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View is_outlier.R
is_outlier <- function(x) {
# Computes a bootstrapped confidence interval
# INPUT:
# x: a numeric vector
# OUTPUT:
# a boolean vector, indicating if each value in x is an outlier
return(x < quantile(x, 0.25) - 1.5 * IQR(x) | x > quantile(x, 0.75) + 1.5 * IQR(x))
}
View bootstrap_confidence_interval.R
bootstrap_ci <- function(data, sample_size_pct = 0.50, samples = 100, conf_level = 0.95){
# Computes a bootstrapped confidence interval
# INPUT:
# data: a numeric vector
# sample_size_pct: the percentage of the input data to be used in each bootsrapped sample
# samples: the number of samples
# conf_level: the desired confidence level
# OUTPUT:
# a bootstrapped conf_level confidence interval
@BrianWeinstein
BrianWeinstein / RemoveSparseTermsLarge.R
Last active October 19, 2016 16:43
remove sparse terms on a large document term matrix
View RemoveSparseTermsLarge.R
# tm::removeSparseTerms attempts to remove sparse terms via slicing a sparse matrix.
# The slicing operation tries to convert the sparse matrix to a dense matrix, but this
# fails if the dense matrix has more than ((2^31) - 1) entries [i.e., if (nrow * ncol) > ((2^31) - 1)]
#
# The error message is
# In nr * nc : NAs produced by integer overflow
#
# Instead of using tm::removeSparseTerms, the following function subsets the sparse matrix directly
# and avoids converting the sparse matrix to a dense one.
View Wave Equation
ic[x_, y_] := 1 E^(-350 ((x - 1/5)^2 + ( y - 1/3)^2))
solnDir =
NDSolve[
{D[u[x, y, t], {t, 2}] == D[u[x, y, t], {x, 2}] + D[u[x, y, t], {y, 2}],
u[x, y, 0] == ic[x, y],
(D[u[x, y, t], t] /. t -> 0) == 0,
u[0, y, t] == ic[0, y],
u[1, y, t] == ic[1, y],
u[x, 0, t] == ic[x, 0],
View Lonely Runner Conjecture
circ = 1; rad = circ/(2 \[Pi]); nRunners = 5;
rList[t_] := {1 t, 2 t, 4 t, 8 t, 9.6 t, 21 t, 31 t, 33 t}[[1 ;; nRunners]]
dist[d\[Theta]_, circ_] :=
N[circ/2 (TriangleWave[(d\[Theta] - \[Pi]/2)/(2 \[Pi])] + 1)/2]
minDist[runnerList_, circ_] :=
Table[
runner = runnerList[[i]];
other = DeleteCases[runnerList, runner];
Min[dist[Abs[runner - other], circ]],
View Harmonograph
x[A1_, A2_, f1_, f2_, p1_, p2_, d1_, d2_, t_] := A1 Sin[t f1 + p1] E^(-d1 t) + A2 Sin[t f2 + p2] E^(-d2 t)
y[A3_, A4_, f3_, f4_, p3_, p4_, d3_, d4_, t_] := A3 Sin[t f3 + p3] E^(-d3 t) + A4 Sin[t f4 + p4] E^(-d4 t)
Manipulate[
ParametricPlot[
{x[A1, A2, f1, f2, p1, p2, d1, d2, t],
y[A3, A4, f3, f4, p3, p4, d3, d4, t]},
{t, 0, tmax},
PlotPoints -> 200, Axes -> False, PlotStyle -> {Thick, Opacity[0.5]}, PlotRange -> All
View Curves of Constant Width and Odd-Sided Reuleaux Polygons
x[n_, \[Theta]_] := 2*Cos[Pi/(2*n)]*Cos[(1/2)*(\[Theta] + (Pi/n)*(2*Floor[(n*\[Theta])/(2*Pi)] + 1))] - Cos[(Pi/n)*(2*Floor[(n*\[Theta])/(2*Pi)] + 1)]
y[n_, \[Theta]_] := 2*Cos[Pi/(2*n)]*Sin[(1/2)*(\[Theta] + (Pi/n)*(2*Floor[(n*\[Theta])/(2*Pi)] + 1))] - Sin[(Pi/n)*(2*Floor[(n*\[Theta])/(2*Pi)] + 1)]
reuRotate[n_, \[Phi]_] :=
{pts[n, \[Phi]] = Table[RotationMatrix[\[Phi]] . {x[n, \[Theta]], y[n, \[Theta]]}, {\[Theta], 0, 2*Pi, (2*Pi)/100}];
xmin = Min[pts[n, \[Phi]][[All,1]]];
ymin = Min[pts[n, \[Phi]][[All,2]]];
xmax = Max[pts[n, \[Phi]][[All,1]]];
ymax = Max[pts[n, \[Phi]][[All,2]]];
View Atomic Models
(* Rutherford model *)
es[t_] := {{Cos[t + Pi], 2.5*Sin[t + Pi], 2*Sin[t + Pi]},
{Cos[t + (4*Pi)/5], 2*Sin[t + (4*Pi)/5], -1.5*Sin[t + (4*Pi)/5]},
{2*Sin[t + (3*Pi)/5], Cos[t + (3*Pi)/5], 2*Sin[t + (3*Pi)/5]},
{2.5*Sin[t + (2*Pi)/5], Cos[t + (2*Pi)/5], -1.5*Sin[t + (2*Pi)/5]}}
Manipulate[Show[
ParametricPlot3D[Evaluate[es[2*u]], {u, 0, 2*Pi}, PlotStyle -> Directive[Thick, Dotted]],
Graphics3D[
{Specularity[White, 200],
View Pursuit-Evasion
nc = 15; nr = 3;
cx = Table[ToExpression[StringJoin["cx", ToString[i]]], {i, 1, nc}];
cy = Table[ToExpression[StringJoin["cy", ToString[i]]], {i, 1, nc}];
rx = Table[ToExpression[StringJoin["rx", ToString[i]]], {i, 1, nr}];
ry = Table[ToExpression[StringJoin["ry", ToString[i]]], {i, 1, nr}];
coordList = Flatten[{Transpose[{cx, cy}], Transpose[{rx, ry}]}];
cspeed = 1;
rspeed = 1.1;
eqns = Flatten[
View Signal Collection and Parabolic Reflectors
xmin = -3.6; xmax = 3.6;
p[x_] := 6 - Sqrt[6^2 - x^2] (* circle *)
p[x_] := x^2/7.5 (* parabola *)
img[t_, rays_] :=
Show[
Graphics[
{Thick, RGBColor[0.243, 0.62, 0.612],
Table[Line[{{xi, -t}, {xi, 20}}], {xi, xmin + 0.25, xmax - 0.25, (xmax - xmin - 0.5)/rays}],