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Fig. 4 To construct initial conditions from artificially generated pinwheel maps, we first took such a pinwheel map with a certain scaling (upper left), then we chose a selection of excited orientations by means of a Gaussian.

Motivated by the work reported in [3 9], in this paper, by higher-order adjacent derivative of set-valued maps, we first discuss some relationships between higher-order adjacent derivative of a set-valued map and its profile map.

In order to have representative element maps, we first microscopically scanned tissue specimens and looked for lesions of centrilobular fibrosis with low magnification because hard metal related elements, tungsten/cobalt, were always found around centrilobular areas according to our experience.

For visualization of the COHCOA-analyzed data as 2D proximity maps, we first applied a filter to remove points with signal-to-noise ratio < 1, then applied a 2D smoothing algorithm to aid visualization of the strongest features.

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To build this map, we first initialize all values to zero.

To send the messages W i i∈{1,2} to the relay node, using a one-to-one mapping, we first map it to lattice codeword (boldsymbol {V}_{i}in mathcal {C}_{i}^{(n_{1})}).

In order to show the exact domains of the Poincaré map, we first need to know under what conditions the trajectory initiating from (P_{i}^in{mathcal{N}}) cannot reach the point (P_{i+1}in {mathcal{M}}).

Using this map, we first tested if chimpanzees have a spatial memory.

To elaborate the difference between 1D-trait mapping and 2D-trait mapping, we first examined the 1D-trait mapping result of these genes.

For multiple QTL mapping, we first calculated genotype probabilities for any missing genotype using the calc.genoprob function before performing the forward/backward model selection function implemented in stepwiseqtl.

For genetic mapping, we first used SSR (simple sequence repeat) markers with known genetic position to localize the approximate position of Mt-NS1.

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