suggests that ideas in urban design have a practical side, too. Such incorporation also demonstrates that if problems (especially those of scale) can be ac- counted for in the design process, they can be addressed effectively (Le Corbusier, 1967, 1971). Any planning exercise that deals with the issues raised by modern urban growth must account for the unique fingerprint of each city. This requires grouping cities according to a "phylum," that is, an organic group in which all members exhibit a basic similarity of ground plan and evolve through similar stages, yet are completely dissimilar from one another. One of the grey areas in this arena is the classification of cities on the basis of their infrastructure. It is characteristic of urban studies- to establish a quantitative variable based on certain attributes of the city (such as population or area). These variables are then most often viewed in isolation from other variables, and cities are ranked or ordered on some common scale. Attempts have also been made to stratify metropolitan areas into relatively homogeneous groups on the basis of predetermined criteria (Go- lob et al., 1 97 1 , 1 9721. There have been few attempts to examine the evolutionary path of a city and, using data across time and space, create a morphology for different urban settings. A classification scheme introduced by Herman and Montroll (1972) for characterizing countries and representing them graphically (in the form of multiaxis phase diagrams) is extended for use in this context to differentiate the form and structure of various cities. In this chapter we shall establish a general framework for studies in the taxonomy of cities. Taxonomic studies, in the classical sense, have gen- erally been restricted to biosystematics the classification of living things (a process in which historical data are relevant). However, if we accept that evolution is the fundamental mode of change for both organic and inorganic systems (as expounded by Herbert Spencer t1820-1903] and Teilhard de Chardin t1881-19551 and discussed recently by Prigogine et al. [19781), then it should be worthwhile to bring a historical perspective to the investigation of a means for differentiating among cities. The study described in this chapter includes historical data for variables that represent several infrastructural attributes of one city, namely, Austin, Texas; it also examines the evolutionary track of the variables from the

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24 HERMAN, ARDEKANI, GOVIND, Al!,'D DONA turn of the century to the present, using as its sources the City Directory of Austin (1959-1985) and the General Directory of the City of Austin (1900-1985~. Similar variables are examined for eight other cities (At- lanta, Chicago, Cincinnati, Houston, Los Angeles, Miami, New York, and Seattle) for the present. Because pictorial representations of data derived from a complex situation may provide insight into the mechanisms of the system, the first set of data will be evaluated from this point of view. The second series of data will be used to determine which variables statistically discriminate or correlate best across the cities under study. Our intention in this chapter is to explore a means of differentiating among cities according to the mutually dependent areas of a city's current character and its evolutionary path. Eventually, formal models might be constructed to describe possible changes for a set of cities with similar ground plans. EVOLUTION OF A CITY The figures that follow are pictorial representations of the evolutionary path taken by certain attributes of the city of Austin. Comparisons across both time and space require the use of data that are either normalized on some scale or reduced to a dimensionless quantity. It is a common practice to use population as a normalizing variable and to represent attributes on a per capita (or its reciprocal) basis. Density functions in two dimensions (involving area) have also been used previously for normalization. It would be worthwhile to investigate density functions formed in one dimension when the functions are normalized with respect to the total length of streets in a city. Figures 2-1, 2-2, and 2-3 show how three basic variables- population, area, and street miles have changed over time. It would be interesting to observe the changes in lane miles, which reflect both road width and length, rather than street miles; unfortunately, such data are extremely difficult to obtain. Figures 2-4, 2-5, and 2-6 show how the basic variables change with respect to one another. The density of population shows an approximate linear increase from 1900 to 1950 (Figure 2-41; from 1950 to 1980, how- ever, the city's growth in area was faster than the corresponding growth in population. The 1985 peak represents the spurt of growth the city has had in the 1980s. Density of street miles may give a general indication of the "efficiency" of land use in Austin (Figure 2-51. The decreasing trend from 1950 onward suggests that even though the city acquired various tracts, this land was not opened up to the same extent as land acquired before 1950. Another interpretation is that the density of streets in the inner city (areas included in the city limits until 1950), may not be greater

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THE DYNAMIC C,IIARACTERI7AIfON OF CITIES 500000 Q o to 400000 300000 200000 1 00000 O '10 '15 '20 '25 '30 '35 '40 '45 '50 '55 '60 '65 '70 '75 '80 '85 Year (1900'S) FIGURE 2-1 Population of Austin, 1910 - 1985. than the density of streets in the suburban areas adjoining the city (de- veloped after 1950), and the decline comes simply from the inclusion of tracts of undeveloped land. The density of population per street mile has remained fairly constant from 1955 to 1980 (Figure 2-6), which supports (although not conclusively) the argument that the effect is due to the inclusion of undeveloped land. One immediate conclusion to be drawn from Figure 2-6 is that growth in the number of street miles in the city has lagged behind growth in population over the last 70 years. This state 150 100 . _ In - ~ 50 '10 '15 '20 '25 '30 '35 '40 '45 '50 '55 '60 '65 '70 '75 '80 '85 Year (1 900's) FIGURE 2-2 Area enclosed by the city limits of Austin, 1910-1985.

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26 2000 - . a, o1 000 in ._ O lIERMAN, ARDEKANI, GOVI1!iD, AND DONA T =.l~4 ~11~ . . . . . . . . . . '15 '20 '25 '30 !35 '40 '45 '50 '55 '60 '65 '70 '75 '80 '85 Year (1900'S) FIGURE 2-3 Miles of streets in Austin, 1915 - 1985. ment reflects a simple measure of the increasing number of people sharing the use of one unit of the transportation infrastructure. Another indicator of the load imposed on infrastructure is the number of motor vehicles in a city. Figure 2-7 shows that the total number of registered vehicles in Austin has grown at an exponential rate that is much faster than the growth in population. The number of vehicles per capita demonstrates this fact (Figure 2-~. As might be expected from the pre- ceding discussions, both the number of vehicles per street mile and the number of vehicles per square mile have increased exponentially since 2000 . . '10 '15 '20 '25 '30 '35 t40 t45 '50 t55 '60 t65 70 75 '80 '85 Year (19O0'S) FIGURE 2-4 Population density of Austin' 1910 - 1985.

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THE DYN~IC CHARACTERIZATION OF CITIES 20 - - 0' 10 ~n o u, a) ._ hi. O 27 '15 20 25 30 t3540 45 50 55 t60 65 70 75 80 85 Year (1 900's) FIGURE 2-S Density of street miles in Austin, l91S-1985. 1950 (Figures 2-9 and 2-10~. It is worth noting that Figures 2-8, 2-9, and 2-10 all have a similar characteristic hump from 1920 to 1945; after 1950 they show exponential growth. This phenomenon indicates that strong correlations exist between the normalizing variables and the number of vehicles. One of the more intriguing findings in this study arises from different functions of the number of restaurants (Figures 2-1 1, 2-12, and 2-131. Except for localized fluctuations, the ratio between the size of the pop- ulation of Austin and the number of restaurants has been remarkably steady 400 - . hi; 300 An ~ 200 o - es - ~100 o o '15 '20 '25 '30 '35 '40 '45 '50 '55 '60 '65 '70 '75 '80 '85 Year (1900's) FIGURE 2-6 Population per street mile in Austin, l91S-1985.

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28 500000 400000 ._ o 200000 Z 1 00000 300000 O HERMAN, ARDEKAfII, GOVIND, AND DONA = - ,,,.. ~ . ._ ~ === ~ ~:~ ~ A_ . '20 '25 '30 '35 '40 '45 '50 '55 '60 '65 '70 '75 '80 '85 Year (1 900's) FIGURE 2-7 Total number of vehicles in Austin, 1920-1985. from 1900 to 1985 (mean = 678, standard deviation = 1591. Charts showing the number of restaurants normalized by area (mean = 4.2, standard deviation = 1.3) and street miles (mean = 0.4, standard de- viation = 0.1), also exhibit a similar consistency over a long period of time (Figures 2-12 and 2-131. It would be interesting to compare these values for different cities, assuming that other cities display such char- acteristic numbers as well. The ratio of population to the number of restaurants could, for example, reflect the degree to which a city is service oriented. Preliminary studies of data from San Antonio indicate that a steady-state ratio of population n ._ Q ' 0.6 In .O 0.4 0.0 '20 '25 '30 '35 '40 '45 '50 '55 '60 '65 '70 '75 '80 '85 Year (1900's) FIGURE 2-8 Number of vehicles per capita in Austin, 1920-1985.

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THE DYNAMIC CHARACTERIZATION OF CITIES 400 - :; 300 200 ~n - c' 100 O ~9 1:P ~1 ~ = -~- I . . . '": t :i '20 '25 '30 '35 '40 '45 '50 '55 '60 '65 '70 '75 '80 '85 Year (1900'S) FIGURE 2-9 Number of vehicles per street mile in Austin, 1920-1985. to the number of restaurants is not unique to Austin. In San Antonio the number of people per restaurant has a mean of 809 and a standard deviation of 359 (City Directory of San Antonio, 1900-1985~. The level of sharing of selected services (auto dealers, doctors, lawyers, and contractors) by the population (Figures 2-14 and 2-15) may represent key factors in the growth of a city. The number of doctors, including both physicians and dentists, indicates the level of health care available to the city's inhabitants. A lower population number per contractor implies higher 4000 - 2000 In - C) ._ ~1 000 ~ o '20 '25 '30 '35 '40 '45 '50 '55 '60 '65 '70 '75 '80 '85 Year (1 900's) FIGURE 2-10Number of vehicles per square mile in Austin, 1920-1985.

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30 ce 800 in a: - o ._ HERMAN, ARDEKANI, GOVIND, AND DONA 600 400 200 o _w _ '10 t15 20 25 t30 '35 t40 '45 t50 t55 t60 65 t70 75 '80 '85 Year (1 900's) FIGURE 2- 1 1 Population per restaurant in Austin, 1910-1985. construction activity. The number of law firms could indicate essential aspects of the city and the type of activity on which it thrives. Various conclusions may also be drawn by looking at the utility hookups in a city (Figures 2-16 and 2-17~. One could reason that every dwelling unit would probably have its own electric meter; in the case of water, however, most apartment complexes do not have separate meters for each apartment. For the most part, charges for this utility are assessed on a fixed rate (which may be included in the rent of the apartment). Data on 6 ._ ~ 4 in - 3 in 0 a: 1 . . . . '10 '15 '20 '25 '30 '35 '40 '45 '50 '55 '60 '65 '70 '75 '80 '85 Year (19OO'S) FIGURE 2-12 Number of restaurants per square mile in Austin, 1910-1985.

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THE DYNAMIC CHARACTERI7A TION OF CI TIES 0.5 - . -0.4 0.3 _. ~0.2 CO lo,0.1 ~: 0.0 31 '15 '20 '25 '30 '35 '40 '45 '50 '55 '60 '65 '70 '75 '80 '85 Year (1900'S) FIGURE 2-13 Number of restaurants per street mile in Austin, 1915-1985. the number of electric meters and water meters could therefore be used to characterize the composition of the housing market (Figure 2-161. Fur- ther, the volume of telephone numbers in use may reflect not only the average family size (assuming one telephone number per family) but also the business activity of the city (Figure 2-17~. Austin's annual per capita consumption of water appears to have re- mained stable at 70,000 gallons since 1970 and shows no signs of in- creasing (Figure 2-181. This variable could be used as an indicator of geographical and climatological differences among cities. Another excel 4000 . ~ a) 3000 ~5 o - 2000 ._ Q 1 000 O '10 '15 '20 '25 '30 '35 '40 '45 '50 '55 '60 '65 '70 '75 '80 Year (1 900's) FIGURE 2-14 Population per auto dealer in Austin, 1910-1985.

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32 1,400 1,200 1,000 - c 800 - lo 600 400 200 O HERMAN, ARDEKANI, GOVIND, A1!iD DONA 1 1 _ _ 1 1 1 1 1111 1 1 T T T. 1 11 . , . '00 '05 '10 '15 '20 '25 '30 '35 '40 '45 '50 '55 '60 '65 '70 '75 '80 Year (1 900's) | HI Population per Doctor HI Population per Contractor ~ Population per Law Firm FIGURE 2-15 Population per doctor, law firm, and contractor in Austin, 1900- 1980. lent scale for the comparison of cities would be per capita annual power consumption because it measures an infrastructural attribute that is often of prime concern (Figure 2-191. Cities that use electrical energy for trans- portation including escalators and elevators as well as rapid transit sys- tems may show higher per capita consumption of electric power than other cities. Weather and industry (among other factors) affect this variable as well. For this reason, per capita power consumption might be an ex- cellent discriminant among cities. 0.45 0.40 0.35 54 0.30 g 0.25 `~, 0.20 0.15 0.10 0.05 ~ moo ~ it, _ . ~ l ~ l '00 '05 '10 '15 '20 '25 '30 '35 '40 '45 '50 '55 '60 '65 '70 '75 '80 '85 Year (1 900's) ~ Electric Meters per Capita Cl5 Gas Meters per Capita [a Water Meters per Capita . FIGURE 2-16 Electric, gas, and water meters per capita in Austin, 1900-1980.

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66 G) L4 Cal _ I: 3 A em Cal ~ o .= 3 ~ Do m ~ z of ~4 o Cal 3 Cal 00 Cot - U' C,: . ~ S oo 00 `4 _ _ ~ _ _ _ ` - ~ en L4 _ ~ __ m ~ ~ ~ . - 4- ~ V, =4 ct C) _ F4 F4 00 - 00 00 _ _ e~ ~ C) c: .= .~ ~ ~5 ^4 F. ~ ~ ~ C~ ~ 00 00 00 00 00 C~ ~ ~ ~ ~ _____ ~_ ~ ~ ~ c~ u, u, ca c'3 en u~ u~ c~ u S: C) C~ ~ ~ S~ S S~ S~ 5 1 ~4 ~ C4_~ -~ t4_ O O O O C ' ~t ~ ~S -~ - a, ~ ~ ~ ~ L4 ~ 4 ~ 4 ~ 4 ~ 4 r m m r r . . . . ~ V~ U) . . . . . ~ ~ ~ 3 ~ _ o-o U~ ~ V~ C-l ~ o o o o o o o o o ~ oo 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 X cr ~ ~o~ ~ ~ ~ ~ ~ ~ cr~ cr ~ ~ ~ c~ cr~ ___ _______________ ~ ~n ~ 00 00 oo ~ cr ~ _ _ _ 00 00 ~o _ _ C~ . ~ . ~. C~3 CD ~0 0 C) ~ ~ e~ ~ ~ ~ ~O ~ ~ (~ C~ ~4 c ~O 00 00 S S . ~ c4 oO oo L4 e4 e4 _ _ o o t4 . 0~ _ _ ~ ~= ~ _ _ O O t' (t et ~ Ct {~ ~ O L L (t ~ ~4 ~4 ~ ~ ~ ~ ~ ~ ~ ~ ~4 - 4 ~ ~ c~ v~ c~ c~ ~ ~ o ~ 3 3 ~ ~ 3 3 ~ ~F4 F4 V] (_) Z Z F4 ~4 Z ~] C~ ~ ~ ~ ~ t~ 00 00 ~ 00 00 00 ~ ~ 00 ~ 0\ ~ ~ ~ ~ ~ ~ C~ _________ o4 o4 o4 o4 o4 o4 o4 o. _ ~`: L4 =4 =4 =4 =4 ~4 ~ ~ ~ ~ =4 =4 L V) ~ ~ ~ ~ ~ ~ g O g O O O ~ g O O ~------ - _ {- ______ _ _ - ~O .. . ~ _ cr, ~ \0 ~ ~ . Oo u~ ~ ~ ~ - In ~ ~ ~ 00 0 ~ ~ ~ ~ 0 In O ~ ~ ~ ~ ~ - ~ _ _ 00 ._ ca C~ L4 O ~ - - 00 1- 00 - ~ _ ~ _ ~_ C) . _4 ._ C,3 ;;^ ~ . _4 ~4 . ~ c c ,, C E ~E E ~ E ' ~ E, ~ 2 2 ,, E r~ ~ ~ ~ 3 ~ u, ~ ~ ~ ~ rr, 0 - ~ ~ ~ ~ ~ r~ oo cr 0 - ~ ~ ~ ~ ~o _________ _~

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67 Up ~ Up <5 ~cr Do oo oo . ~ ;> ;> ;> _ ox ~~ \~) ~ ~ .,4 ~ ~ ~0 ~ ~=4 ~ a c O ~ to ~ ~= a ~ ~ ,~- ~ ~ ~ ~ oo 0 oo Do x ,3 ~0 cry oo ~ ~ at ~ ON At ^ O~ cry (~N ^ ~ ~ ~ _ ~ ~ ~ ~ ~ ~ ~ c, - _ _ at, ~ lo,, ~ A,. ~ ~ ~ ~ ~_ ._ ._ ._ E z a 0 0 -c ~ c~ ~ ~ ~ c ~.8 c c c . ~.=C a c c c c e. c ^= C~ a a | c ~ ~ ~ s ~ ~= s s ~ ~ E ~ E ~ E E ~ E ~ ~ ~t ~ ~ u) ~ v) ~ u~ u~ oo oo oo oo oo oo oo oo oo oo oo ~ ~ ~ ~ ~ ~ a~ ox o~ ~ - ~ - - - - - - - - ~ ~ o o g 8 8 _ 8 0 _ _' _ ~ _ _ C) _ _ oo oo oo oo oo c ~cr~ C5~ ~ o~ _ ~_ _ _ _ _ _ ~ Ce au c~ E ~ a ,~, m~ `t . ~ cr~ == 0 Z 0 - 8 . g _ ~ cn ~ o ~ o- _ _ Ct ~ ~ ~ ~ ~ ~ o V) C ~ ~ ( C~ _ ~V~ ~- -- =o ~ ~ ~t_ ~ _~ ~_u~ _ ~ ~ ~ . . . .. . . . . . . .. _ ~ oo ~ 0 0 oo 0 ~ c~ oo _ - - \~:} ~o ~ =\ _4 . t- _ oo _ 0 _ u~ - c ~D s - oC E Y E j E E o e ~ -~ E ~c ~ ~= o u, c' ~ ~ o~ ~ m m ~ ~ ~ ~ ~ CQ ~ ~ 3 3 ~Q cn ~ ~ ~: oo ~ O _ ~ ~ ~ u~ ~ ~ oo ~ O - ~ ~ ~ ~D ~oo ~ O _ ~ ~ ~ u~ ~ ~ ~ c~ ~ ~ ~ ~ ~ c~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ v~ ~ u~ ~ u~

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68 U. ._ o C~ =, CQ a~ ~: .= a, C~ C~ ~D . - o a~ C~ ._ o o .~ Ct o x Ct m m E~ 0 a~ 00 U~ 0 00 t_ C~ 0D D ~1 Ct > D D ~ Z O 1 1 1 O ~ O - O \0 0 - 1 1 1 1 O ~ ~ - ~ d - d=N . . . . . . . . 1 1 _ 1 1 1 O ~ - ~ - ~ ~ - O O _t 1 1 1 1 o o ~ - ~ o ~ U~ o - o _ _ 1 1 O - O ~ - - ~ ~ ~ ~ ~ O . . . . . . . . . . 1 1 1 1 o ~ _ o _ ~ U~ ~ ~ O ~ C~ . . . . . . . . . . . 1 1 1 1 o U) _ ~ ~ o ~ ~ _ oo ~ ~ _ ~ . . . . . . . . . . . . . 1 1 1 1 o _ _ ~ ~ ~ o U~ ~ _ ~ ~ _ ~ ~ 1 1 1 1 O ~ ~ ~ ~ ~ ~ _ ~ ~ ', ~ ~' C - , ,~, 1 1 1 1 1 1 - O - ~ ~ - X ~ o ~ V~ ~ oo ~ ~ ~ _ 1 1 1 1 1 1 1 1 o o ~ ~ V) ~ ~ O o - ~ ~ ~ ~ ~ ~ ~o 1 1 1 1 1 1 1 1 r~ oo cr 0 - ~ ~ ~ ~ ~ ~ 00 0N

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69 0 ~ 0 ~ ~-~ _ ~ r ~ r ~- -~ ~0 oo-to oo ~ -, - - 1 1 1 1 1 ~ - 0 ~ ~ ~ ~ ~-~ e~ r r ~ U~ ~ ~ _ ~-0 ~ 0 ~O .................. . . 1 1 1 1 1 1 1 1 1 1 1 1 1 1 - O \0 ~ O ~ O 0 - - - ~ 'd - ~) . . . . . . . . . . . . . . . . . . . 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 ~ ~ ~ r ~ ~ r ~-0 cot oo ~ ~ -~ 0 ~ cot r ~ . . . . . . . . . . . . . . . . . . . 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 I ~-r ~ 0-~ ~ ~ 0-~ ~ r oo r ~ O .. . . . . . . . . . . . . . . I I I i I I r ~ ~ ~ r .. 1 1 1 (~} -) -] Cod ~ ~ U) . . . . . . . . 1 1 1 1 1 1 1 1 1 1 1 1 1 1 cot ~ ~ cot-O r rot ~ ~ 0 ~ 0-~ cut ~- . . . . . . . . . . . . . . . . 1 1 1 1 1 1 1 1 1 1 - } ~ ~ ~ ~ _ - ) ~ ~ _ ~ ~t C~4 . . . . . . . . . . . . . . . . . . . 1 1 1 1 1 1 1 C~ CA o. . . . ~ ~ o.. . . . ~ ~ C . . , ~ c~ ~> c~ ~ _ _ _ ~ ~ ~ oo ~-~ r 1 1 1 1 1 1 1 1 1 - ~ C~ ~ ~ O ~ ~ ~ ~ ~ oo ~ ~ . . . . . . . . . . . . . . . 1 1 1 1 1 1 1 1 1 1 0 ~ _ ~ ~ ~ . . . . . 1 1 1 1 1 1 1 1 1 1 1 1 1 I _ 0 ~ ~ U~ ~ 0 0 ~ ~ C~ 0 ~ 0 ~ C~ . . . . . . . . . . . 1 1 1 1 1 1 1 1 r ~ -- - r = --- ~ -- r . . . . . . . . . . . . . . . . 1 1 1 1 1 oo ~ oo ~ ~ 0 ~-~ ~-~ ~-~ ~ r oo . . . . . . . . . . . . . . . . . . . . . 1 1 1 1 1 1 1 1 -~ r ~ ~ r ~ ~ ~ ~ oo u~ ~ ~ ~ ~--r" . .. . . . . . . . . . . . . . . . . . . . 1 1 1 1 1 1 0-~ ~ ~ ~ r~ oo ~ o-~ ~ ~ ~ r x ~ oo ~ ~ ~ ~ ~ ~ ~ ~ C~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ V~ 1 1 1 1

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70 c m J ',: U~ O oo o0 C~ r~ C~ O 2 oo C) eD ~ ;> z o _ o _ 1 o, _ _ o ~ ~ X _ o ~ o _ ~o _ 1 1 1 1 o ~ ~ ~ ~ 1 1 1 1 1 o oo _ ~ ~ ~ - , _ _ 1 1 1 1 o ~ _ ~ o . . . . . . . . - 1 1 1 o oo ~ ~ ~ _ ~ C~) oo tr] - 1 1 1 1 1 1 1 . o U~ ~ ~ ~ ~ ~ _ ~ ~ _ - 1 1 1 1 1 1 o ~ ~ ~ V~ ~ ~ ~ ~ o _ 1 1 1 o ~ ~ ~ _ ~ ~ - , ~ _ ~ - , ~t _ 1 1 1 1 1 o ~ ~ o ~ ~ ~ ~ o ~ o ~ U~ o _ 1 1 1 O ~ ~ ~ ~ 0~ oo d- ~ ~ - d - Ox . . . . . . . . . . . . . . . - 1 1 1 1 1 1 1 oo o ~ ~ ~ ~ ~ ~ ~ ~ X o ~ _ ~ ~ _ . - 1 1 1 1 1 1 ~ O - ~ _ ~1 t_ c-3 ~ ~ ~D ................. E 1 1 1 1 1 1 1 1 1 .= O ~ oo oo ~ ~ ~ O X ~ ~ ~ ~ o ~ _ ~ ~ C) ....... ..... .... O 1 1 1 1 O O ~ O O ~ O ~ \0 ~ M0 ~ - ~ O . . . . . . . . . . . . . . . . . _ _ - 1 c~ o ~ - ~ ~ ~ - ~ U. ~ ~ ~ o ~ - ~ o _ ~ - CD ............ ... ... ~ 1 1 , 1 1 1 1 1 1 eD C) r~ oo oS o-~ ~ U~ oo ~ X o ~ ~ .= C4 C~ ~ ~ ~ ~ ~ ~ ~ ~ ~ V ~Ct 1 1 1 1 1 1 1