genome wide pertub-seq

 CRISPi + scRNA

https://gwps.wi.mit.edu/

matrix file in H5AD format

https://doi.org/10.25452/figshare.plus.20029387

Genome wide screen targeted n=9867 genes. 

Essential-wide screen targeted n=2285 essential genes. 

Growth phenotypes were measured log2-guide enrichment per cell doubling (gamma)

"The relative homogeneity of CRISPRi reduces selection for unperturbed cells, especially when studying essential genes.  Unlike CRISPR knockout, CRISPRi does not lead to activation of the DNA damage response which can alter transcriptional signatures (Haapaniemi et al., 2018)."

"We use a compact, multiplexed CRISPR interference (CRISPRi) library to assay thousands of loss-of-function genetic perturbations with single-cell RNA sequencing (scRNA-seq) in chronic myeloid leukemia (CML) (K562) and retinal pigment epithelial (RPE1) cell lines."

There are four datasets on SRA:

1. K562 day 8 Perturb-seq (KD8): targeting all expressed genes at day 8 after transduction
2. RPE1 day 7 Perturb-seq (RD7): targeting DepMap essential genes at day 7 after transduction
3. K562 day 6 Perturb-seq (KD7): targeting DepMap essential genes at day 6 after transduction
4. K562 day 8 Perturb-seq (KD8_ultima): scRNA-seq libraries from the KD8 experiment sequenced on the Ultima sequencing platform rather than the Illumina sequencing platform

Potential problem: essential gene cannot be deleted? 

This is good data set for graph controllability, graph neural network analysis. 

metabolic control of longevity

 

metabolic control of longevity

microbiome -> u, B is the gene target, A -> gene/metabolite network

x = A x + B u

linear dynamic systems, laplace transform

 

https://see.stanford.edu/Course/EE263 

https://see.stanford.edu/materials/lsoeldsee263/13-lin-sys.pdf

advantages of temporal network, continued

 Li, ..., Barabasi, Science, 2017,

temporal network advantages.

Energy needed from state vector x0 to final state xf
  E(x0, xf) = 1/2 d^T x W^01_eff  x d

where Weff encode the energy structure of the network.

I did not follow S1.1 method. 

After reading Laplace transformation, and watched YouTube movies on solving differential equations with Laplace transformation, it seems the Li17 presented a general solution. 

Li17 cited a yeast dynamic protein network: 

27. J. Wang, X. Peng, M. Li, Y. Pan, Construction and application of dynamic protein interaction

network based on time course gene expression data. Proteomics 13, 301–312 (2013).

doi:10.1002/pmic.201200277 Medline

In Figure S6, a digram is presented to describe the construct of a yeast dynamic PPI. An interaction is consider as active when both protein are active at that time point. based on  X. Tang, J. Wang, B. Liu, M. Li, G. Chen, Y. Pan, A comparison of the functional modules identified from time course and static PPI network data. BMC Bioinformatics 12, 339

(2011). doi:10.1186/1471-2105-12-339 Medline

https://bmcbioinformatics.biomedcentral.com/articles/10.1186/1471-2105-12-339#Sec17

In Fig 2. Protein networks used contain only 84, 74, and 85 nodes. So, it seems Li17 only used a small subset of PPI. 

Li17 fixed the number of driver nodes to 20% of the nodes. Hong did not find the criteria on the reasons behind this choice. 

geometric multiplicity == algebraic multiplicity-for-a-symmetric-matrix

 good post to prove that geometric and algebraic multiplicity are the same for a symmetric matrix.

https://math.stackexchange.com/questions/393149/geometric-multiplicity-algebraic-multiplicity-for-a-symmetric-matrix

yeast genome hybrid

A yeast living ancestor reveals the origin of genomic introgressions

Melania D’Angiolo, 

Matteo De Chiara, 

Jia-Xing Yue, 

Agurtzane Irizar, 

Simon Stenberg, 

Karl Persson, 

Agnès Llored, 

Benjamin Barré, 

Joseph Schacherer, 

Roberto Marangoni, 

Eric Gilson, 

Jonas Warringer & 

Gianni Liti 

 

Nature, 

https://www.nature.com/articles/s41586-020-2889-1

"Genome introgressions drive evolution across the animal1, plant2 and fungal3 kingdoms. Introgressions initiate from archaic admixtures followed by repeated backcrossing to one parental species. However, how introgressions arise in reproductively isolated species, such as yeast4, has remained unclear. Here we identify a clonal descendant of the ancestral yeast hybrid that founded the extant Saccharomyces cerevisiae Alpechin lineage5, which carries abundant Saccharomyces paradoxus introgressions. We show that this clonal descendant, hereafter defined as a ‘living ancestor’, retained the ancestral genome structure of the first-generation hybrid with contiguous S. cerevisiae and S. paradoxus subgenomes. The ancestral first-generation hybrid underwent catastrophic genomic instability through more than a hundred mitotic recombination events, mainly manifesting as homozygous genome blocks generated by loss of heterozygosity. These homozygous sequence blocks rescue hybrid fertility by restoring meiotic recombination and are the direct origins of the introgressions present in the Alpechin lineage. We suggest a plausible route for introgression evolution through the reconstruction of extinct stages and propose that genome instability allows hybrids to overcome reproductive isolation and enables introgressions to emerge."

Network controllability analysis on the LOH blocks (genomic instability) regions might be interesting. 

Source data are provided on nature web site

https://github.com/mdangiolo89/A-yeast-living-ancestor-reveals-the-origin-of-genomic-introgressions 

Liu et al, Genome biology, 2020, Genome-wide studies reveal the essential and opposite roles of ARID1A in controlling human cardiogenesis and neurogenesis from pluripotent stem cells

 in virto human embryonic stem cell study. hESC

ARID1A in H9 hESC were deleted using dual guided-RNA mediated CRISP-Cas9 method. 

" Mutations in 4 different SWI/SNF subunits including ARID1A/B were identified in three congenital syndromes that include both neural and cardiac defects: Coffin-Siris syndrome (CSS), Nicolaides- Baraitser syndrome (NCBRS), and ARID1B-related intellectual disability (ID) syndrome  Patients with these syndromes show severe intellectual deficits as well as cardiac defects such as atrial/ventricular septal defects, patent ductus

arteriosus (PDA), mitral and pulmonary atresia, aortic stenosis, and single right ventricle. These data indicate that abnormal ARID1A activity can lead to defective  formation of both the heart and brain in humans. However, the molecular mechanisms  by which ARID1A controls human cardiogenesis and neurogenesis still remain. elusive." 

in hESC, Surprisingly, knockout-of-ARID1A in hESCs (ARID1A−/−) led to spontaneous neural. differentiation even under pluripotent stem cell culture conditions. Additionally, under conditions of targeted cardiac differentiation, ARID1A−/− hESCs gave rise to robustly increased numbers of neural cells, including neural stem cells and neurons, whereas cardiac differentiation was significantly suppressed

single-cell RNA reveals spontaneous differentiation neural differentiation in ARIA-/- cells. 

So, scRNA data are available for WT and KO in cardiac differential and neural differentiation. Based on my understanding of Liu, GB, 2020, there are WT and ARID1A-/- hESC cells, and the hESC cells are induced for cardiac differentation in CDM3 and neural differentation in N2B27 medium. The scRNA results show ARIDA-/- lead to different clusters of ScRNA in WT and KO in both differentation conditions. So, it seems to me that these data sets can be used to contruct weight single-cell gene network to study network control.

The noise levels seem to be good testing data sets on noises and weight in controllability analysis. 

https://genomebiology.biomedcentral.com/articles/10.1186/s13059-020-02082-4 

geometric multiplicity and algebraic multiplicity are equal for symmetric matrice

𝜆$\lambda$ be an eigen value of a symmetric matrix 𝐴$A$ then how to show that the geometric multiplicity and algebraic multiplicity are equal?

in general, geometric multiplicity <= algebraic multipliciy

https://youtu.be/Xcln3xG8QGQ

advantage of temporal networks

Li, ..., Barabasi, Science, 2017,
tempoal network advantages.

Energy needed from state vector x0 to final state xf
  E(x0, xf) = 1/2 d^T x W^01_eff  x d

where Weff encode the energy structure of the network.

I did not follow S1.1 method

algebraic multiplicity and geometric multiplicity

https://people.math.carleton.ca/~kcheung/math/notes/MATH1107/wk10/10_algebraic_and_geometric_multiplicities.html

The algebraic multiplicity of λ is the number of times λ is repeated as a root of the characteristic polynomial.

 Let A be an n × n matrix with eigenvalue λ. The geometric multiplicity of λ is the dimension of the eigenspace of λ.

In general, the algebraic multiplicity and geometric multiplicity of an eigenvalue can differ. However, the geometric multiplicity can never exceed the algebraic multiplicity.

It is a fact that summing up the algebraic multiplicities of all the eigenvalues of an n×n$n\times n$ matrix A$A$ gives exactly n$n$. If for every eigenvalue of A$A$, the geometric multiplicity equals the algebraic multiplicity, then 
$A$ is said to be diagonalizable. As we will see, it is relatively easy to compute powers of a diagonalizable matrix.

yeast PIN nD

controllability for yPIN with Dang's data



```{r eigen-spectrum}
e=eig$values;
summary(e)
digits = c(1:30)
zeros = digits
debug = 0
for ( i in 1:length(digits ) ) {
 tmp = sort(table(round(e, roundings[i])), decreasing = T)
 if (debug > 0) { print(tmp[1:3]) }
 zeros[i] = tmp[1]
}
cbind( digits , zeros)
```

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
-59.919  -1.696   0.000   0.000   1.384  97.758 
      digits zeros
 [1,]      1   228
 [2,]      2   158
 [3,]      3   140
 [4,]      4   136
 [5,]      5   135
 [6,]      6   135
 [7,]      7   135
 [8,]      8   135
 [9,]      9   135
[10,]     10   135
[11,]     11   135
[12,]     12   135
[13,]     13   135
[14,]     14   135
[15,]     15   112
[16,]     16    45
[17,]     17     9
[18,]     18     3
[19,]     19     2
[20,]     20     1
[21,]     21     1
[22,]     22     1
[23,]     23     1
[24,]     24     1
[25,]     25     1
[26,]     26     1
[27,]     27     1
[28,]     28     1
[29,]     29     1
[30,]     30     1

Conclusion: frequency of zero eigen values stabilize between 5 and 14 at 135. 

Yuan method on adjacency matrix controllability

Yuan clearly used weighted matrix, and j->i as direction. So, column to row indicate direction? 

Wikipedia, “In directed graphs, the in-degree of a vertex can be computed by summing the entries of the corresponding column, and the out-degree can be computed by summing the entries of the corresponding row.” The question now is does i->j and j->i matters? It can be tested using a star shaped network with outward and inwarding arrows. A quick exam on these show both star networks should have the same number of minimal control nodes. Well, eigen values of a matrix and its transpose are the same, see  https://yutsumura.com/eigenvalues-of-a-matrix-and-its-transpose-are-the-same/.  

So, i->j and j->i does not matter! This is somewhat shocking to me. 

RLS ration and n_D

JK showed a results of 800 data points of n_D and RLS ratio. There was no obvious linear correlation, but there seems to be three clusters of data points.

EG: Driver node cannot be indispensable node

Note that, I also found that a driver node cannot be indispensable; it has to be either dispensable or neutral. 

I confirmed it with the genes that was removed so far. 

They are either neutral or dispensable.

structural controllability and edge weight

structural controllability only considers topology. So networks with the same topology but different weight have exactly the same number of minimum driver nodes.

This suggests that gene duplication will provide controllability advantage.

controllability and mirror effect of adjacency matrix

using the matrix eigen value genometric multiplicity, the adjacentcy matric matrix can be mirrored, and its control nodes should not be changed, based on my intuitive understanding.

multiplicity of eigen value

The number of linearly independent eigenvectors associated with a given eigen value $lambda$ is called the geometric multiplicity of eigenvalue $lambda$.

pairwise interaction to adjancency matrix, rank and eigen values, igraph

igraph_48states

H Qin

11/19/2017

require(Matrix)

## Loading required package: Matrix

## Warning: package 'Matrix' was built under R version 3.4.2

require(igraph)

## Loading required package: igraph

## Warning: package 'igraph' was built under R version 3.4.1

## 
## Attaching package: 'igraph'

## The following objects are masked from 'package:stats':
## 
##     decompose, spectrum

## The following object is masked from 'package:base':
## 
##     union

#URL = "https://docs.google.com/spreadsheet/pub?key=0ArLJZixvTlU7dDI5c3dnTzdRX1dndzBORUk1UC0wYlE&single=true&gid=0&output=csv"
#states = read.csv(textConnection(getURL(URL)), colClass = c("character", "character"))
states = read.csv("48states.csv", colClass = c("character", "character"))

g = graph.data.frame(states, directed=F)
g.degree = degree(g)
g.degree [g.degree == max(g.degree)] #TN and MO have 8 bordering states

##  MISSOURI TENNESSEE 
##         8         8

g.shortestpath.m = shortest.paths(g)
str(g.shortestpath.m)

##  num [1:48, 1:48] 0 4 3 4 3 7 3 1 2 4 ...
##  - attr(*, "dimnames")=List of 2
##   ..$ : chr [1:48] "TEXAS" "WISCONSIN" "VIRGINIA" "WASHINGTON" ...
##   ..$ : chr [1:48] "TEXAS" "WISCONSIN" "VIRGINIA" "WASHINGTON" ...

sorted.names = sort( rownames(g.shortestpath.m) )
gsm = g.shortestpath.m[, sorted.names]
gsm = gsm[sorted.names, ]

A = as_adjacency_matrix(g, type = c("both", "upper", "lower"), attr = NULL,
  edges = FALSE, names = TRUE, sparse = igraph_opt("sparsematrices"))

rankMatrix(A)

## [1] 48
## attr(,"method")
## [1] "tolNorm2"
## attr(,"useGrad")
## [1] FALSE
## attr(,"tol")
## [1] 1.065814e-14

eigen(A)

## eigen() decomposition
## $values
##  [1]  5.46905036  4.71349007  4.10283310  3.98769817  3.56553201
##  [6]  3.29609990  2.92589988  2.47279120  2.21403386  1.98027335
## [11]  1.64326053  1.37137510  1.32589358  1.05103630  0.87007730
## [16]  0.72474178  0.49265884  0.25786926  0.13794547  0.06087911
## [21] -0.18440602 -0.30846880 -0.37586922 -0.69511879 -0.76035086
## [26] -0.82759766 -1.00000000 -1.04901188 -1.11963361 -1.21597743
## [31] -1.29093275 -1.39362399 -1.45885353 -1.51222782 -1.59093188
## [36] -1.64174682 -1.67854299 -1.74845653 -1.83665486 -1.93900022
## [41] -2.03895713 -2.13101810 -2.21289102 -2.25499195 -2.37505991
## [46] -2.39627221 -2.78120712 -2.84563603
## 
## $vectors
##                [,1]         [,2]         [,3]         [,4]        [,5]
##  [1,] -0.1269362183 -0.037595880  0.191120477  0.017179147  0.14085327
##  [2,] -0.1342561539  0.071741990 -0.239778162  0.127059399  0.02027220
##  [3,] -0.1354063391  0.211752293  0.086709716 -0.111031700 -0.18431323
##  [4,] -0.0338266747 -0.080078900 -0.010949302 -0.067103579 -0.12131413
##  [5,] -0.2582273680 -0.119195635 -0.097785210  0.095623439  0.14619647
##  [6,] -0.0058462038  0.027364688 -0.040557097 -0.200221510  0.21938914
##  [7,] -0.2334173178  0.027787111 -0.247476898  0.182905195  0.11339213
##  [8,] -0.2359207076 -0.083804838  0.195581899  0.037136383  0.20370474
##  [9,] -0.3334726731  0.105698197  0.058235559  0.141495543  0.15033629
## [10,] -0.0582955868 -0.140444357 -0.001589589 -0.123980447 -0.20834424
## [11,] -0.1879761471 -0.107183098 -0.248112711  0.107153245  0.06329444
## [12,] -0.0312374324  0.048998675  0.099388387  0.009141556 -0.03555842
## [13,] -0.0214983987  0.076277237 -0.082433313 -0.377517079  0.29194375
## [14,] -0.1831862658 -0.295982537  0.043295372 -0.161989688 -0.14129937
## [15,] -0.0892716733  0.133319468  0.164494910 -0.016744545 -0.10958822
## [16,] -0.2048646256 -0.246091640 -0.098168091 -0.042349949 -0.03808803
## [17,] -0.2344864497  0.238516369  0.291341321  0.033186539 -0.06563561
## [18,] -0.0320928344  0.054511479  0.090408412 -0.001137113 -0.05484129
## [19,] -0.1720858750 -0.194330230  0.142128166 -0.079235812  0.04390342
## [20,] -0.0078784656  0.038151177 -0.058338963 -0.289781327  0.32467730
## [21,] -0.1381976245  0.130455228 -0.248376998  0.065730253 -0.06531480
## [22,] -0.2546395582 -0.265142754  0.077424414 -0.061291765  0.07187651
## [23,] -0.0636729692  0.141296550 -0.024125732 -0.214479862 -0.12652124
## [24,] -0.0025963189  0.014554770 -0.025626722 -0.131124543  0.16561797
## [25,] -0.1978881589 -0.076895257  0.056901330  0.053405145  0.16045684
## [26,] -0.0689963439  0.164487874 -0.095056328 -0.339631128 -0.04453663
## [27,] -0.0065734019  0.030814251 -0.045368949 -0.223348667  0.24034822
## [28,] -0.0862456542  0.123619846  0.206435714  0.012210082 -0.08595017
## [29,] -0.2375124487  0.274479950 -0.027411095 -0.036509914 -0.16411286
## [30,] -0.1030970866 -0.219091774  0.023876785 -0.172477505 -0.23869805
## [31,] -0.1156005468  0.210479995 -0.048543911 -0.208213126 -0.19131677
## [32,] -0.0217080078  0.067899758 -0.053519840 -0.229092867  0.06070853
## [33,] -0.1266371117  0.200078700 -0.139284127 -0.128638496 -0.16266212
## [34,] -0.0551935383 -0.125805661  0.023884271 -0.111207145 -0.15864067
## [35,] -0.1415520797  0.015845772 -0.279065375  0.136080784  0.04106613
## [36,] -0.1106762297  0.094787206  0.228891818  0.042138321  0.04154739
## [37,] -0.1096814151 -0.135439731 -0.134255585 -0.004765675 -0.05166695
## [38,] -0.0803082094 -0.048112344 -0.161213887  0.059801004  0.01477861
## [39,] -0.0809742399  0.027674606  0.169795412  0.034068250  0.09571926
## [40,] -0.1322777780  0.163165916 -0.152071194  0.005652420 -0.11469594
## [41,] -0.2210866450  0.164067046 -0.208850510  0.121958301 -0.01686227
## [42,] -0.2052397480  0.073252655  0.276629943  0.076536430  0.15888943
## [43,] -0.1267042007 -0.237006745 -0.043333571 -0.143608372 -0.22420519
## [44,] -0.0845934368  0.107334924  0.201338251  0.024243685 -0.04083453
## [45,] -0.0065734019  0.030814251 -0.045368949 -0.223348667  0.24034822
## [46,] -0.1404635674 -0.233447603  0.075705982 -0.147002579 -0.11859609
## [47,] -0.0282274455  0.079279722 -0.042093328 -0.196404999 -0.03094891
## [48,] -0.0004747294  0.003087897 -0.006246104 -0.032882264  0.04644972
##              [,6]         [,7]         [,8]         [,9]        [,10]
##  [1,] -0.15433668  0.038758775 -0.293507694  0.120178849 -0.143275371
##  [2,]  0.01694524  0.184338924 -0.056227569  0.236909835  0.140575869
##  [3,]  0.04006946 -0.133528566  0.108782578 -0.116138102 -0.098408554
##  [4,]  0.08392612  0.098508725 -0.129072682 -0.198773911  0.110653949
##  [5,]  0.02977982 -0.221290476  0.179044831 -0.155536557  0.151313884
##  [6,]  0.10208301  0.120761438  0.058680015 -0.052201859 -0.084134168
##  [7,]  0.07972409  0.008937100 -0.001401282  0.027433737  0.274619285
##  [8,] -0.23919868 -0.025809991 -0.037673906  0.018941326  0.008109148
##  [9,] -0.08386704  0.022720468  0.073271203 -0.292015812  0.241261140
## [10,]  0.09826935  0.211230394 -0.162414860 -0.211783340  0.250504572
## [11,]  0.25054231 -0.242523726 -0.106249402  0.012933933 -0.095694147
## [12,]  0.17798879  0.008820393  0.083862174  0.195012840  0.055165717
## [13,]  0.09821281  0.052621287 -0.013424752  0.030928690  0.072812396
## [14,] -0.02858334  0.060517228  0.090454156  0.135162051 -0.128800640
## [15,]  0.23165796 -0.044429880  0.199935346  0.098389473  0.006291263
## [16,]  0.15220564 -0.209432256  0.039493019 -0.092483240 -0.218156736
## [17,]  0.22996360  0.020424308  0.029461374 -0.075320379  0.001226677
## [18,]  0.16880256 -0.015620114  0.160127611  0.157959001  0.038899640
## [19,] -0.20836085  0.036727560  0.048275195  0.289270338 -0.151333179
## [20,]  0.15302117  0.183119342  0.087739197 -0.074571757 -0.108707118
## [21,] -0.07324914  0.247516264 -0.044333611  0.238644837 -0.102605141
## [22,] -0.16224479 -0.112155780  0.249804229  0.133196413 -0.069585274
## [23,] -0.08779489 -0.270436182 -0.079090516  0.035525224  0.099024296
## [24,]  0.08524184  0.117595247  0.070788981 -0.071933615 -0.130713928
## [25,] -0.13820294 -0.115019581  0.187822715 -0.133428235  0.167198583
## [26,] -0.12130606 -0.249679525 -0.154008998  0.131871679  0.161878247
## [27,]  0.10941770  0.122405444  0.050458235 -0.035948806 -0.036617054
## [28,]  0.32473215 -0.001273010  0.196026802  0.251337104  0.070740658
## [29,] -0.10582075  0.084475348  0.123606375 -0.241941621 -0.176862830
## [30,]  0.04824161  0.238780622 -0.067440959 -0.035397007  0.181523143
## [31,] -0.13593296 -0.180724809 -0.004915977 -0.073786387 -0.124555243
## [32,] -0.02891431 -0.145047523 -0.126523292  0.135276715  0.248385592
## [33,] -0.17319637  0.040386229 -0.011445625  0.027317260 -0.232284588
## [34,]  0.01337832  0.203753366 -0.048349464 -0.006415738  0.235269940
## [35,]  0.14064709  0.021593873 -0.152453774  0.269864177  0.025998673
## [36,]  0.13068497  0.051263418 -0.281291971  0.028443975 -0.050887494
## [37,]  0.23383146 -0.174321331 -0.158640892 -0.102208036 -0.257864287
## [38,]  0.18962437 -0.135087050 -0.168774488  0.081566085 -0.165411387
## [39,] -0.01973913  0.049035616 -0.377559179  0.033133192 -0.112292798
## [40,] -0.13456361  0.216578784  0.051349572  0.005692832 -0.217842011
## [41,] -0.09126884  0.261309997  0.059149631 -0.011416353  0.080365830
## [42,] -0.04141045  0.053451109 -0.358825352 -0.075264815 -0.028207569
## [43,]  0.17835954  0.076996271 -0.156754932 -0.228308830 -0.031379505
## [44,]  0.26193669  0.027080595  0.011346845  0.180427927  0.038502542
## [45,]  0.10941770  0.122405444  0.050458235 -0.035948806 -0.036617054
## [46,] -0.10241469  0.146150933  0.110297690  0.232975685  0.033871077
## [47,] -0.07221118 -0.227336293 -0.145431934  0.136706860  0.257180725
## [48,]  0.02586142  0.040191138  0.028627156 -0.032489844 -0.066008023
##              [,11]         [,12]         [,13]        [,14]        [,15]
##  [1,] -0.099643714  0.0786030590  0.2370736975  0.036692213 -0.042633056
##  [2,] -0.098633485 -0.0064999438  0.0536957489 -0.241128573 -0.218745333
##  [3,] -0.375033353  0.0997258651 -0.0302497029 -0.128345136 -0.158346501
##  [4,]  0.089195340  0.0190103318  0.3001843694 -0.005352065 -0.274709457
##  [5,]  0.095691459 -0.0769909062 -0.0971445877  0.038261855 -0.025641418
##  [6,] -0.103819289 -0.3181593563  0.0822591603 -0.013989263  0.070083529
##  [7,] -0.142555115 -0.0270085509 -0.0836957817 -0.123901657 -0.081112303
##  [8,] -0.024560936  0.0600514551  0.2892976722  0.198297298 -0.076475454
##  [9,]  0.017006868  0.0043081711 -0.0104030456  0.019535764  0.126085494
## [10,] -0.019075383  0.0051379051  0.1783576845  0.191515550 -0.114601223
## [11,] -0.101788822  0.0123431395 -0.0866681007  0.169721385  0.099128714
## [12,]  0.244525623 -0.1343661512 -0.0144036069  0.227319797 -0.270714179
## [13,]  0.101338864  0.1627843947 -0.0301120660 -0.011006893  0.100423671
## [14,]  0.035547280 -0.0104612744 -0.1211327029 -0.300407387 -0.001160090
## [15,] -0.206350645  0.1671324222  0.2770769979 -0.130231670  0.190226522
## [16,]  0.205948306 -0.0253112279 -0.0274459817 -0.234395234  0.010171534
## [17,] -0.048614118  0.0188998355 -0.1495438401 -0.094079021  0.099364083
## [18,] -0.046076065  0.1171084083  0.3543778446 -0.021786901  0.221766619
## [19,] -0.112286634  0.0558605404  0.0743453049 -0.014734192 -0.065860493
## [20,] -0.087266285 -0.0405380757 -0.0017131960  0.012387413 -0.081953763
## [21,]  0.127005817 -0.0117059955  0.1253423447 -0.012917658 -0.057811614
## [22,]  0.077709352 -0.0351055099 -0.0328740149 -0.017630605 -0.094974618
## [23,] -0.198015018 -0.0727613649 -0.0005962075 -0.091762512 -0.274172027
## [24,] -0.184674719 -0.5585621371  0.1408921544 -0.016083743  0.042508180
## [25,]  0.100925410 -0.0348094333  0.1122835395  0.226884945 -0.081608837
## [26,]  0.130110372 -0.0669632747  0.0315346816  0.044822684  0.057526387
## [27,]  0.021876951  0.3291720956 -0.0976553822  0.027049760 -0.142160744
## [28,]  0.130635666 -0.0065328673  0.1927903106  0.107332846  0.002727578
## [29,] -0.012334739  0.0472626052 -0.1089745114  0.045839007  0.110269886
## [30,] -0.105035973 -0.0142405484 -0.1204985350  0.080599418  0.116131949
## [31,] -0.150962987 -0.0237719300 -0.0580703255  0.135338800 -0.263462159
## [32,]  0.183747454 -0.0094450194  0.0433047234 -0.108888997  0.326041691
## [33,]  0.207201221 -0.0398640635  0.0312906685  0.271691948  0.035489811
## [34,] -0.181151755 -0.0186561788 -0.1628573692  0.323183205  0.183282825
## [35,] -0.229997268  0.0247938150  0.0087165519  0.111823594 -0.123857648
## [36,]  0.119078201 -0.1217401490 -0.3097837498 -0.102269321 -0.038690660
## [37,]  0.065620891  0.0545709729  0.0817741120  0.060837618  0.155914672
## [38,] -0.161973828  0.0668729712  0.0028830091  0.325757159  0.150774808
## [39,] -0.002821714 -0.0216139605 -0.0524609283 -0.102667791  0.012789940
## [40,]  0.246667125  0.0005100111  0.0516559070  0.072475266  0.184356379
## [41,]  0.083466053  0.0050068703  0.0208317337 -0.228439162  0.072456217
## [42,] -0.024071298  0.0134962428  0.0031524444 -0.042330467  0.092451953
## [43,]  0.165646564  0.0209323905  0.2196548433 -0.197140765 -0.124417239
## [44,]  0.271183639 -0.1777335264 -0.2118879605  0.131588512 -0.238269840
## [45,]  0.021876951  0.3291720956 -0.0976553822  0.027049760 -0.142160744
## [46,] -0.173568174 -0.0164819758 -0.2737906895  0.067562310  0.157939499
## [47,]  0.070495704 -0.1087737843  0.0559948390 -0.148262079  0.125731416
## [48,] -0.112383104 -0.4073007730  0.1062620384 -0.015302747  0.048855636
##              [,16]        [,17]        [,18]         [,19]        [,20]
##  [1,]  0.004569971 -0.328816297  0.031924327  0.0098454584  0.140469516
##  [2,]  0.006847243  0.094120659 -0.003154881  0.0682422178 -0.142952082
##  [3,] -0.032344214  0.105422429 -0.010157843  0.0879556730  0.194945179
##  [4,] -0.029275772  0.125935121  0.215556117 -0.2310458442  0.331326772
##  [5,]  0.340588556 -0.093979374  0.038939005 -0.0313837807  0.173275821
##  [6,] -0.017953074  0.022664822  0.372401038  0.4158130272  0.027376347
##  [7,]  0.035031621 -0.299110229  0.165970726 -0.1451006657 -0.013715246
##  [8,] -0.185746153  0.090816539 -0.055511539  0.0622958624 -0.116376646
##  [9,] -0.186767093 -0.065975219 -0.016820694 -0.0158290167 -0.221328780
## [10,]  0.077517410  0.045403832  0.044656524 -0.0361971078  0.210516854
## [11,]  0.048639755 -0.135868884  0.057752284 -0.0722649824  0.167524947
## [12,] -0.183183036 -0.306458831 -0.052417179  0.1130354697 -0.002808344
## [13,] -0.029624613  0.031794440  0.223336340 -0.0041593901 -0.013949092
## [14,] -0.075874782 -0.010145324  0.067421208 -0.0735415823 -0.230116107
## [15,]  0.189833127  0.097373493  0.008452687 -0.0124499873  0.057737064
## [16,]  0.137426263 -0.066956996 -0.059638536  0.0814462550  0.016763430
## [17,] -0.130275138  0.252386528  0.077087770 -0.1016898762  0.015830336
## [18,]  0.284119329 -0.142338990 -0.044756282 -0.0003806891 -0.140942987
## [19,] -0.227401201 -0.097073686  0.148084039 -0.1562178981  0.203415476
## [20,]  0.020497436 -0.016837237 -0.033759983  0.1396254155  0.018413771
## [21,]  0.153850443  0.291136083 -0.132867307  0.1232947880 -0.017632673
## [22,]  0.107806438  0.218478992 -0.001583840  0.0046159858  0.158511719
## [23,] -0.003617855 -0.047036321 -0.305111864  0.2528411415  0.049541251
## [24,] -0.003884165 -0.003791178 -0.093545577 -0.0781065019 -0.002798032
## [25,]  0.104701770  0.303132566 -0.135638767  0.1428031736 -0.097207192
## [26,]  0.054378724 -0.028187579  0.101602573 -0.0964576923 -0.181133034
## [27,]  0.033158600 -0.029481549 -0.255448732 -0.1571432208 -0.004754105
## [28,]  0.016080020 -0.167498055 -0.019993957  0.0123974729 -0.066317547
## [29,] -0.184356659 -0.106204106  0.095207349 -0.0893704916  0.103404388
## [30,]  0.041476285 -0.057927593 -0.076340744  0.0804508246 -0.262249182
## [31,]  0.104975322 -0.144582303  0.121744663 -0.0371976998 -0.214644952
## [32,] -0.144710482  0.096986903  0.128245413 -0.1452680778  0.144001918
## [33,]  0.242020004  0.004775827  0.149853992 -0.1600998847 -0.179825177
## [34,]  0.142714377 -0.062278148 -0.138628601  0.1412764123  0.134084463
## [35,] -0.006145550  0.248883933  0.116195334 -0.1056669255 -0.089614763
## [36,]  0.189507284  0.229708295 -0.003006369 -0.0233022951  0.057322500
## [37,] -0.222826628 -0.028111583 -0.188836374  0.1794841212 -0.077829861
## [38,] -0.248823000  0.172337242 -0.057737616  0.0112523687  0.001319388
## [39,]  0.353987284 -0.170732323 -0.044060413  0.0719044431  0.112458474
## [40,]  0.046554178 -0.009809241 -0.147044539  0.0776460419  0.299058674
## [41,] -0.177774031 -0.194540413 -0.150112299  0.1368865080  0.112259886
## [42,]  0.062472119  0.014995214 -0.040279784  0.0233757289 -0.190945645
## [43,] -0.098734785  0.016639218  0.010928772  0.0043253802 -0.190345976
## [44,] -0.148840419  0.016518403  0.006477177  0.0031952581  0.066146578
## [45,]  0.033158600 -0.029481549 -0.255448732 -0.1571432208 -0.004754105
## [46,] -0.015562624 -0.018158120 -0.004063834 -0.0247652757  0.059895270
## [47,] -0.129631843  0.044174594 -0.291868363  0.0805780092  0.203848834
## [48,] -0.005359378 -0.007695342 -0.362763583 -0.5662128808 -0.045960460
##               [,21]       [,22]         [,23]        [,24]        [,25]
##  [1,]  0.2208684340  0.10690302 -0.0567608955 -0.155898463 -0.074579510
##  [2,]  0.1898046899 -0.22211101  0.1754099184  0.087867822 -0.235829896
##  [3,]  0.2808638752 -0.05587835 -0.1674022699 -0.054751545  0.074018912
##  [4,] -0.2787962425 -0.07958535  0.0279084092  0.319894237  0.166149094
##  [5,]  0.0520892097  0.11095478 -0.0643586902 -0.043754704  0.072364435
##  [6,] -0.0478331810  0.01395297 -0.0001071867 -0.024016761  0.133456083
##  [7,] -0.0989230516  0.03892521  0.0645295180 -0.161341370  0.045281001
##  [8,]  0.0914676161  0.05799847  0.1431359915 -0.123311586 -0.033412692
##  [9,] -0.1265634291  0.06725144 -0.0103623344  0.138102034  0.090524393
## [10,]  0.0545418416  0.01449414  0.0704037353 -0.110304763 -0.117276487
## [11,] -0.0051836656  0.16303815  0.0342795235 -0.089469119  0.065430389
## [12,]  0.1802470852 -0.03223512 -0.2896552122  0.309137322  0.101932694
## [13,]  0.1853353149 -0.19391493 -0.0228618240 -0.070137157  0.309809532
## [14,] -0.1256251896  0.10716955 -0.2517133008 -0.017923935  0.037348054
## [15,]  0.0941576011  0.02557857 -0.0097242616 -0.061422279  0.132601719
## [16,]  0.2388284314  0.09181721  0.1550428935  0.166849340 -0.114027888
## [17,]  0.0733705996  0.19886519  0.1253007131  0.052873786 -0.004976271
## [18,] -0.3401693852 -0.18118989  0.0577320441 -0.055263294 -0.155497131
## [19,] -0.1015483111  0.02870859  0.1735511930 -0.199138324 -0.004286802
## [20,] -0.1405522589  0.13785758  0.0159622374  0.050803287 -0.232596797
## [21,]  0.1558267223  0.16072970  0.0287623700  0.080857412  0.160951232
## [22,] -0.0168191971 -0.16525633  0.0224517576  0.149096634 -0.089010287
## [23,] -0.1928507401  0.09047383  0.0432072719 -0.049798085  0.283260448
## [24,] -0.0359623294  0.05175330  0.0069398748  0.036028371 -0.178686184
## [25,] -0.0009446519 -0.23000177 -0.2417509076 -0.172822804 -0.053219967
## [26,] -0.0333347697 -0.04913203  0.1575154865 -0.006986629  0.149008983
## [27,] -0.0378105609  0.04284195  0.0050147111  0.011405613 -0.043862129
## [28,] -0.0314283182  0.03031286 -0.0119754366  0.099836833 -0.014369342
## [29,] -0.0150338247 -0.09208359 -0.1584579914  0.072905644 -0.337252118
## [30,]  0.0570007973  0.11728702 -0.2531948113 -0.278750797  0.025068562
## [31,] -0.0114366257 -0.20559727  0.0625956283  0.023499761 -0.129914121
## [32,]  0.2631643832 -0.12854571 -0.1748069035  0.006142532 -0.197707958
## [33,] -0.0375355580  0.17004049  0.1016097330  0.022295489 -0.070255911
## [34,]  0.2148677369 -0.05222812  0.2797174524  0.147591205 -0.092991259
## [35,] -0.0050779836  0.14876701 -0.2356485522  0.066328791 -0.113326538
## [36,] -0.2218555310 -0.19065963  0.1309069246 -0.243077379 -0.034582124
## [37,]  0.0546275776 -0.25428436  0.2819585060 -0.001869257  0.009623732
## [38,] -0.2405882843 -0.18647203 -0.2144082928  0.035978865  0.050335206
## [39,] -0.0387887502 -0.29418764 -0.3544232848  0.104440738 -0.061571454
## [40,] -0.0890997193  0.13363101 -0.1286074642 -0.185774201  0.210625167
## [41,] -0.0868268148 -0.27990760  0.0764254754 -0.046923408  0.086407770
## [42,]  0.0081399761  0.17450432  0.0590707737  0.326377123  0.155977543
## [43,] -0.0031301357  0.01005546 -0.0808936472 -0.112059731 -0.009055120
## [44,] -0.0018103297 -0.02036933  0.1208479147 -0.314723993 -0.063135270
## [45,] -0.0378105609  0.04284195  0.0050147111  0.011405613 -0.043862129
## [46,] -0.1511655434 -0.11567042  0.0776538960  0.286462141  0.162913909
## [47,] -0.2005296421  0.28269930 -0.0689491284  0.072853997 -0.308491100
## [48,]  0.1950171100 -0.16777483 -0.0184635360 -0.051830524  0.235004907
##              [,26]         [,27]       [,28]        [,29]       [,30]
##  [1,] -0.127166434  2.731135e-16  0.26359174  0.181976368  0.11436565
##  [2,] -0.088739549  1.015117e-16  0.07560462 -0.032232181 -0.13898014
##  [3,] -0.015547383 -1.467448e-16 -0.21577436  0.061910783  0.05873831
##  [4,] -0.093074515 -1.330338e-16 -0.07201234  0.179951085  0.04546114
##  [5,] -0.114359259  2.437475e-16  0.14059459  0.099344900  0.22366027
##  [6,]  0.086523021 -1.810011e-16  0.12570137  0.130224023 -0.31930645
##  [7,] -0.124905760 -1.124855e-16 -0.21934319 -0.110444882 -0.18685123
##  [8,]  0.196662154 -4.120809e-16 -0.28275058 -0.095230236 -0.12657648
##  [9,] -0.044553819  2.388999e-16  0.08002881  0.082750215  0.10707304
## [10,]  0.188131678  5.687204e-17  0.14269228 -0.312112389  0.02548184
## [11,]  0.089516659 -5.609270e-16 -0.16896008  0.047125885 -0.01931472
## [12,]  0.017756690 -1.171073e-16 -0.29880890 -0.144789663 -0.06144100
## [13,]  0.160135921 -3.936951e-16  0.10218335  0.074237929 -0.08866092
## [14,]  0.089955733 -2.375453e-16  0.07185781 -0.107852977  0.05731813
## [15,] -0.264309423 -2.138098e-16 -0.12016699 -0.334234233 -0.07822829
## [16,]  0.250433771  1.199660e-16  0.09980885 -0.026968192  0.01226232
## [17,] -0.089870376  2.733304e-17  0.21566856  0.014346740 -0.02147510
## [18,]  0.347154187  4.278574e-16 -0.12232562  0.303191345  0.09430460
## [19,] -0.099963598 -4.771598e-17  0.04193232  0.015298876  0.05797566
## [20,] -0.126565698  8.964093e-16 -0.11423107 -0.103925705  0.21699915
## [21,] -0.063161280  4.018948e-16  0.03720737  0.219864132  0.30107951
## [22,]  0.145137539  1.928977e-16  0.03757852 -0.244356030 -0.09706321
## [23,]  0.137450244 -2.676872e-16  0.08695401  0.080444357  0.04133720
## [24,] -0.105176472 -3.699221e-16 -0.11981451 -0.116115417  0.25993120
## [25,] -0.220984935  7.246944e-18  0.02340170  0.140663114 -0.08807204
## [26,] -0.088612459 -6.291678e-16  0.13886957 -0.240204897  0.02608926
## [27,] -0.018368497 -7.071068e-01  0.00587977  0.014006089 -0.05791495
## [28,] -0.022994568 -1.554468e-16  0.24848802 -0.005228987 -0.03644398
## [29,]  0.140468545  3.650444e-16  0.09964179  0.132796322 -0.18001404
## [30,] -0.037092085 -2.640402e-16 -0.05328392  0.017814319  0.05643042
## [31,]  0.089127988  3.231950e-16 -0.05574751  0.037329420  0.16695576
## [32,]  0.032864017  3.852128e-16 -0.26929096  0.102775121  0.29985762
## [33,] -0.247521062  2.463818e-16 -0.05121122 -0.076741839 -0.14916518
## [34,]  0.085572692  2.696332e-16  0.04276084  0.041053011 -0.05211534
## [35,]  0.196419524  1.493479e-16  0.01406534  0.131085293 -0.13472675
## [36,]  0.088239879 -3.161639e-16 -0.23349785 -0.051687982 -0.01580170
## [37,] -0.306405646  1.949212e-16 -0.11862103  0.125299610 -0.09874961
## [38,]  0.024733592  6.132436e-17  0.26073658 -0.271080454  0.20789126
## [39,] -0.176230024  4.727516e-16  0.11423177 -0.054105927 -0.13010028
## [40,]  0.127025056 -6.710082e-16 -0.16625005 -0.063862235 -0.13272900
## [41,]  0.065088158 -3.188850e-16  0.08876034 -0.204416310  0.18949518
## [42,]  0.184774109 -2.860682e-16 -0.14992437 -0.069709571  0.05963505
## [43,] -0.111103428  1.321714e-16 -0.06715047  0.110633106 -0.08076156
## [44,]  0.008299174  3.048275e-16  0.06496607  0.167340360  0.11115484
## [45,] -0.018368497  7.071068e-01  0.00587977  0.014006089 -0.05791495
## [46,] -0.221859353  1.236200e-16 -0.13426499  0.248333739 -0.01854118
## [47,] -0.098721646  6.055661e-16  0.04143650  0.050896488 -0.30204844
## [48,]  0.127086479  2.956172e-16  0.11421654  0.103708406 -0.21376318
##              [,31]        [,32]        [,33]        [,34]        [,35]
##  [1,] -0.141762811  0.103918920  0.210191184 -0.153130736  0.025104254
##  [2,] -0.102362255  0.366476860 -0.012958516 -0.208060316  0.224704625
##  [3,]  0.085976489  0.038582144  0.040415597 -0.075883211 -0.047972690
##  [4,] -0.214721441  0.045615920  0.236311489  0.067142648  0.067701012
##  [5,]  0.151260130  0.286498930 -0.033246153 -0.157871173 -0.064528887
##  [6,]  0.148578211  0.150335130  0.092644667  0.154786200 -0.203840715
##  [7,] -0.045340049 -0.073908874 -0.069966033 -0.130020320 -0.310352671
##  [8,] -0.145269681 -0.027901139  0.091434246  0.193019398 -0.078669819
##  [9,]  0.213021394 -0.187779542  0.031107495 -0.014078023 -0.058076830
## [10,]  0.273651514  0.042957846 -0.292027716  0.057361623  0.034323506
## [11,] -0.111261711  0.002857108 -0.001056778  0.387608054  0.370903641
## [12,]  0.316258203  0.054203513  0.085352875 -0.120065576  0.199516272
## [13,]  0.010975443 -0.026917547 -0.030197563 -0.067793679  0.118711708
## [14,]  0.031434024 -0.152707972  0.158819055 -0.044663859 -0.007394071
## [15,]  0.032721338 -0.066890443  0.288763839  0.075551516 -0.037865934
## [16,] -0.060972464 -0.128514736  0.189567683  0.005107489  0.038598615
## [17,] -0.043274516  0.022285713 -0.140473516 -0.056937069  0.127591038
## [18,]  0.179497435  0.087744078  0.070703146 -0.183747715  0.096867613
## [19,]  0.369834848 -0.105056178 -0.188080626 -0.029966534  0.138861006
## [20,] -0.090723679 -0.083009855 -0.050624307 -0.089174946  0.159232506
## [21,]  0.269609439 -0.071769895 -0.029353536  0.255633115 -0.067884491
## [22,] -0.093447295  0.137690421 -0.126988343  0.011966087 -0.174796343
## [23,] -0.043387653 -0.081276842 -0.170895789 -0.137403535  0.016650137
## [24,] -0.112056243 -0.099583241 -0.054333130 -0.077103374  0.046352478
## [25,] -0.097266530 -0.149616160  0.025837244 -0.021846106  0.236384652
## [26,] -0.098117537 -0.129182855  0.082111471 -0.101249796  0.297662454
## [27,]  0.034810378  0.045925092  0.032869737  0.062481843 -0.107275771
## [28,] -0.264440455 -0.055391809 -0.391909372  0.202316891 -0.116243839
## [29,]  0.018131010  0.013862385 -0.002327383 -0.002286040  0.191473015
## [30,] -0.131147571  0.329818692  0.005597738  0.201206155  0.136293811
## [31,] -0.075180044  0.058250186 -0.034027587  0.235827831 -0.221526975
## [32,] -0.043526311  0.007520335 -0.145817484  0.013194342 -0.227364944
## [33,]  0.134450073  0.076836312  0.100337370 -0.039802825 -0.105378590
## [34,] -0.010936115 -0.328772410  0.236832572 -0.196196042 -0.116569979
## [35,] -0.041736163 -0.315799160 -0.050592296 -0.093042677 -0.012069958
## [36,]  0.177128548  0.006980632  0.056944208  0.006065066  0.109189003
## [37,]  0.097186778  0.011292019 -0.221363130 -0.045866193 -0.043560903
## [38,]  0.043233156  0.216450086  0.187141614 -0.164458807 -0.198168623
## [39,]  0.021287307 -0.251592819 -0.124535644  0.153349687 -0.057811929
## [40,] -0.288008870  0.021759251 -0.162780491 -0.327734170 -0.032073845
## [41,] -0.050390440 -0.049253017  0.168816443  0.282064480  0.032817368
## [42,] -0.062846218  0.239726236 -0.085456127 -0.084833993 -0.042318415
## [43,]  0.003539426 -0.106529287 -0.052716135 -0.158896602 -0.142031204
## [44,] -0.143827616 -0.020147507  0.267392029 -0.020750387 -0.201172959
## [45,]  0.034810378  0.045925092  0.032869737  0.062481843 -0.107275771
## [46,] -0.128386154  0.085408581 -0.059074057  0.038125335  0.014837579
## [47,]  0.143331635  0.145619882  0.160812444  0.149090623 -0.054652024
## [48,]  0.086802541  0.071456320  0.037243718  0.050986613 -0.029135426
##              [,36]        [,37]        [,38]        [,39]        [,40]
##  [1,] -0.043845131 -0.033831445  0.164383465  0.145682409  0.281244048
##  [2,]  0.204396537  0.027015341 -0.181766767 -0.053608619 -0.270393246
##  [3,] -0.092797272 -0.014164134 -0.244892720 -0.013535116  0.188789030
##  [4,]  0.085831433  0.029569550 -0.098934967 -0.137437060  0.013489470
##  [5,]  0.028961498  0.021884627  0.147215092 -0.223195375 -0.145763960
##  [6,]  0.147970209 -0.060812857  0.022145907  0.061498179 -0.006099202
##  [7,] -0.057111001  0.034175824 -0.093820013  0.056489224  0.259653541
##  [8,] -0.100428211  0.014135492 -0.138145912 -0.294039244 -0.142517360
##  [9,] -0.054469875 -0.009969256 -0.058197022 -0.023515272 -0.257871763
## [10,] -0.076284248 -0.039661260 -0.066130031  0.379527200 -0.067526461
## [11,]  0.119763225 -0.006335031 -0.173265135  0.125915817 -0.006332030
## [12,]  0.015414504 -0.035646000  0.110315118 -0.011830029  0.060182508
## [13,] -0.092883453 -0.002427860 -0.022317731 -0.069531939  0.007925255
## [14,]  0.311404818  0.096472020 -0.283416823  0.202430070  0.061821713
## [15,]  0.012771875  0.012177372  0.225105353  0.071924342 -0.272534672
## [16,] -0.009343961 -0.013385332  0.022467738 -0.049298602 -0.096448981
## [17,] -0.001906742 -0.036859025 -0.009474814  0.023063412  0.114872354
## [18,] -0.134800361 -0.063017802 -0.114750769  0.083312904  0.050853308
## [19,]  0.202405624  0.031755416  0.054162720 -0.143377772 -0.162583087
## [20,] -0.213648796  0.632261078  0.016127554  0.018456463 -0.001292040
## [21,] -0.073566783  0.010439035 -0.018422743 -0.028680935  0.087746295
## [22,] -0.314906720 -0.063576672  0.040454905  0.012997185  0.210560540
## [23,] -0.004188593 -0.019173724 -0.169286930 -0.096182925 -0.029808686
## [24,]  0.063602629 -0.527756223 -0.032530978 -0.061875455  0.005193140
## [25,]  0.268520884  0.022356180  0.004960339  0.287344518  0.173075041
## [26,] -0.163123402 -0.141679495  0.093637520 -0.002381537  0.019564698
## [27,]  0.116033924 -0.235140231  0.002252238  0.018005530 -0.002256963
## [28,]  0.208536189  0.093600719 -0.024468622 -0.224941393  0.173930096
## [29,] -0.106107432 -0.051130911  0.033563794 -0.120540758 -0.010877655
## [30,] -0.140250033 -0.040251118  0.017319909 -0.261277289 -0.016910864
## [31,]  0.251780518  0.118761396  0.348276873  0.146595264 -0.167713310
## [32,]  0.149225256  0.044587003 -0.097393873  0.014122006 -0.023026601
## [33,] -0.047143166  0.026802155 -0.321968637 -0.036604571  0.157528757
## [34,]  0.244287256  0.087227200 -0.041872977 -0.171243372  0.092984840
## [35,] -0.155213415 -0.072594163  0.308375283  0.017502118 -0.042762304
## [36,]  0.161866890  0.035584297  0.218090369 -0.239337942  0.214535025
## [37,] -0.065253169 -0.016004588 -0.009385422  0.099499575  0.025357954
## [38,]  0.061339152  0.056557254 -0.071906121 -0.132260837  0.012241556
## [39,] -0.137167723 -0.018642119 -0.239211866 -0.091068828 -0.272148235
## [40,]  0.168414243  0.018621405  0.105892724  0.072237927 -0.234168322
## [41,] -0.049676166 -0.017367108  0.121678763  0.053150123  0.219655030
## [42,]  0.107172915  0.029538747  0.035777715  0.260917538  0.031916413
## [43,] -0.064629235 -0.009972501  0.239113521 -0.127102756  0.041370376
## [44,] -0.233842902 -0.033767375 -0.168412566  0.246669073 -0.290623992
## [45,]  0.116033924 -0.235140231  0.002252238  0.018005530 -0.002256963
## [46,] -0.184523545 -0.066502226  0.122023203  0.196265061 -0.095860300
## [47,]  0.011016765  0.069266153  0.098969165  0.045976224  0.017158631
## [48,] -0.038740827  0.314413289  0.018605540  0.033689212 -0.002678256
##              [,41]        [,42]        [,43]        [,44]         [,45]
##  [1,]  0.174638599  0.086475669 -0.128844507 -0.066787468 -0.1843365161
##  [2,]  0.042921951 -0.065172035 -0.008706158  0.022217078 -0.0820102678
##  [3,] -0.255840269 -0.251605622  0.028329069 -0.267404453  0.1529234772
##  [4,] -0.042423702  0.237827234 -0.021868689 -0.087856472  0.0869758000
##  [5,] -0.128645278 -0.038463324 -0.010234596  0.097329556 -0.0244278280
##  [6,]  0.110327377  0.025438955  0.279132222 -0.127645951 -0.0480987316
##  [7,] -0.049263044  0.074828765 -0.076949310 -0.095252760 -0.0341359262
##  [8,] -0.034443512 -0.109947371 -0.080731941 -0.075208101 -0.2382728679
##  [9,]  0.099056832  0.052445245 -0.092568793 -0.174000407 -0.0715978172
## [10,]  0.104477458 -0.081742706 -0.163976394 -0.128921211 -0.0671039415
## [11,] -0.008442478 -0.124256733  0.123284612  0.244249571 -0.1688774714
## [12,]  0.047429364  0.081435826  0.049046648 -0.004587643 -0.1098595039
## [13,] -0.161476099 -0.040994424 -0.485690580  0.230403525  0.0955577025
## [14,] -0.128820080  0.163084454 -0.159639288  0.037256317 -0.1992566016
## [15,]  0.198333572  0.122311299 -0.097172616  0.194827907  0.0279455548
## [16,]  0.213511290 -0.093842420 -0.079754815 -0.374946851  0.2297491410
## [17,] -0.044700659  0.134086638  0.220137704 -0.022991886 -0.2697181001
## [18,] -0.090938159  0.018405815  0.107682369 -0.036565081 -0.0569922882
## [19,] -0.081009274 -0.012777777  0.175621052  0.017109475  0.3403501942
## [20,]  0.021937711  0.005253277  0.061345508 -0.029077001 -0.0121573489
## [21,] -0.133807182  0.048068627 -0.062290284  0.020155019 -0.1990730286
## [22,] -0.047030736  0.240717358  0.119862969  0.203257393 -0.0654176813
## [23,]  0.435094960  0.129307956 -0.013434578  0.226647936  0.0007791075
## [24,] -0.085414404 -0.018469727 -0.193344116  0.086514069  0.0308370156
## [25,]  0.054470343 -0.067926175  0.028773383 -0.022784312  0.1682973101
## [26,] -0.204098319 -0.040179742  0.287176174 -0.241675530 -0.0974015232
## [27,]  0.045916537  0.011415184  0.132075775 -0.061851619 -0.0247107772
## [28,] -0.012914563 -0.161534425 -0.141116732 -0.112373944  0.1074145443
## [29,]  0.095162050  0.057685069 -0.092832713  0.212056368 -0.0157858278
## [30,] -0.005665475  0.296538787  0.064443207 -0.119369692  0.2291019426
## [31,] -0.162242581  0.092785173 -0.079386940 -0.007545437 -0.1064231545
## [32,]  0.309243000  0.074017002  0.182974873  0.002543627 -0.0198761104
## [33,]  0.260487245 -0.092934544 -0.033563306  0.087390577  0.2122461344
## [34,] -0.146958533  0.064900601  0.107917953  0.170905609 -0.0172330667
## [35,]  0.060209821  0.113376281  0.017630132 -0.061423262  0.2225127560
## [36,]  0.181033903 -0.028401342 -0.200167693 -0.136776978 -0.0924284905
## [37,] -0.104424447  0.383969577 -0.109154401 -0.063627554  0.0517804022
## [38,]  0.025825508 -0.175075530 -0.014352421 -0.052859947 -0.0443844327
## [39,] -0.110730912  0.003078414  0.114422858 -0.004095152 -0.0428839037
## [40,] -0.126136295  0.039686070  0.021605701 -0.180055469 -0.0854137511
## [41,]  0.035344386 -0.097390885  0.140875241  0.086421670  0.2054754982
## [42,] -0.129896921 -0.064634482  0.075806883  0.212798982  0.3786168471
## [43,] -0.017977350 -0.425071436  0.212369418  0.327036849 -0.1394687945
## [44,] -0.083791877 -0.012006795  0.032581845  0.122719041  0.1535083592
## [45,]  0.045916537  0.011415184  0.132075775 -0.061851619 -0.0247107772
## [46,]  0.200830165 -0.353100437 -0.139277484 -0.137099869 -0.1210684352
## [47,] -0.264958803 -0.076557405 -0.206389046  0.005536147  0.0490507736
## [48,]  0.041891221  0.008667091  0.087371730 -0.038365578 -0.0129836790
##              [,46]        [,47]         [,48]
##  [1,] -0.030848335 -0.126766284  0.1007814759
##  [2,] -0.018453210 -0.100900566  0.0960549006
##  [3,] -0.148642320 -0.162440681  0.0938082324
##  [4,]  0.006845561  0.011134134 -0.0093233898
##  [5,] -0.298386254  0.027624094 -0.3158573581
##  [6,] -0.106188735  0.035521380  0.0207724730
##  [7,]  0.225354164  0.350138263  0.0607705280
##  [8,] -0.094049193  0.110358157 -0.3079094291
##  [9,]  0.007629335 -0.369241788  0.3788546259
## [10,] -0.081101869  0.030051818 -0.0656968616
## [11,]  0.018212194 -0.165041747  0.1834181509
## [12,]  0.107739983 -0.012002600 -0.0689488832
## [13,]  0.214315476 -0.091176877 -0.0551474253
## [14,] -0.274675004 -0.005723569 -0.1393900941
## [15,] -0.056555925  0.093830593  0.0773181781
## [16,]  0.273700340  0.155016030 -0.0001809073
## [17,]  0.374044115 -0.051103162 -0.3704530068
## [18,]  0.104875201 -0.026056556 -0.0725731171
## [19,]  0.154959825  0.057319530  0.0578178206
## [20,] -0.027325139  0.012013812  0.0072858703
## [21,]  0.067876736  0.296734133  0.1812933094
## [22,]  0.050684913 -0.204311204  0.2927710111
## [23,]  0.025529481  0.061753287 -0.0524860522
## [24,]  0.067466777 -0.019629249 -0.0112493425
## [25,]  0.139433741  0.156612119 -0.0168183314
## [26,] -0.236713818  0.159550944  0.1206335047
## [27,] -0.055057524  0.020935924  0.0124456799
## [28,] -0.194753606 -0.021361913  0.1291984983
## [29,] -0.209019087  0.434925604  0.1256666421
## [30,]  0.136591263  0.001886812  0.0647991506
## [31,]  0.222188876 -0.087625142 -0.0469898470
## [32,] -0.033215481  0.004623796 -0.0166537076
## [33,]  0.036420715 -0.250085484 -0.1539063257
## [34,] -0.013792710 -0.035583126  0.0392457598
## [35,] -0.189844551 -0.185171103 -0.1991281445
## [36,] -0.135057180 -0.067785700  0.1195317553
## [37,] -0.216394410 -0.022661111 -0.1126547489
## [38,]  0.161929336  0.134069109  0.0451093328
## [39,]  0.109502388  0.005426871 -0.0994873521
## [40,]  0.068393345 -0.108046011  0.0573577756
## [41,] -0.059167437 -0.181075919 -0.3162729785
## [42,] -0.096492013  0.179458733  0.0627915620
## [43,]  0.064698042 -0.061018150  0.0922278354
## [44,] -0.063420721  0.054743631  0.0670049278
## [45,] -0.055057524  0.020935924  0.0124456799
## [46,] -0.022438305  0.067025413 -0.1107814369
## [47,]  0.101991676 -0.081233801 -0.0180956891
## [48,] -0.028154888  0.007057816  0.0039531909

#URL2 = "https://docs.google.com/spreadsheet/pub?key=0ArLJZixvTlU7dC1rTlRhTkw5UlY0eWZGT1JOVUVCWGc&single=true&gid=0&output=csv"
#state.year.tb = read.csv(textConnection(getURL(URL2)), colClass = c("character", NA))

# http://igraph.org/r/doc/as_adjacency_matrix.html