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             \author[1]{João Francisco De  Abreu}

             \author[2]{Dr.Leonidas Conceicao  Barroso}

             \author[3]{Christiano Ottoni  Carvalho}

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\date{\small \em Received: 8 April 2021 Accepted: 1 May 2021 Published: 15 May 2021}

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\begin{abstract}
        


Introduction-Brazil finds itself in an advanced phase of the process of demographic transition. The shrinking of the base of the aging pyramid and the growth of its vertex are already noticeable. This essay intends to compare the migration flow figures of two distinct periods: 1995/200 and 2005/2010, in order to ascertain what kind of migration flows is occurring in this period, that could eventually explain some of its migration behavior.(Figures 1-7)A new phenomena that concern these migratory fluctuations has been taken to note and has been the studies of various research projects in the academic environment: a decline in net migration rate from traditionally underdeveloped regions (mainly the northeast) to more industrialized regions (primarily the southeast).This decline in the net migration rate can be partly explained by return migration. Considering that fact, it is of fundamental importance to know migratory patterns of the population so as to foresee the spatial redistribution of the population in general that will eventually result in the reformulation of social policy to better regionally allocate national resources.

\end{abstract}


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\let\tabcellsep& 	 	 		 
\section[{Introduction}]{Introduction}\par
razil finds itself in an advanced phase of the process of demographic transition. The shrinking of the base of the aging pyramid and the growth of its vertex are already noticeable. This essay intends to compare the migration flow figures of two distinct periods: 1995/200 and 2005/2010, in order to ascertain what kind of migration flows is occurring in this period, that could eventually explain some of its migration behavior.(Figures  {\ref 1-7})\par
A new phenomena that concern these migratory fluctuations has been taken to note and has been the studies of various research projects in the academic environment: a decline in net migration rate from traditionally underdeveloped regions (mainly the northeast) to more industrialized regions (primarily the southeast).\par
This decline in the net migration rate can be partly explained by return migration. Considering that fact, it is of fundamental importance to know migratory patterns of the population so as to foresee the spatial redistribution of the population in general that will eventually result in the reformulation of social policy to better regionally allocate national resources.\par
Spatial analysis and GIS are widely used in order to study such events  {\ref (Bailey and Gatrell, 1996)}. Specifically in this case, Tobler's approach is used  {\ref (Tobler, 1976)} for mapping the flows and, for the identification of migration patterns. 
\section[{II.}]{II.} 
\section[{Tobler's Approach}]{Tobler's Approach}\par
If a potential migrant is taken at random in a population sample and is "thrown in the air", there will be a general migration tendency that this person will follow. Tobler calls this tendency a "wind"  {\ref (Tobler, 1976)}. He has focused on the difficulties associated with the symmetry of the gravity model and tried to remove this problem introducing the "wind" in order to account for interaction in particular directions. The approach facilitates the description of large flow matrices by analyzing the asymmetric part of the from-to-tables.\par
It is interesting to see that the antecedents of the approach were motivated by the calculation of geographical locations from data on separations or on interaction. The inversion of models was used: for example, the social gravity model can be written as: 
\section[{And the inversion is}]{And the inversion is}\par
The problem was that the social gravity model is symmetric, i. e, D ij = D ji and M ij must be equal to M ij . In practice the data are different (M ij ? M ji ). This would imply that if the model is inverted, D ij ? D ji .\par
He stated that has "the consequence that the tri-lateration solution can result in more than one geometrical configuration or that the standard errors of the position determination are increased"  {\ref (Tobler, 1976. p. 2)}.\par
To overcome this problem, a "wind" was introduced in order to facilitate interaction in some direction. This vector is estimated by the data. In its formal aspect, each location i, with coordinates (x, y), has associated with a vector with magnitude and direction: 
\section[{B}]{B}\par
Volume XXI Issue III Version I ( ) ij j i ij D f P P K M . . = ? ? ? ? ? ? ? ? = ? j i ij ij P KP M f D 1 ( )( ) [ ] ? = = ? ? + ? ? = n j i i j i j ij ji ij ji ij y x x x D m m m m n i 1 1 . 1 . 1 1 ? 
\section[{Where}]{Where}\par
. For the complete algebraic development, see  {\ref Tobler (1979)}.( ) ( ) 2 2 2 i j i j ij y y x x D ? + ? =\par
Sometimes we have an incomplete matrix for a set of data, so in order to overcome this situation a complete set of data is generated, using Baxter entropy program  {\ref (Tobler, 1976)}. The program follows Wilson's derivations of the gravity model using entropymaximizing techniques. It has three variations and one can use a complete matrix or only the marginals as input. The program permits two variations with the gravity model or with the entropy model.\par
In the research described here we have used a  
\section[{Results}]{Results}\par
In the comparison of the data migration between the periods of 1995/2000 and 2005/2010 for the Northern region, the States of Rondônia, Amazonas, Roraima, Amapá and Tocantins continued to receive immigrants, showing a positive balance for both periods, with the exception of the States of Acre and Pará that continued to show a negative balance, but with a significant decrease in the number of emigrants in the comparison between the two periods considered.\par
In the Northeast region it was observed a quite expressive negative balance for almost all States, especially for the States of Bahia and Maranhão, who contributed with significant numbers of emigrants by repeating the tendency observed in the 1995/2000 period, without major modifications. The States of Piauí, Ceará and Alagoas kept negative figures, but decreased their numbers in absolute values for both periods, perhaps showing some modification in their migratory pattern, which should be better measured in the future. Only the States of Sergipe and Rio Grande do Norte presented a positive migratory balance, perhaps due to new investments in the tourism sector, typical of these States.\par
In the Southeast region the negative highlights went to the State of Minas Gerais, which was the only one to make a considerable change in its demographic profile presenting, in the 1995/2000 period, an expressive number of immigrants, but in the period 2005/2010 presented a negative number in its migratory balance. The State of Espírito Santo showed a significant increase of immigrants, nearly doubling its values of the previous decade, probably due to the new investments in oil extraction and in agribusiness. The States of Rio de Janeiro and São Paulo also presented a positive migratory balance, but with much smaller values than the previous decade, perhaps explained by the so called return migration, which has been shown to be significant in Brazil in the past two decades.\par
In the Southern region the Santa Catarina State occupies a prominent position showing an expressive positive migratory balance, almost tripling the number of immigrants in the last decade. The States of Paraná and Rio Grande do Sul have maintained the tendency of negative balances in the last two decades, but the State of Rio Grande do Sul, presented an even more expressive negative balance for the last evaluated period.\par
All This decrease is also well perceived in interregional migration. According to the 2000 Census, 3.3 million people had changed regions in the five previous years. The national survey samples (PNAD) of 2004 already shows a reduction to 2.8 million. Finally, the National Household Survey of 2009 shows that just over 2 million people had chosen another region to live.\par
In the South, the States of Paraná and Rio Grande do Sul perceived a considerable flow of return migration, while Santa Catarina is the southern State that attracts more new immigrants -its current migratory balance is 80 thousand immigrants. The same process can be observed in the Midwestern region, being the region that more retains its immigrants. According to the 2009 PNAD, in absolute terms, São Paulo remains as the State that receives more immigrants (535.000), followed by Minas Gerais (288.000), Goiás (264.000) Bahia and Paraná (both with 203.000 new immigrants). On the other hand, São Paulo is also the place that Migration Flows in Brazil: A Spatial Analysis using Tobler´S Approach generates more emigrants (588.000), followed by Bahia (312.000), Minas Gerais (276.000), Paraná (171.000) and Rio de Janeiro (165.000). (Figures  {\ref 1-3}).  
\section[{Tables and Maps}]{Tables and Maps}\begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-2.png}
\caption{\label{fig_0}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-3.png}
\caption{\label{fig_1}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{} \par 
\begin{longtable}{P{0.85\textwidth}}
III.\end{longtable} \par
 
\caption{\label{tab_0}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{1} \par 
\begin{longtable}{P{0.1552941176470588\textwidth}P{0.15176470588235294\textwidth}P{0.1164705882352941\textwidth}P{0.10470588235294118\textwidth}P{0.11588235294117648\textwidth}P{0.10647058823529412\textwidth}P{0.09941176470588235\textwidth}}
\tabcellsep \tabcellsep 1995/2000\tabcellsep \tabcellsep \tabcellsep 2005/2010\tabcellsep \\
Federation Units\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
\tabcellsep \multicolumn{6}{l}{Immigrants Emigrants Net Migration Immigrants Emigrants Net Migration}\\
BRASIL\tabcellsep 5 196 093\tabcellsep 5 196 093\tabcellsep 0\tabcellsep \multicolumn{2}{l}{4 643 754 '4 643 754}\tabcellsep 0\\
Rondônia\tabcellsep 83 325\tabcellsep 72 735\tabcellsep 10 590\tabcellsep 65 864\tabcellsep 53 643\tabcellsep 12 221\\
Acre\tabcellsep 13 634\tabcellsep 16 070\tabcellsep -2 436\tabcellsep 13 882\tabcellsep 14 746\tabcellsep -865\\
Amazonas\tabcellsep 89 627\tabcellsep 58 657\tabcellsep 30 970\tabcellsep 71 451\tabcellsep 51 301\tabcellsep 20 150\\
Roraima\tabcellsep 47 752\tabcellsep 14 379\tabcellsep 33 373\tabcellsep 25 556\tabcellsep 11 204\tabcellsep 14 352\\
Pará\tabcellsep 182 043\tabcellsep 234 239\tabcellsep -52 195\tabcellsep 162 004\tabcellsep 201 834\tabcellsep -39 830\\
Amapá\tabcellsep 44 582\tabcellsep 15 113\tabcellsep 29 469\tabcellsep 37 028\tabcellsep 15 228\tabcellsep 21 800\\
Tocantins\tabcellsep 95 430\tabcellsep 82 515\tabcellsep 12 915\tabcellsep 85 706\tabcellsep 77 052\tabcellsep 8 654\\
Maranhão\tabcellsep 100 816\tabcellsep 274 469\tabcellsep -173 653\tabcellsep 105 684\tabcellsep 270 664\tabcellsep -164 980\\
Piauí\tabcellsep 88 740\tabcellsep 140 815\tabcellsep -52 075\tabcellsep 73 614\tabcellsep 144 037\tabcellsep -70 423\\
Ceará\tabcellsep 162 925\tabcellsep 186 710\tabcellsep -23 785\tabcellsep 112 373\tabcellsep 181 221\tabcellsep -68 849\\
Rio G. do Norte\tabcellsep 77 916\tabcellsep 71 287\tabcellsep 6 630\tabcellsep 67 728\tabcellsep 54 017\tabcellsep 13 711\\
Paraíba\tabcellsep 102 005\tabcellsep 163 485\tabcellsep -61 480\tabcellsep 96 028\tabcellsep 125 521\tabcellsep -29 493\\
Pernambuco\tabcellsep 164 871\tabcellsep 280 290\tabcellsep -115 419\tabcellsep 148 498\tabcellsep 223 584\tabcellsep -75 086\\
Alagoas\tabcellsep 55 966\tabcellsep 127 948\tabcellsep -71 982\tabcellsep 53 589\tabcellsep 130 306\tabcellsep -76 717\\
Sergipe\tabcellsep 52 111\tabcellsep 56 928\tabcellsep -4 817\tabcellsep 53 039\tabcellsep 45 144\tabcellsep 7 895\\
Bahia\tabcellsep 250 571\tabcellsep 518 036\tabcellsep -267 465\tabcellsep 229 224\tabcellsep 466 360\tabcellsep -237 136\\
Minas Gerais\tabcellsep 447 782\tabcellsep 408 658\tabcellsep 39 124\tabcellsep 376 520\tabcellsep 390 625\tabcellsep -14 105\\
Espírito Santo\tabcellsep 129 169\tabcellsep 95 168\tabcellsep 34 001\tabcellsep 130 820\tabcellsep 70 120\tabcellsep 60 700\\
Rio de Janeiro\tabcellsep 319 749\tabcellsep 274 213\tabcellsep 45 536\tabcellsep 270 413\tabcellsep 247 309\tabcellsep 23 104\\
São Paulo\tabcellsep 1 223 811\tabcellsep 883 885\tabcellsep 339 926\tabcellsep 991 314\tabcellsep 735 519\tabcellsep 255 796\\
Paraná\tabcellsep 297 311\tabcellsep 336 998\tabcellsep -39 687\tabcellsep 272 184\tabcellsep 293 693\tabcellsep -21 509\\
Santa Catarina\tabcellsep 199 653\tabcellsep 139 667\tabcellsep 59 986\tabcellsep 301 341\tabcellsep 128 888\tabcellsep 172 453\\
Rio G. do Sul\tabcellsep 113 395\tabcellsep 152 890\tabcellsep -39 495\tabcellsep 102 613\tabcellsep 177 263\tabcellsep -74 650\\
Mato G. do Sul\tabcellsep 97 709\tabcellsep 108 738\tabcellsep -11 029\tabcellsep 98 973\tabcellsep 80 908\tabcellsep 18 065\\
Mato Grosso\tabcellsep 166 299\tabcellsep 123 724\tabcellsep 42 575\tabcellsep 143 954\tabcellsep 121 589\tabcellsep 22 365\\
Goiás\tabcellsep 372 702\tabcellsep 169 900\tabcellsep 202 802\tabcellsep 363 934\tabcellsep 156 107\tabcellsep 207 827\\
Distrito Federal\tabcellsep 216 200\tabcellsep 188 577\tabcellsep 27 623\tabcellsep 190 422\tabcellsep \tabcellsep \end{longtable} \par
 
\caption{\label{tab_1}Table 1}\end{figure}
 			\footnote{© 2021 Global JournalsMigration Flows in Brazil: A Spatial Analysis using Tobler´S Approach} 		 		\backmatter  			  				\begin{bibitemlist}{1}
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