tomleslie

5323 Reputation

15 Badges

9 years, 270 days

MaplePrimes Activity


These are answers submitted by tomleslie

(I'm on a Windows machine, so I can't debug/reproduce fully)

  1. Open relevant help page with ?Physics,Geodesics
  2. In the help page menu system, ensure that "View->Display Examples with 2D math input" is unchecked. In other words  all the executable math in the help page should be displayed as 1-D input
  3. In the help page menu system, use View->Open Page as Worksheet. which does exactly what it says. It will open a worksheet called [Physics, Geodesics], which you can execute in the standard way
  4. Execute this worksheet one "group" at a time - What happens?
  5. If this "works" you can try steps 1-4 gain, except at step (2) above, ensure that "View->Display Examples with 2D math input" is checked. - Again, What happens?

the conditions f(0)=0 and f'(0)=0 do not impose any restrictions on the values of the parameters n[1], n[2], n[3].

See the attached

   restart;
#
# Define the function
#
  f:=x-> 0.8680555556e-1*x*(3.262720*x^5*n[2]-.63360*x^5*n[1]^2+2.69184*x^5*n[1]-.480*x^3*n[1]^2+2.5920*x^3*n[2]+5.760*n[1]*x+1.920*n[2]*x^2+0.96e-1*x^4*n[1]^3+3.04320*x^4*n[2]-.5280*x^4*n[1]^2-0.32e-1*x^5*n[1]^4+.2976*x^5*n[1]^3-.1184*x^5*n[2]^2+.5376*x^5*n[3]-0.576e-1*x^4*n[1]+.576*x^4*n[3]-6.3360*x^3-6.96960*x^4-7.349760*x^5+11.520-.192*x^5*n[1]*n[3]-.7104*x^4*n[1]*n[2]+.2528*x^5*n[1]^2*n[2]-1.81824*x^5*n[1]*n[2]):
#
# Rewrite the above equation in a somewhat "neater"
# form by collecting powers of 'x', just to make
# it easier to read/interpret
#
  collect(expand(f(x)), x);
#
# Evaluate f(x) at x=0
#
  eval(f(x), x=0);
#
# Differentiate the above expression wrt 'x' and
# evaluate at x=0
#
  D(f)(0);

(.2832222222*n[2]-0.5500000000e-1*n[1]^2+.2336666667*n[1]-0.2777777778e-2*n[1]^4+0.2583333333e-1*n[1]^3-0.1027777778e-1*n[2]^2+0.4666666667e-1*n[3]-.6380000000-0.1666666667e-1*n[1]*n[3]+0.2194444445e-1*n[1]^2*n[2]-.1578333333*n[1]*n[2])*x^6+(0.8333333334e-2*n[1]^3+.2641666667*n[2]-0.4583333334e-1*n[1]^2-0.5000000000e-2*n[1]+0.5000000000e-1*n[3]-.6050000000-0.6166666667e-1*n[1]*n[2])*x^5+(-0.4166666667e-1*n[1]^2+.2250000000*n[2]-.5500000000)*x^4+.1666666667*x^3*n[2]+.5000000000*n[1]*x^2+1.000000000*x

 

0.

 

1.000000000

(1)

 


 

Download poly.mw

which

  1. plots all dependent variables
  2. produces a matrix of dependent variable values for T=0..20

restart; _local(gamma)

M__h := .50; beta__o := 0.34e-1; beta__1 := 0.25e-1; mu__r := 0.4e-3; sigma := .7902; alpha := .11; psi := 0.136e-3; xi := 0.5e-1; gamma := .7; M__c := .636; mu__b := 0.5e-2

ODEs := diff(B(T), T) = M__h-beta__1*psi*B(T)*G(T)-mu__r*B(T), diff(C(T), T) = beta__1*psi*B(T)*G(T)-sigma*psi*beta__1*E(T)*DD(T)-(alpha+xi+mu__r)*C(T), diff(DD(T), T) = alpha*C(T)-(gamma+mu__r)*DD(T), diff(E(T), T) = gamma*DD(T)+sigma*psi*beta__1*E(T)*G(T)-mu__r*E(T), diff(F(T), T) = M__c-psi*beta__o*F(T)*C(T)-mu__b*F(T), diff(G(T), T) = psi*beta__o*F(T)*C(T)-mu__b*G(T); bcs := B(0) = .50, C(0) = .30, DD(0) = .21, E(0) = .14, F(0) = .70, G(0) = .45

ans := dsolve([ODEs, bcs], numeric); for j in indets([ODEs], function(name)) do plots:-odeplot(ans, [T, j], T = 0 .. 30, title = convert(j, string), titlefont = [tims, bold, 20], thickness = 2, color = red) end do

 

 

 

 

 

 

interface(rtablesize = [22, 10]); M := Matrix([`~`[lhs](ans(0)), seq(`~`[rhs](ans(j)), j = 0 .. 20)])

Matrix(%id = 18446744074595705910)

(1)

 

``


 

Download odeRes.mw

just because I like alternatives

  restart;
#
# Random matrix for test purposes
#
  A:=LinearAlgebra:-RandomMatrix(10):
#
# Sort columns of A in ascending order
#
  B:=Matrix([seq(sort(A[..,j]), j=1..10)], scan=rows);
#
# Define "finder" function
#
  g:=(mat, col, val)-> ListTools:-SelectFirst
                       ( x-> evalb( x>val ),
                         mat[..,col],
                         output=indices
                       ):
#
# Usage example
#
# In the matrix B, output the row index of the
# first entry in column 2 which is >50
#
  g(B, 2, 50);
#
# Returns NULL if no entry exceeds supplied value
#
  g(B, 2, 100);

Matrix(10, 10, {(1, 1) = -63, (1, 2) = -35, (1, 3) = -82, (1, 4) = -68, (1, 5) = -95, (1, 6) = -61, (1, 7) = -80, (1, 8) = -81, (1, 9) = -98, (1, 10) = -31, (2, 1) = -38, (2, 2) = -14, (2, 3) = -70, (2, 4) = -67, (2, 5) = -25, (2, 6) = -48, (2, 7) = -50, (2, 8) = -50, (2, 9) = -93, (2, 10) = -4, (3, 1) = -26, (3, 2) = 12, (3, 3) = -32, (3, 4) = -62, (3, 5) = -20, (3, 6) = -44, (3, 7) = -2, (3, 8) = -38, (3, 9) = -77, (3, 10) = 8, (4, 1) = -23, (4, 2) = 19, (4, 3) = -13, (4, 4) = -59, (4, 5) = 9, (4, 6) = 9, (4, 7) = 10, (4, 8) = -22, (4, 9) = -76, (4, 10) = 27, (5, 1) = -1, (5, 2) = 21, (5, 3) = -1, (5, 4) = -33, (5, 5) = 14, (5, 6) = 20, (5, 7) = 12, (5, 8) = -18, (5, 9) = -74, (5, 10) = 29, (6, 1) = 10, (6, 2) = 45, (6, 3) = 29, (6, 4) = 12, (6, 5) = 16, (6, 6) = 24, (6, 7) = 25, (6, 8) = -16, (6, 9) = -72, (6, 10) = 44, (7, 1) = 22, (7, 2) = 60, (7, 3) = 41, (7, 4) = 18, (7, 5) = 22, (7, 6) = 65, (7, 7) = 31, (7, 8) = -9, (7, 9) = -32, (7, 10) = 67, (8, 1) = 30, (8, 2) = 80, (8, 3) = 52, (8, 4) = 42, (8, 5) = 51, (8, 6) = 76, (8, 7) = 43, (8, 8) = 33, (8, 9) = -2, (8, 10) = 69, (9, 1) = 63, (9, 2) = 88, (9, 3) = 70, (9, 4) = 72, (9, 5) = 60, (9, 6) = 77, (9, 7) = 50, (9, 8) = 45, (9, 9) = 27, (9, 10) = 92, (10, 1) = 91, (10, 2) = 90, (10, 3) = 91, (10, 4) = 82, (10, 5) = 99, (10, 6) = 86, (10, 7) = 94, (10, 8) = 87, (10, 9) = 57, (10, 10) = 99})

 

7

(1)

 


 

Download searchMat.mw

is shown in the attached

restart;
f:=k->sum((r+1)*(r+2)*(r+3)*(r+4)*F(r+4)*(k-r+1)*F(k-r+1), r = 0 .. k) =c:
g:=h->isolate( h, indets(h, function)[-1]):
(g @ f)(0);
(g @ f)(1);
(g @ f)(2);

F(4) = (1/24)*c/F(1)

 

F(5) = (1/120)*(c-48*F(4)*F(2))/F(1)

 

F(6) = (1/360)*(c-72*F(4)*F(3)-240*F(5)*F(2))/F(1)

(1)

 

Download altSum.mw

If I strip out all the redundant stuff you neither want nor need the I am left wiith the worksheet shown in the attached.

There are two reasons why no solution can be obtained from this worksheet, both of which you will have to fix

  1. You have six ODES , but seven independent variables, namely A(T), B(T), C(T), G(T), R(T), S(T), I(T). Rouben has already pointed out that one of these dependent variables ( ie I(T) ) has a name which will cause problems. You need to work out if you really do have seven dependent variables: if you do, then don;'t call one of them I(T) - any other name will be fine: eg P(T), Q(T), Z(T), whatever, just not I(T). However if you do have seven dependent variables, then either
    1. One of these is going to have to be defined in terms of the other six, or
    2. You are going to need another equation
  2. The variable mu__r is used in a couple of these equations and is never defined

see the attached

  restart:

#
# Define gamma as local (don't like doing this!)
#
  local gamma:

  A__h:= .18:        beta__1:= 0.8354e-1: psi:= 0.7258e-1:
  mu__r:= 0.51e-1:   sigma:= .165:        alpha:= .65:
  xi:= 0.5e-1:       gamma:= .131:        A__b:= .7241:
  beta__o:= 0.65e-1: mu__b = 0.17e-1:

  odes:=  diff(S(T), T) = A__h-psi*beta__1*S(T)*G(T)-mu__r*S(T),
          diff(G(T), T) = psi*beta__1*S(T)*G(T)-sigma*psi*beta__1*R(T)*B(T)-(alpha+xi+mu__r)*G(T),
          diff(A(T), T) = alpha*G(T)-(gamma+mu__r)*A(T),
          diff(R(T), T) = gamma*A(T)+sigma*psi*beta__1*R(T)*B(T)- mu__r*R(T),
          diff(C(T), T) = A__b - psi*beta__o*C(T)*I(T)- mu__b*C(T),
          diff(B(T), T) = psi*beta__o*C(T)*I(T)- mu__b*B(T):
  ics:= S(0)=100, G(0)=190, A(0)=45, R(0)=20, C(0)=35, B(0)=25:

#
# Solve system
#
  ans:= dsolve([ odes, ics ], numeric);

Warning, The use of global variables in numerical ODE problems is deprecated, and will be removed in a future release. Use the 'parameters' argument instead (see ?dsolve,numeric,parameters)

 

(1)

 

Download odeProb.mw

 

 

maybe?


You can adjust the decay rate by adding a parameter to the exponent in the definition of the function g(). I used 0.5, just for illustration.

restart;
g:=z->exp(-0.5*(z-24*floor(z/24)));
f:=(t)->g(t)*(t-24*floor(t/24))*150;
plot(f, 0..100);

proc (z) options operator, arrow; exp(-.5*z+12.0*floor((1/24)*z)) end proc

 

proc (t) options operator, arrow; 150*g(t)*(t-24*floor((1/24)*t)) end proc

 

 

 


 

Download staircase2.mw

It seems as if you want to add a "staircase" component to a function whcih already exists (I might be wrong!)

You might want to consider the "toy" example in the attached which adds 150 to the function 20*sin(z), at z=24, 48, etc

restart;
g:=z->20*sin(z);
f:=(t)->g(t)+(floor(t/24))*150;
plot(f, 0..100);

proc (z) options operator, arrow; 20*sin(z) end proc

 

proc (t) options operator, arrow; g(t)+150*floor((1/24)*t) end proc

 

 

 


 

Download staircase.mw

In the attached, I'm pretty sure that I am comparing the results using Physics:-Version(426) and Physics:-Version(429), although the message returned by the Physics:-Version() command is somewhat ambiguous.

In any case the two execution groups return different answers.

The first, using Physics:-Version(426) returns what I would consider to be the "correct" answer and the pdetest() command comfirms it (ie returns 0).

The second using Physics:-Version(429), returns the answer in your original post, which I agree is wrong!

Are you some kind of official beta-tester for Maplesoft??

restart;
Physics:-Version(426);
restart;
Physics:-Version();
pde:=diff(u(x,t),t$2)=4*diff(u(x,t),x$2);
ic:=u(x,0)=0,D[2](u)(x,0)=sin(x)^2;
bc:=u(-Pi,t)=0,u(Pi,t)=0;
sol:=pdsolve([pde,ic,bc],u(x,t));
pdetest(sol,pde);
simplify(diff(rhs(sol),t$2)-4*diff(rhs(sol),x$2));

Warning, this package updates content shipped in a standard Maple install.  Use the 'restart' command to clear your session before using these commands.

 

Kernel(`The "Physics Updates" version "426" is installed but is not active. The active version of Physics is within the library C:\Users\TomLeslie\maple\toolbox/2019/Physics Updates/lib\Physics Updates.maple, created 2019, September 23, 10:13 hours`), [`The "Physics Updates" version "426" is installed but is not active. The active version of Physics is within the library C:\Users\TomLeslie\maple\toolbox/2019/Physics Updates/lib\Physics Updates.maple, created 2019, September 23, 10:13 hours`]

 

`The "Physics Updates" version "426" is installed but is not active. The active version of Physics is within the library C:\Users\TomLeslie\maple\toolbox/2019/Physics Updates/lib\Physics Updates.maple, created 2019, September 23, 10:13 hours`

 

diff(diff(u(x, t), t), t) = 4*(diff(diff(u(x, t), x), x))

 

u(x, 0) = 0, (D[2](u))(x, 0) = sin(x)^2

 

u(-Pi, t) = 0, u(Pi, t) = 0

 

u(x, t) = Sum((1/2)*(Int(sin(n*x)*sin(x)^2, x = -Pi .. Pi))*sin(2*n*t)*sin(n*x)/((Int(sin(n*x)^2, x = -Pi .. Pi))*n), n = 1 .. infinity)

 

0

 

0

(1)

restart;
Physics:-Version(429);
restart;
Physics:-Version();
pde:=diff(u(x,t),t$2)=4*diff(u(x,t),x$2);
ic:=u(x,0)=0,D[2](u)(x,0)=sin(x)^2;
bc:=u(-Pi,t)=0,u(Pi,t)=0;
sol:=pdsolve([pde,ic,bc],u(x,t));
pdetest(sol,pde);
simplify(diff(rhs(sol),t$2)-4*diff(rhs(sol),x$2));

Warning, this package updates content shipped in a standard Maple install.  Use the 'restart' command to clear your session before using these commands.

 

Kernel(`The "Physics Updates" version "429" is installed but is not active. The active version of Physics is within the library C:\Users\TomLeslie\maple\toolbox/2019/Physics Updates/lib\Physics Updates.maple, created 2019, September 23, 10:14 hours`), [`The "Physics Updates" version "429" is installed but is not active. The active version of Physics is within the library C:\Users\TomLeslie\maple\toolbox/2019/Physics Updates/lib\Physics Updates.maple, created 2019, September 23, 10:14 hours`]

 

`The "Physics Updates" version "429" is installed but is not active. The active version of Physics is within the library C:\Users\TomLeslie\maple\toolbox/2019/Physics Updates/lib\Physics Updates.maple, created 2019, September 23, 10:14 hours`

 

diff(diff(u(x, t), t), t) = 4*(diff(diff(u(x, t), x), x))

 

u(x, 0) = 0, (D[2](u))(x, 0) = sin(x)^2

 

u(-Pi, t) = 0, u(Pi, t) = 0

 

u(x, t) = t*sin(x)^2

 

-8*t*(2*cos(x)^2-1)

 

-16*t*cos(x)^2+8*t

(2)

 

Download WaveEq.mw

just because alternatives are good!


 

restart;
with(inttrans):
alias( U__1(s)=laplace(u__1(t), t, s),
       U__2(s)=laplace(u__2(t), t, s),
       Y__1(s)=laplace(y__1(t), t, s),
       Y__2(s)=laplace(y__2(t), t, s)
     ):
sys:=[ 2*diff(y__1(t),t)=-2*y__1(t)-3*y__2(t)+2*u__1(t),
       diff(y__2(t),t)=4*y__1(t)-6*y__2(t)+2*u__1(t)+4*u__2(t)
     ];
lsys:=eval( laplace~(sys, t,s), [y__1(0)=0, y__2(0)=0]);

[2*(diff(y__1(t), t)) = -2*y__1(t)-3*y__2(t)+2*u__1(t), diff(y__2(t), t) = 4*y__1(t)-6*y__2(t)+2*u__1(t)+4*u__2(t)]

 

[2*s*Y__1(s) = -2*Y__1(s)-3*Y__2(s)+2*U__1(s), s*Y__2(s) = 4*Y__1(s)-6*Y__2(s)+2*U__1(s)+4*U__2(s)]

(1)

eq1:=isolate( subs(isolate(lsys[1], Y__2(s)),lsys[2]),Y__1(s));
eq2:=simplify(isolate( subs(eq1, lsys[2]),Y__2(s)));

Y__1(s) = (-2*U__1(s)+4*U__2(s)-(2/3)*s*U__1(s))/(-(2/3)*s^2-(14/3)*s-8)

 

Y__2(s) = ((2*s+6)*U__1(s)+4*U__2(s)*(s+1))/(s^2+7*s+12)

(2)

G_11:= simplify(eval(eq1, U__2(s)=0))/U__1(s);
G_12:= simplify(eval(eq1, U__1(s)=0))/U__2(s);
G_21:= simplify(eval(eq2, U__2(s)=0))/U__1(s);
G_22:= simplify(eval(eq2, U__1(s)=0))/U__2(s);

Y__1(s)/U__1(s) = 1/(s+4)

 

Y__1(s)/U__2(s) = -6/(s^2+7*s+12)

 

Y__2(s)/U__1(s) = 2/(s+4)

 

Y__2(s)/U__2(s) = 4*(s+1)/(s^2+7*s+12)

(3)

 


 

Download lap.mw

Isn't this a "straightforward" z-gradient scheme with a defined zrange, as in the attached (which has the additional benefit of working in Maple 2015).

Or am I missing something??

PS Plot colours render a lot better in Maple than they do on this site!
 

  restart:
  interface(version);
  with(plots):
  with(Statistics):
  randomize():
  N := 10:
  P := 3:
  A := Sample(Uniform(0, 1), [N, P]):
  C := CorrelationMatrix(A);
  matrixplot
  ( C,
    heights=histogram,
    axes=frame,
    gap=0.25,
    colorscheme=[ "zgradient",
                  [ "Blue", "White", "Red" ],
                  zrange=-1..1
                ],
    orientation=[0, 0, 0],
    lightmodel=none,
    tickmarks=[[seq(i+1/2=A||i, i=1..P)], [seq(i+1/2=A||i, i=1..P)], default],
    labels=[("")$3]
  );

`Standard Worksheet Interface, Maple 2015.2, Windows 7, December 21 2015 Build ID 1097895`

 

C := Matrix(3, 3, {(1, 1) = 1.0, (1, 2) = -.1563106801276543, (1, 3) = -0.6792568803622306e-1, (2, 1) = -.1563106801276543, (2, 2) = 1.0, (2, 3) = -.37067762598813236, (3, 1) = -0.6792568803622306e-1, (3, 2) = -.37067762598813236, (3, 3) = 1.0}, datatype = float[8])

 

 

 


 

Download zgrad.mw

In the attached worksheet (on my machine)

  1. it starts with Physics:-Version 419 and everything works
  2. it sets the Physics:-Version to 426 repeats the commands, and all integrals return unevaluated!!
  3. it sets the Physics:-Version back to 419 and everything works again

If you re-execute this worksheet, your experience will be somewhat different, because you will be starting  with Physics:-Version 426, so the first two sets of commands *should* give the same "unevaluated integrals. But what happens with the last set of commands where you should be using Physicss:-Version 419??

restart;

version()

 User Interface: 1399874

         Kernel: 1399874
        Library: 1399874

 

1399874

(1)

interface(version)

`Standard Worksheet Interface, Maple 2019.1, Windows 7, May 21 2019 Build ID 1399874`

(2)

Physics:-Version();

`The "Physics Updates" version "419" is installed but is not active. The active version of Physics is within the library C:\Users\TomLeslie\maple\toolbox\2019\Physics Updates\lib\Physics Updates.maple, created 2019, September 21, 9:30 hours`

(3)

restart;

int(exp(x),x=0..1)

-1+exp(1)

(4)

int(sin(n*x),x=0..Pi)

-(-1+cos(Pi*n))/n

(5)

int(tan(x),x=0..Pi)

undefined

(6)

int(cos(x),x=0..1)

sin(1)

(7)

int(sin(x),x=0 .. Pi)

2

(8)

int(cos(x),x)

sin(x)

(9)

int(x,x=0 .. 1)

1/2

(10)

Physics:-Version(426);

Warning, this package updates content shipped in a standard Maple install.  Use the 'restart' command to clear your session before using these commands.

 

`The "Physics Updates" version "426" is installed but is not active. The active version of Physics is within the library C:\Users\TomLeslie\maple\toolbox/2019/Physics Updates/lib\Physics Updates.maple, created 2019, September 21, 9:34 hours`

(11)

restart;

int(exp(x),x=0..1)

int(exp(x), x = 0 .. 1)

(12)

int(sin(n*x),x=0..Pi)

int(sin(n*x), x = 0 .. Pi)

(13)

int(tan(x),x=0..Pi)

int(tan(x), x = 0 .. Pi)

(14)

int(cos(x),x=0..1)

int(cos(x), x = 0 .. 1)

(15)

int(sin(x),x=0 .. Pi)

int(sin(x), x = 0 .. Pi)

(16)

int(cos(x),x)

sin(x)

(17)

int(x,x=0 .. 1)

1/2

(18)

Physics:-Version(419);

Warning, this package updates content shipped in a standard Maple install.  Use the 'restart' command to clear your session before using these commands.

 

`The "Physics Updates" version "419" is installed but is not active. The active version of Physics is within the library C:\Users\TomLeslie\maple\toolbox/2019/Physics Updates/lib\Physics Updates.maple, created 2019, September 21, 9:34 hours`

(19)

restart;

int(exp(x),x=0..1)

-1+exp(1)

(20)

int(sin(n*x),x=0..Pi)

-(-1+cos(Pi*n))/n

(21)

int(tan(x),x=0..Pi)

undefined

(22)

int(cos(x),x=0..1)

sin(1)

(23)

int(sin(x),x=0 .. Pi)

2

(24)

int(cos(x),x)

sin(x)

(25)

int(x,x=0 .. 1)

1/2

(26)

 


 

Download PhysVer.mw

If you want better control over the x-values at which the function is evaluated, use the attached.

You will have to change the filename in the Export() command to something appropriate for your machine

  restart;
  f:= x->x^3-2*x:
  startVal:= 1;
  stopVal:= 10;
  spacing:= 0.1;
  M:= Matrix
      ( 1+round((stopVal-startVal)/spacing),
        2,
        (i,j)-> `if`( j=1,
                      startVal+(i-1)*spacing,
                      f( startVal+(i-1)*spacing)
                    )
      );
  Export("C:/Users/TomLeslie/Desktop/data.csv", M);

startVal := 1

 

stopVal := 10

 

spacing := .1

 

_rtable[18446744074396479230]

 

1037

(1)

 


 

Download expData.mw

 

Your ODE is third order. You therefore need three intial conditions

The only thing you really need to remember is that is that ODEs and BCs/ICs have to be supplied to dsolve() as a simple list. Not a pair of lists, or a listlist or anything else. Just a plain ordinary simple list.

So I'd fix your problem as shown in the attached

Lindas signal transduction model

 

NULLNULLNULLNULL

Mod1 := [diff(Depot(t), t) = piecewise(t = 0, -Ka*Depot(t)+150, t = 24, -Ka*Depot(t)+150, -Ka*Depot(t)), diff(Central(t), t) = Ka*Depot(t)-ce*Ke, diff(EGFR(t), t) = Kin*(1-ce/IC50-ce)-Kout*EGFR(t), diff(PPi3k(t), t) = (EGFR(t)-PPi3k(t))/t1, diff(PAKT(t), t) = (PPi3k(t)-PAKT(t))/t1, diff(PRas(t), t) = (EGFR(t)-PRas(t))/t1, diff(PRaf(t), t) = (PRas(t)-PRaf(t))/t1, diff(PMEK(t), t) = (PRaf(t)-PMEK(t))/t1, diff(PERK(t), t) = (PMEK(t)-PERK(t))/t1, diff(Pmyc(t), t) = (PAKT(t)+PERK(t)-Pmyc(t))/t1, diff(ACII(t), t) = Pmyc(t)-ACII(t)*ACIIdeg, diff(SPC(t), t) = ACIIloss-SPC(t)*Ke0]

[diff(Depot(t), t) = piecewise(t = 0, -Ka*Depot(t)+150, t = 24, -Ka*Depot(t)+150, -Ka*Depot(t)), diff(Central(t), t) = Ka*Depot(t)-ce*Ke, diff(EGFR(t), t) = Kin*(1-ce/IC50-ce)-Kout*EGFR(t), diff(PPi3k(t), t) = (EGFR(t)-PPi3k(t))/t1, diff(PAKT(t), t) = (PPi3k(t)-PAKT(t))/t1, diff(PRas(t), t) = (EGFR(t)-PRas(t))/t1, diff(PRaf(t), t) = (PRas(t)-PRaf(t))/t1, diff(PMEK(t), t) = (PRaf(t)-PMEK(t))/t1, diff(PERK(t), t) = (PMEK(t)-PERK(t))/t1, diff(Pmyc(t), t) = (PAKT(t)+PERK(t)-Pmyc(t))/t1, diff(ACII(t), t) = Pmyc(t)-ACII(t)*ACIIdeg, diff(SPC(t), t) = ACIIloss-SPC(t)*Ke0]

(1.1)

pars := [Ka = .95, Ke = 0.18e-1, IC50 = 0.786872e-2, Kin = .1, Kout = 0.1e-1, ACIIdeg = .1, t1 = 6, Ke0 = 0.1e-1]

[Ka = .95, Ke = 0.18e-1, IC50 = 0.786872e-2, Kin = .1, Kout = 0.1e-1, ACIIdeg = .1, t1 = 6, Ke0 = 0.1e-1]

(1.2)

Initial := [Depot(0) = 0, Central(0) = 0, EGFR(0) = 100, PPi3k(0) = 0, PAKT(0) = 0, PRas(0) = 0, PRaf(0) = 0, PMEK(0) = 0, PERK(0) = 0, Pmyc(0) = 0, ACII(0) = 100, SPC(0) = 0]

[Depot(0) = 0, Central(0) = 0, EGFR(0) = 100, PPi3k(0) = 0, PAKT(0) = 0, PRas(0) = 0, PRaf(0) = 0, PMEK(0) = 0, PERK(0) = 0, Pmyc(0) = 0, ACII(0) = 100, SPC(0) = 0]

(1.3)

transform model to put ce and ACIIloss in terms of the variables

trans := [ce = (1/233000)*Central(t), ACIIloss = 100/ACII(t)]

[ce = (1/233000)*Central(t), ACIIloss = 100/ACII(t)]

(1.4)

Mod2 := subs(trans, Mod1)

[diff(Depot(t), t) = piecewise(t = 0, -Ka*Depot(t)+150, t = 24, -Ka*Depot(t)+150, -Ka*Depot(t)), diff(Central(t), t) = Ka*Depot(t)-(1/233000)*Central(t)*Ke, diff(EGFR(t), t) = Kin*(1-(1/233000)*Central(t)/IC50-(1/233000)*Central(t))-Kout*EGFR(t), diff(PPi3k(t), t) = (EGFR(t)-PPi3k(t))/t1, diff(PAKT(t), t) = (PPi3k(t)-PAKT(t))/t1, diff(PRas(t), t) = (EGFR(t)-PRas(t))/t1, diff(PRaf(t), t) = (PRas(t)-PRaf(t))/t1, diff(PMEK(t), t) = (PRaf(t)-PMEK(t))/t1, diff(PERK(t), t) = (PMEK(t)-PERK(t))/t1, diff(Pmyc(t), t) = (PAKT(t)+PERK(t)-Pmyc(t))/t1, diff(ACII(t), t) = Pmyc(t)-ACII(t)*ACIIdeg, diff(SPC(t), t) = 100/ACII(t)-SPC(t)*Ke0]

(1.5)

Numerically integrate

 

soln := dsolve([eval(Mod2[], pars), Initial[]], numeric)

proc (x_rkf45) local _res, _dat, _vars, _solnproc, _xout, _ndsol, _pars, _n, _i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; if 1 < nargs then error "invalid input: too many arguments" end if; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then _xout := evalf[_EnvDSNumericSaveDigits](x_rkf45) else _xout := evalf(x_rkf45) end if; _dat := Array(1..4, {(1) = proc (_xin) local _xout, _dtbl, _dat, _vmap, _x0, _y0, _val, _dig, _n, _ne, _nd, _nv, _pars, _ini, _par, _i, _j, _k, _src; option `Copyright (c) 2002 by Waterloo Maple Inc. All rights reserved.`; table( [( "complex" ) = false ] ) _xout := _xin; _pars := []; _dtbl := array( 1 .. 4, [( 1 ) = (array( 1 .. 26, [( 1 ) = (datatype = float[8], order = C_order, storage = rectangular), ( 2 ) = (datatype = float[8], order = C_order, storage = rectangular), ( 3 ) = ([0, 0, 0, Array(1..0, 1..2, {}, datatype = float[8], order = C_order)]), ( 4 ) = (Array(1..63, {(1) = 12, (2) = 12, (3) = 0, (4) = 0, (5) = 0, (6) = 0, (7) = 1, (8) = 0, (9) = 0, (10) = 0, (11) = 0, (12) = 0, (13) = 0, (14) = 0, (15) = 0, (16) = 0, (17) = 0, (18) = 1, (19) = 30000, (20) = 0, (21) = 0, (22) = 1, (23) = 4, (24) = 0, (25) = 1, (26) = 15, (27) = 1, (28) = 0, (29) = 1, (30) = 3, (31) = 3, (32) = 0, (33) = 1, (34) = 0, (35) = 0, (36) = 0, (37) = 0, (38) = 0, (39) = 0, (40) = 0, (41) = 0, (42) = 0, (43) = 1, (44) = 0, (45) = 0, (46) = 0, (47) = 0, (48) = 0, (49) = 0, (50) = 50, (51) = 1, (52) = 0, (53) = 0, (54) = 0, (55) = 0, (56) = 0, (57) = 0, (58) = 0, (59) = 10000, (60) = 0, (61) = 1000, (62) = 0, (63) = 0}, datatype = integer[8])), ( 5 ) = (Array(1..28, {(1) = .0, (2) = 0.10e-5, (3) = .0, (4) = 0.500001e-14, (5) = .0, (6) = 0.3365105837227697e-4, (7) = .0, (8) = 0.10e-5, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = 1.0, (14) = .0, (15) = .49999999999999, (16) = .0, (17) = 1.0, (18) = 1.0, (19) = .0, (20) = .0, (21) = 1.0, (22) = 1.0, (23) = .0, (24) = .0, (25) = 0.10e-14, (26) = .0, (27) = .0, (28) = .0}, datatype = float[8], order = C_order)), ( 6 ) = (Array(1..12, {(1) = 100.0, (2) = .0, (3) = .0, (4) = 100.0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0}, datatype = float[8], order = C_order)), ( 7 ) = ([Array(1..4, 1..7, {(1, 1) = .0, (1, 2) = .203125, (1, 3) = .3046875, (1, 4) = .75, (1, 5) = .8125, (1, 6) = .40625, (1, 7) = .8125, (2, 1) = 0.6378173828125e-1, (2, 2) = .0, (2, 3) = .279296875, (2, 4) = .27237892150878906, (2, 5) = -0.9686851501464844e-1, (2, 6) = 0.1956939697265625e-1, (2, 7) = .5381584167480469, (3, 1) = 0.31890869140625e-1, (3, 2) = .0, (3, 3) = -.34375, (3, 4) = -.335235595703125, (3, 5) = .2296142578125, (3, 6) = .41748046875, (3, 7) = 11.480712890625, (4, 1) = 0.9710520505905151e-1, (4, 2) = .0, (4, 3) = .40350341796875, (4, 4) = 0.20297467708587646e-1, (4, 5) = -0.6054282188415527e-2, (4, 6) = -0.4770040512084961e-1, (4, 7) = .77858567237854}, datatype = float[8], order = C_order), Array(1..6, 1..6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = 1.0, (2, 1) = .25, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = 1.0, (3, 1) = .1875, (3, 2) = .5625, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = 2.0, (4, 1) = .23583984375, (4, 2) = -.87890625, (4, 3) = .890625, (4, 4) = .0, (4, 5) = .0, (4, 6) = .2681884765625, (5, 1) = .1272735595703125, (5, 2) = -.5009765625, (5, 3) = .44921875, (5, 4) = -0.128936767578125e-1, (5, 5) = .0, (5, 6) = 0.626220703125e-1, (6, 1) = -0.927734375e-1, (6, 2) = .626220703125, (6, 3) = -.4326171875, (6, 4) = .1418304443359375, (6, 5) = -0.861053466796875e-1, (6, 6) = .3131103515625}, datatype = float[8], order = C_order), Array(1..6, {(1) = .0, (2) = .386, (3) = .21, (4) = .63, (5) = 1.0, (6) = 1.0}, datatype = float[8], order = C_order), Array(1..6, {(1) = .25, (2) = -.1043, (3) = .1035, (4) = -0.362e-1, (5) = .0, (6) = .0}, datatype = float[8], order = C_order), Array(1..6, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = 1.544, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (3, 1) = .9466785280815533, (3, 2) = .25570116989825814, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (4, 1) = 3.3148251870684886, (4, 2) = 2.896124015972123, (4, 3) = .9986419139977808, (4, 4) = .0, (4, 5) = .0, (5, 1) = 1.2212245092262748, (5, 2) = 6.019134481287752, (5, 3) = 12.537083329320874, (5, 4) = -.687886036105895, (5, 5) = .0, (6, 1) = 1.2212245092262748, (6, 2) = 6.019134481287752, (6, 3) = 12.537083329320874, (6, 4) = -.687886036105895, (6, 5) = 1.0}, datatype = float[8], order = C_order), Array(1..6, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = -5.6688, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (3, 1) = -2.4300933568337584, (3, 2) = -.20635991570891224, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (4, 1) = -.10735290581452621, (4, 2) = -9.594562251021896, (4, 3) = -20.470286148096154, (4, 4) = .0, (4, 5) = .0, (5, 1) = 7.496443313968615, (5, 2) = -10.246804314641219, (5, 3) = -33.99990352819906, (5, 4) = 11.708908932061595, (5, 5) = .0, (6, 1) = 8.083246795922411, (6, 2) = -7.981132988062785, (6, 3) = -31.52159432874373, (6, 4) = 16.319305431231363, (6, 5) = -6.0588182388340535}, datatype = float[8], order = C_order), Array(1..3, 1..5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (2, 1) = 10.126235083446911, (2, 2) = -7.487995877607633, (2, 3) = -34.800918615557414, (2, 4) = -7.9927717075687275, (2, 5) = 1.0251377232956207, (3, 1) = -.6762803392806898, (3, 2) = 6.087714651678606, (3, 3) = 16.43084320892463, (3, 4) = 24.767225114183653, (3, 5) = -6.5943891257167815}, datatype = float[8], order = C_order)]), ( 9 ) = ([Array(1..12, {(1) = .1, (2) = .1, (3) = .1, (4) = .1, (5) = .1, (6) = .1, (7) = .1, (8) = .1, (9) = .1, (10) = .1, (11) = .1, (12) = .1}, datatype = float[8], order = C_order), Array(1..12, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0}, datatype = float[8], order = C_order), Array(1..12, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0}, datatype = float[8], order = C_order), Array(1..12, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0}, datatype = float[8], order = C_order), Array(1..12, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0}, datatype = float[8], order = C_order), Array(1..12, 1..12, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = .0, (1, 7) = .0, (1, 8) = .0, (1, 9) = .0, (1, 10) = .0, (1, 11) = .0, (1, 12) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = .0, (2, 7) = .0, (2, 8) = .0, (2, 9) = .0, (2, 10) = .0, (2, 11) = .0, (2, 12) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = .0, (3, 7) = .0, (3, 8) = .0, (3, 9) = .0, (3, 10) = .0, (3, 11) = .0, (3, 12) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (4, 5) = .0, (4, 6) = .0, (4, 7) = .0, (4, 8) = .0, (4, 9) = .0, (4, 10) = .0, (4, 11) = .0, (4, 12) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (5, 5) = .0, (5, 6) = .0, (5, 7) = .0, (5, 8) = .0, (5, 9) = .0, (5, 10) = .0, (5, 11) = .0, (5, 12) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = .0, (6, 5) = .0, (6, 6) = .0, (6, 7) = .0, (6, 8) = .0, (6, 9) = .0, (6, 10) = .0, (6, 11) = .0, (6, 12) = .0, (7, 1) = .0, (7, 2) = .0, (7, 3) = .0, (7, 4) = .0, (7, 5) = .0, (7, 6) = .0, (7, 7) = .0, (7, 8) = .0, (7, 9) = .0, (7, 10) = .0, (7, 11) = .0, (7, 12) = .0, (8, 1) = .0, (8, 2) = .0, (8, 3) = .0, (8, 4) = .0, (8, 5) = .0, (8, 6) = .0, (8, 7) = .0, (8, 8) = .0, (8, 9) = .0, (8, 10) = .0, (8, 11) = .0, (8, 12) = .0, (9, 1) = .0, (9, 2) = .0, (9, 3) = .0, (9, 4) = .0, (9, 5) = .0, (9, 6) = .0, (9, 7) = .0, (9, 8) = .0, (9, 9) = .0, (9, 10) = .0, (9, 11) = .0, (9, 12) = .0, (10, 1) = .0, (10, 2) = .0, (10, 3) = .0, (10, 4) = .0, (10, 5) = .0, (10, 6) = .0, (10, 7) = .0, (10, 8) = .0, (10, 9) = .0, (10, 10) = .0, (10, 11) = .0, (10, 12) = .0, (11, 1) = .0, (11, 2) = .0, (11, 3) = .0, (11, 4) = .0, (11, 5) = .0, (11, 6) = .0, (11, 7) = .0, (11, 8) = .0, (11, 9) = .0, (11, 10) = .0, (11, 11) = .0, (11, 12) = .0, (12, 1) = .0, (12, 2) = .0, (12, 3) = .0, (12, 4) = .0, (12, 5) = .0, (12, 6) = .0, (12, 7) = .0, (12, 8) = .0, (12, 9) = .0, (12, 10) = .0, (12, 11) = .0, (12, 12) = .0}, datatype = float[8], order = C_order), Array(1..12, 1..12, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = .0, (1, 7) = .0, (1, 8) = .0, (1, 9) = .0, (1, 10) = .0, (1, 11) = .0, (1, 12) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = .0, (2, 7) = .0, (2, 8) = .0, (2, 9) = .0, (2, 10) = .0, (2, 11) = .0, (2, 12) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = .0, (3, 7) = .0, (3, 8) = .0, (3, 9) = .0, (3, 10) = .0, (3, 11) = .0, (3, 12) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (4, 5) = .0, (4, 6) = .0, (4, 7) = .0, (4, 8) = .0, (4, 9) = .0, (4, 10) = .0, (4, 11) = .0, (4, 12) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (5, 5) = .0, (5, 6) = .0, (5, 7) = .0, (5, 8) = .0, (5, 9) = .0, (5, 10) = .0, (5, 11) = .0, (5, 12) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = .0, (6, 5) = .0, (6, 6) = .0, (6, 7) = .0, (6, 8) = .0, (6, 9) = .0, (6, 10) = .0, (6, 11) = .0, (6, 12) = .0, (7, 1) = .0, (7, 2) = .0, (7, 3) = .0, (7, 4) = .0, (7, 5) = .0, (7, 6) = .0, (7, 7) = .0, (7, 8) = .0, (7, 9) = .0, (7, 10) = .0, (7, 11) = .0, (7, 12) = .0, (8, 1) = .0, (8, 2) = .0, (8, 3) = .0, (8, 4) = .0, (8, 5) = .0, (8, 6) = .0, (8, 7) = .0, (8, 8) = .0, (8, 9) = .0, (8, 10) = .0, (8, 11) = .0, (8, 12) = .0, (9, 1) = .0, (9, 2) = .0, (9, 3) = .0, (9, 4) = .0, (9, 5) = .0, (9, 6) = .0, (9, 7) = .0, (9, 8) = .0, (9, 9) = .0, (9, 10) = .0, (9, 11) = .0, (9, 12) = .0, (10, 1) = .0, (10, 2) = .0, (10, 3) = .0, (10, 4) = .0, (10, 5) = .0, (10, 6) = .0, (10, 7) = .0, (10, 8) = .0, (10, 9) = .0, (10, 10) = .0, (10, 11) = .0, (10, 12) = .0, (11, 1) = .0, (11, 2) = .0, (11, 3) = .0, (11, 4) = .0, (11, 5) = .0, (11, 6) = .0, (11, 7) = .0, (11, 8) = .0, (11, 9) = .0, (11, 10) = .0, (11, 11) = .0, (11, 12) = .0, (12, 1) = .0, (12, 2) = .0, (12, 3) = .0, (12, 4) = .0, (12, 5) = .0, (12, 6) = .0, (12, 7) = .0, (12, 8) = .0, (12, 9) = .0, (12, 10) = .0, (12, 11) = .0, (12, 12) = .0}, datatype = float[8], order = C_order), Array(1..12, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0}, datatype = float[8], order = C_order), Array(1..12, 1..12, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = .0, (1, 7) = .0, (1, 8) = .0, (1, 9) = .0, (1, 10) = .0, (1, 11) = .0, (1, 12) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = .0, (2, 7) = .0, (2, 8) = .0, (2, 9) = .0, (2, 10) = .0, (2, 11) = .0, (2, 12) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = .0, (3, 7) = .0, (3, 8) = .0, (3, 9) = .0, (3, 10) = .0, (3, 11) = .0, (3, 12) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (4, 5) = .0, (4, 6) = .0, (4, 7) = .0, (4, 8) = .0, (4, 9) = .0, (4, 10) = .0, (4, 11) = .0, (4, 12) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (5, 5) = .0, (5, 6) = .0, (5, 7) = .0, (5, 8) = .0, (5, 9) = .0, (5, 10) = .0, (5, 11) = .0, (5, 12) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = .0, (6, 5) = .0, (6, 6) = .0, (6, 7) = .0, (6, 8) = .0, (6, 9) = .0, (6, 10) = .0, (6, 11) = .0, (6, 12) = .0, (7, 1) = .0, (7, 2) = .0, (7, 3) = .0, (7, 4) = .0, (7, 5) = .0, (7, 6) = .0, (7, 7) = .0, (7, 8) = .0, (7, 9) = .0, (7, 10) = .0, (7, 11) = .0, (7, 12) = .0, (8, 1) = .0, (8, 2) = .0, (8, 3) = .0, (8, 4) = .0, (8, 5) = .0, (8, 6) = .0, (8, 7) = .0, (8, 8) = .0, (8, 9) = .0, (8, 10) = .0, (8, 11) = .0, (8, 12) = .0, (9, 1) = .0, (9, 2) = .0, (9, 3) = .0, (9, 4) = .0, (9, 5) = .0, (9, 6) = .0, (9, 7) = .0, (9, 8) = .0, (9, 9) = .0, (9, 10) = .0, (9, 11) = .0, (9, 12) = .0, (10, 1) = .0, (10, 2) = .0, (10, 3) = .0, (10, 4) = .0, (10, 5) = .0, (10, 6) = .0, (10, 7) = .0, (10, 8) = .0, (10, 9) = .0, (10, 10) = .0, (10, 11) = .0, (10, 12) = .0, (11, 1) = .0, (11, 2) = .0, (11, 3) = .0, (11, 4) = .0, (11, 5) = .0, (11, 6) = .0, (11, 7) = .0, (11, 8) = .0, (11, 9) = .0, (11, 10) = .0, (11, 11) = .0, (11, 12) = .0, (12, 1) = .0, (12, 2) = .0, (12, 3) = .0, (12, 4) = .0, (12, 5) = .0, (12, 6) = .0, (12, 7) = .0, (12, 8) = .0, (12, 9) = .0, (12, 10) = .0, (12, 11) = .0, (12, 12) = .0}, datatype = float[8], order = C_order), Array(1..12, 1..6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (4, 5) = .0, (4, 6) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (5, 5) = .0, (5, 6) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = .0, (6, 5) = .0, (6, 6) = .0, (7, 1) = .0, (7, 2) = .0, (7, 3) = .0, (7, 4) = .0, (7, 5) = .0, (7, 6) = .0, (8, 1) = .0, (8, 2) = .0, (8, 3) = .0, (8, 4) = .0, (8, 5) = .0, (8, 6) = .0, (9, 1) = .0, (9, 2) = .0, (9, 3) = .0, (9, 4) = .0, (9, 5) = .0, (9, 6) = .0, (10, 1) = .0, (10, 2) = .0, (10, 3) = .0, (10, 4) = .0, (10, 5) = .0, (10, 6) = .0, (11, 1) = .0, (11, 2) = .0, (11, 3) = .0, (11, 4) = .0, (11, 5) = .0, (11, 6) = .0, (12, 1) = .0, (12, 2) = .0, (12, 3) = .0, (12, 4) = .0, (12, 5) = .0, (12, 6) = .0}, datatype = float[8], order = C_order), Array(1..12, {(1) = 0, (2) = 0, (3) = 0, (4) = 0, (5) = 0, (6) = 0, (7) = 0, (8) = 0, (9) = 0, (10) = 0, (11) = 0, (12) = 0}, datatype = integer[8]), Array(1..12, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0}, datatype = float[8], order = C_order), Array(1..12, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0}, datatype = float[8], order = C_order), Array(1..12, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0}, datatype = float[8], order = C_order), Array(1..12, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0}, datatype = float[8], order = C_order), Array(1..12, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0}, datatype = float[8], order = C_order), Array(1..24, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = .0, (14) = .0, (15) = .0, (16) = .0, (17) = .0, (18) = .0, (19) = .0, (20) = .0, (21) = .0, (22) = .0, (23) = .0, (24) = .0}, datatype = float[8], order = C_order), Array(1..12, {(1) = 0, (2) = 0, (3) = 0, (4) = 0, (5) = 0, (6) = 0, (7) = 0, (8) = 0, (9) = 0, (10) = 0, (11) = 0, (12) = 0}, datatype = integer[8])]), ( 8 ) = ([Array(1..12, {(1) = 100.0, (2) = .0, (3) = .0, (4) = 100.0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0}, datatype = float[8], order = C_order), Array(1..12, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0}, datatype = float[8], order = C_order), Array(1..12, {(1) = -10.0, (2) = .0, (3) = 150.0, (4) = -.9, (5) = .0, (6) = .0, (7) = .0, (8) = 16.666666666666664, (9) = .0, (10) = 16.666666666666664, (11) = .0, (12) = 1.0}, datatype = float[8], order = C_order), 0, 0]), ( 11 ) = (Array(1..6, 0..12, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = .0, (1, 7) = .0, (1, 8) = .0, (1, 9) = .0, (1, 10) = .0, (1, 11) = .0, (1, 12) = .0, (2, 0) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = .0, (2, 7) = .0, (2, 8) = .0, (2, 9) = .0, (2, 10) = .0, (2, 11) = .0, (2, 12) = .0, (3, 0) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = .0, (3, 7) = .0, (3, 8) = .0, (3, 9) = .0, (3, 10) = .0, (3, 11) = .0, (3, 12) = .0, (4, 0) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (4, 5) = .0, (4, 6) = .0, (4, 7) = .0, (4, 8) = .0, (4, 9) = .0, (4, 10) = .0, (4, 11) = .0, (4, 12) = .0, (5, 0) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (5, 5) = .0, (5, 6) = .0, (5, 7) = .0, (5, 8) = .0, (5, 9) = .0, (5, 10) = .0, (5, 11) = .0, (5, 12) = .0, (6, 0) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = .0, (6, 5) = .0, (6, 6) = .0, (6, 7) = .0, (6, 8) = .0, (6, 9) = .0, (6, 10) = .0, (6, 11) = .0, (6, 12) = .0}, datatype = float[8], order = C_order)), ( 10 ) = ([proc (N, X, Y, YP) option `[Y[1] = ACII(t), Y[2] = Central(t), Y[3] = Depot(t), Y[4] = EGFR(t), Y[5] = PAKT(t), Y[6] = PERK(t), Y[7] = PMEK(t), Y[8] = PPi3k(t), Y[9] = PRaf(t), Y[10] = PRas(t), Y[11] = Pmyc(t), Y[12] = SPC(t)]`; YP[1] := Y[11]-.1*Y[1]; YP[2] := .95*Y[3]-0.7725321888e-7*Y[2]; YP[3] := piecewise(X = 0, -.95*Y[3]+150, X = 24, -.95*Y[3]+150, -.95*Y[3]); YP[4] := .1-0.5497230584e-4*Y[2]-0.1e-1*Y[4]; YP[5] := (1/6)*Y[8]-(1/6)*Y[5]; YP[6] := (1/6)*Y[7]-(1/6)*Y[6]; YP[7] := (1/6)*Y[9]-(1/6)*Y[7]; YP[8] := (1/6)*Y[4]-(1/6)*Y[8]; YP[9] := (1/6)*Y[10]-(1/6)*Y[9]; YP[10] := (1/6)*Y[4]-(1/6)*Y[10]; YP[11] := (1/6)*Y[5]+(1/6)*Y[6]-(1/6)*Y[11]; YP[12] := 100/Y[1]-0.1e-1*Y[12]; 0 end proc, -1, 0, 0, 0, 0, 0, 0, 0, 0]), ( 13 ) = (), ( 12 ) = (), ( 15 ) = ("rkf45"), ( 14 ) = ([0, 0]), ( 18 ) = ([]), ( 19 ) = (0), ( 16 ) = ([0, 0, 0, 0, 0, []]), ( 17 ) = ([proc (N, X, Y, YP) option `[Y[1] = ACII(t), Y[2] = Central(t), Y[3] = Depot(t), Y[4] = EGFR(t), Y[5] = PAKT(t), Y[6] = PERK(t), Y[7] = PMEK(t), Y[8] = PPi3k(t), Y[9] = PRaf(t), Y[10] = PRas(t), Y[11] = Pmyc(t), Y[12] = SPC(t)]`; YP[1] := Y[11]-.1*Y[1]; YP[2] := .95*Y[3]-0.7725321888e-7*Y[2]; YP[3] := piecewise(X = 0, -.95*Y[3]+150, X = 24, -.95*Y[3]+150, -.95*Y[3]); YP[4] := .1-0.5497230584e-4*Y[2]-0.1e-1*Y[4]; YP[5] := (1/6)*Y[8]-(1/6)*Y[5]; YP[6] := (1/6)*Y[7]-(1/6)*Y[6]; YP[7] := (1/6)*Y[9]-(1/6)*Y[7]; YP[8] := (1/6)*Y[4]-(1/6)*Y[8]; YP[9] := (1/6)*Y[10]-(1/6)*Y[9]; YP[10] := (1/6)*Y[4]-(1/6)*Y[10]; YP[11] := (1/6)*Y[5]+(1/6)*Y[6]-(1/6)*Y[11]; YP[12] := 100/Y[1]-0.1e-1*Y[12]; 0 end proc, -1, 0, 0, 0, 0, 0, 0, 0, 0]), ( 22 ) = (0), ( 23 ) = (0), ( 20 ) = ([]), ( 21 ) = (0), ( 26 ) = (Array(1..0, {})), ( 25 ) = (Array(1..0, {})), ( 24 ) = (0)  ] ))  ] ); _y0 := Array(0..12, {(1) = 0., (2) = 100., (3) = 0., (4) = 0., (5) = 100., (6) = 0., (7) = 0., (8) = 0., (9) = 0., (10) = 0., (11) = 0., (12) = 0.}); _vmap := array( 1 .. 12, [( 1 ) = (1), ( 2 ) = (2), ( 3 ) = (3), ( 4 ) = (4), ( 5 ) = (5), ( 6 ) = (6), ( 7 ) = (7), ( 9 ) = (9), ( 8 ) = (8), ( 11 ) = (11), ( 10 ) = (10), ( 12 ) = (12)  ] ); _x0 := _dtbl[1][5][5]; _n := _dtbl[1][4][1]; _ne := _dtbl[1][4][3]; _nd := _dtbl[1][4][4]; _nv := _dtbl[1][4][16]; if not type(_xout, 'numeric') then if member(_xout, ["start", "left", "right"]) then if _Env_smart_dsolve_numeric = true or _dtbl[1][4][10] = 1 then if _xout = "left" then if type(_dtbl[2], 'table') then return _dtbl[2][5][1] end if elif _xout = "right" then if type(_dtbl[3], 'table') then return _dtbl[3][5][1] end if end if end if; return _dtbl[1][5][5] elif _xout = "method" then return _dtbl[1][15] elif _xout = "storage" then return evalb(_dtbl[1][4][10] = 1) elif _xout = "leftdata" then if not type(_dtbl[2], 'array') then return NULL else return eval(_dtbl[2]) end if elif _xout = "rightdata" then if not type(_dtbl[3], 'array') then return NULL else return eval(_dtbl[3]) end if elif _xout = "enginedata" then return eval(_dtbl[1]) elif _xout = "enginereset" then _dtbl[2] := evaln(_dtbl[2]); _dtbl[3] := evaln(_dtbl[3]); return NULL elif _xout = "initial" then return procname(_y0[0]) elif _xout = "laxtol" then return _dtbl[`if`(member(_dtbl[4], {2, 3}), _dtbl[4], 1)][5][18] elif _xout = "numfun" then return `if`(member(_dtbl[4], {2, 3}), _dtbl[_dtbl[4]][4][18], 0) elif _xout = "parameters" then return [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] elif _xout = "initial_and_parameters" then return procname(_y0[0]), [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] elif _xout = "last" then if _dtbl[4] <> 2 and _dtbl[4] <> 3 or _x0-_dtbl[_dtbl[4]][5][1] = 0. then error "no information is available on last computed point" else _xout := _dtbl[_dtbl[4]][5][1] end if elif _xout = "function" then if _dtbl[1][4][33]-2. = 0 then return eval(_dtbl[1][10], 1) else return eval(_dtbl[1][10][1], 1) end if elif _xout = "map" then return copy(_vmap) elif type(_xin, `=`) and type(rhs(_xin), 'list') and member(lhs(_xin), {"initial", "parameters", "initial_and_parameters"}) then _ini, _par := [], []; if lhs(_xin) = "initial" then _ini := rhs(_xin) elif lhs(_xin) = "parameters" then _par := rhs(_xin) elif select(type, rhs(_xin), `=`) <> [] then _par, _ini := selectremove(type, rhs(_xin), `=`) elif nops(rhs(_xin)) < nops(_pars)+1 then error "insufficient data for specification of initial and parameters" else _par := rhs(_xin)[-nops(_pars) .. -1]; _ini := rhs(_xin)[1 .. -nops(_pars)-1] end if; _xout := lhs(_xout); _i := false; if _par <> [] then _i := `dsolve/numeric/process_parameters`(_n, _pars, _par, _y0) end if; if _ini <> [] then _i := `dsolve/numeric/process_initial`(_n-_ne, _ini, _y0, _pars, _vmap) or _i end if; if _i then `dsolve/numeric/SC/reinitialize`(_dtbl, _y0, _n, procname, _pars); if _Env_smart_dsolve_numeric = true and type(_y0[0], 'numeric') and _dtbl[1][4][10] <> 1 then procname("right") := _y0[0]; procname("left") := _y0[0] end if end if; if _xout = "initial" then return [_y0[0], seq(_y0[_vmap[_i]], _i = 1 .. _n-_ne)] elif _xout = "parameters" then return [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] else return [_y0[0], seq(_y0[_vmap[_i]], _i = 1 .. _n-_ne)], [seq(_y0[_n+_i], _i = 1 .. nops(_pars))] end if elif _xin = "eventstop" then if _nv = 0 then error "this solution has no events" end if; _i := _dtbl[4]; if _i <> 2 and _i <> 3 then return 0 end if; if _dtbl[_i][4][10] = 1 and assigned(_dtbl[5-_i]) and _dtbl[_i][4][9] < 100 and 100 <= _dtbl[5-_i][4][9] then _i := 5-_i; _dtbl[4] := _i; _j := round(_dtbl[_i][4][17]); return round(_dtbl[_i][3][1][_j, 1]) elif 100 <= _dtbl[_i][4][9] then _j := round(_dtbl[_i][4][17]); return round(_dtbl[_i][3][1][_j, 1]) else return 0 end if elif _xin = "eventstatus" then if _nv = 0 then error "this solution has no events" end if; _i := [selectremove(proc (a) options operator, arrow; _dtbl[1][3][1][a, 7] = 1 end proc, {seq(_j, _j = 1 .. round(_dtbl[1][3][1][_nv+1, 1]))})]; return ':-enabled' = _i[1], ':-disabled' = _i[2] elif _xin = "eventclear" then if _nv = 0 then error "this solution has no events" end if; _i := _dtbl[4]; if _i <> 2 and _i <> 3 then error "no events to clear" end if; if _dtbl[_i][4][10] = 1 and assigned(_dtbl[5-_i]) and _dtbl[_i][4][9] < 100 and 100 < _dtbl[5-_i][4][9] then _dtbl[4] := 5-_i; _i := 5-_i end if; if _dtbl[_i][4][9] < 100 then error "no events to clear" elif _nv < _dtbl[_i][4][9]-100 then error "event error condition cannot be cleared" else _j := _dtbl[_i][4][9]-100; if irem(round(_dtbl[_i][3][1][_j, 4]), 2) = 1 then error "retriggerable events cannot be cleared" end if; _j := round(_dtbl[_i][3][1][_j, 1]); for _k to _nv do if _dtbl[_i][3][1][_k, 1] = _j then if _dtbl[_i][3][1][_k, 2] = 3 then error "range events cannot be cleared" end if; _dtbl[_i][3][1][_k, 8] := _dtbl[_i][3][1][_nv+1, 8] end if end do; _dtbl[_i][4][17] := 0; _dtbl[_i][4][9] := 0; if _dtbl[1][4][10] = 1 then if _i = 2 then try procname(procname("left")) catch:  end try else try procname(procname("right")) catch:  end try end if end if end if; return  elif type(_xin, `=`) and member(lhs(_xin), {"eventdisable", "eventenable"}) then if _nv = 0 then error "this solution has no events" end if; if type(rhs(_xin), {('list')('posint'), ('set')('posint')}) then _i := {op(rhs(_xin))} elif type(rhs(_xin), 'posint') then _i := {rhs(_xin)} else error "event identifiers must be integers in the range 1..%1", round(_dtbl[1][3][1][_nv+1, 1]) end if; if select(proc (a) options operator, arrow; _nv < a end proc, _i) <> {} then error "event identifiers must be integers in the range 1..%1", round(_dtbl[1][3][1][_nv+1, 1]) end if; _k := {}; for _j to _nv do if member(round(_dtbl[1][3][1][_j, 1]), _i) then _k := `union`(_k, {_j}) end if end do; _i := _k; if lhs(_xin) = "eventdisable" then _dtbl[4] := 0; _j := [evalb(assigned(_dtbl[2]) and member(_dtbl[2][4][17], _i)), evalb(assigned(_dtbl[3]) and member(_dtbl[3][4][17], _i))]; for _k in _i do _dtbl[1][3][1][_k, 7] := 0; if assigned(_dtbl[2]) then _dtbl[2][3][1][_k, 7] := 0 end if; if assigned(_dtbl[3]) then _dtbl[3][3][1][_k, 7] := 0 end if end do; if _j[1] then for _k to _nv+1 do if _k <= _nv and not type(_dtbl[2][3][4][_k, 1], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to defined init `, _dtbl[2][3][4][_k, 1]); _dtbl[2][3][1][_k, 8] := _dtbl[2][3][4][_k, 1] elif _dtbl[2][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[2][3][1][_k, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to rate hysteresis init `, _dtbl[2][5][24]); _dtbl[2][3][1][_k, 8] := _dtbl[2][5][24] elif _dtbl[2][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[2][3][1][_k, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to initial init `, _x0); _dtbl[2][3][1][_k, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #2, event code `, _k, ` to fireinitial init `, _x0-1); _dtbl[2][3][1][_k, 8] := _x0-1 end if end do; _dtbl[2][4][17] := 0; _dtbl[2][4][9] := 0; if _dtbl[1][4][10] = 1 then procname(procname("left")) end if end if; if _j[2] then for _k to _nv+1 do if _k <= _nv and not type(_dtbl[3][3][4][_k, 2], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to defined init `, _dtbl[3][3][4][_k, 2]); _dtbl[3][3][1][_k, 8] := _dtbl[3][3][4][_k, 2] elif _dtbl[3][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[3][3][1][_k, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to rate hysteresis init `, _dtbl[3][5][24]); _dtbl[3][3][1][_k, 8] := _dtbl[3][5][24] elif _dtbl[3][3][1][_k, 2] = 0 and irem(iquo(round(_dtbl[3][3][1][_k, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to initial init `, _x0); _dtbl[3][3][1][_k, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #3, event code `, _k, ` to fireinitial init `, _x0+1); _dtbl[3][3][1][_k, 8] := _x0+1 end if end do; _dtbl[3][4][17] := 0; _dtbl[3][4][9] := 0; if _dtbl[1][4][10] = 1 then procname(procname("right")) end if end if else for _k in _i do _dtbl[1][3][1][_k, 7] := 1 end do; _dtbl[2] := evaln(_dtbl[2]); _dtbl[3] := evaln(_dtbl[3]); _dtbl[4] := 0; if _dtbl[1][4][10] = 1 then if _x0 <= procname("right") then try procname(procname("right")) catch:  end try end if; if procname("left") <= _x0 then try procname(procname("left")) catch:  end try end if end if end if; return  elif type(_xin, `=`) and lhs(_xin) = "eventfired" then if not type(rhs(_xin), 'list') then error "'eventfired' must be specified as a list" end if; if _nv = 0 then error "this solution has no events" end if; if _dtbl[4] <> 2 and _dtbl[4] <> 3 then error "'direction' must be set prior to calling/setting 'eventfired'" end if; _i := _dtbl[4]; _val := NULL; if not assigned(_EnvEventRetriggerWarned) then _EnvEventRetriggerWarned := false end if; for _k in rhs(_xin) do if type(_k, 'integer') then _src := _k elif type(_k, 'integer' = 'anything') and type(evalf(rhs(_k)), 'numeric') then _k := lhs(_k) = evalf[max(Digits, 18)](rhs(_k)); _src := lhs(_k) else error "'eventfired' entry is not valid: %1", _k end if; if _src < 1 or round(_dtbl[1][3][1][_nv+1, 1]) < _src then error "event identifiers must be integers in the range 1..%1", round(_dtbl[1][3][1][_nv+1, 1]) end if; _src := {seq(`if`(_dtbl[1][3][1][_j, 1]-_src = 0., _j, NULL), _j = 1 .. _nv)}; if nops(_src) <> 1 then error "'eventfired' can only be set/queried for root-finding events and time/interval events" end if; _src := _src[1]; if _dtbl[1][3][1][_src, 2] <> 0. and _dtbl[1][3][1][_src, 2]-2. <> 0. then error "'eventfired' can only be set/queried for root-finding events and time/interval events" elif irem(round(_dtbl[1][3][1][_src, 4]), 2) = 1 then if _EnvEventRetriggerWarned = false then WARNING(`'eventfired' has no effect on events that retrigger`) end if; _EnvEventRetriggerWarned := true end if; if _dtbl[_i][3][1][_src, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_src, 4]), 32), 2) = 1 then _val := _val, undefined elif type(_dtbl[_i][3][4][_src, _i-1], 'undefined') or _i = 2 and _dtbl[2][3][1][_src, 8] < _dtbl[2][3][4][_src, 1] or _i = 3 and _dtbl[3][3][4][_src, 2] < _dtbl[3][3][1][_src, 8] then _val := _val, _dtbl[_i][3][1][_src, 8] else _val := _val, _dtbl[_i][3][4][_src, _i-1] end if; if type(_k, `=`) then if _dtbl[_i][3][1][_src, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_src, 4]), 32), 2) = 1 then error "cannot set event code for a rate hysteresis event" end if; userinfo(3, {'events', 'eventreset'}, `manual set event code `, _src, ` to value `, rhs(_k)); _dtbl[_i][3][1][_src, 8] := rhs(_k); _dtbl[_i][3][4][_src, _i-1] := rhs(_k) end if end do; return [_val] elif type(_xin, `=`) and lhs(_xin) = "direction" then if not member(rhs(_xin), {-1, 1, ':-left', ':-right'}) then error "'direction' must be specified as either '1' or 'right' (positive) or '-1' or 'left' (negative)" end if; _src := `if`(_dtbl[4] = 2, -1, `if`(_dtbl[4] = 3, 1, undefined)); _i := `if`(member(rhs(_xin), {1, ':-right'}), 3, 2); _dtbl[4] := _i; _dtbl[_i] := `dsolve/numeric/SC/IVPdcopy`(_dtbl[1], `if`(assigned(_dtbl[_i]), _dtbl[_i], NULL)); if 0 < _nv then for _j to _nv+1 do if _j <= _nv and not type(_dtbl[_i][3][4][_j, _i-1], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to defined init `, _dtbl[_i][3][4][_j, _i-1]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][3][4][_j, _i-1] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to rate hysteresis init `, _dtbl[_i][5][24]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][5][24] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to initial init `, _x0); _dtbl[_i][3][1][_j, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #4, event code `, _j, ` to fireinitial init `, _x0-2*_i+5.0); _dtbl[_i][3][1][_j, 8] := _x0-2*_i+5.0 end if end do end if; return _src elif _xin = "eventcount" then if _dtbl[1][3][1] = 0 or _dtbl[4] <> 2 and _dtbl[4] <> 3 then return 0 else return round(_dtbl[_dtbl[4]][3][1][_nv+1, 12]) end if else return "procname" end if end if; if _xout = _x0 then return [_x0, seq(evalf(_dtbl[1][6][_vmap[_i]]), _i = 1 .. _n-_ne)] end if; _i := `if`(_x0 <= _xout, 3, 2); if _xin = "last" and 0 < _dtbl[_i][4][9] and _dtbl[_i][4][9] < 100 then _dat := eval(_dtbl[_i], 2); _j := _dat[4][20]; return [_dat[11][_j, 0], seq(_dat[11][_j, _vmap[_i]], _i = 1 .. _n-_ne-_nd), seq(_dat[8][1][_vmap[_i]], _i = _n-_ne-_nd+1 .. _n-_ne)] end if; if not type(_dtbl[_i], 'array') then _dtbl[_i] := `dsolve/numeric/SC/IVPdcopy`(_dtbl[1], `if`(assigned(_dtbl[_i]), _dtbl[_i], NULL)); if 0 < _nv then for _j to _nv+1 do if _j <= _nv and not type(_dtbl[_i][3][4][_j, _i-1], 'undefined') then userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to defined init `, _dtbl[_i][3][4][_j, _i-1]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][3][4][_j, _i-1] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 32), 2) = 1 then userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to rate hysteresis init `, _dtbl[_i][5][24]); _dtbl[_i][3][1][_j, 8] := _dtbl[_i][5][24] elif _dtbl[_i][3][1][_j, 2] = 0 and irem(iquo(round(_dtbl[_i][3][1][_j, 4]), 2), 2) = 0 then userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to initial init `, _x0); _dtbl[_i][3][1][_j, 8] := _x0 else userinfo(3, {'events', 'eventreset'}, `reinit #5, event code `, _j, ` to fireinitial init `, _x0-2*_i+5.0); _dtbl[_i][3][1][_j, 8] := _x0-2*_i+5.0 end if end do end if end if; if _xin <> "last" then if 0 < 0 then if `dsolve/numeric/checkglobals`(op(_dtbl[1][14]), _pars, _n, _y0) then `dsolve/numeric/SC/reinitialize`(_dtbl, _y0, _n, procname, _pars, _i) end if end if; if _dtbl[1][4][7] = 0 then error "parameters must be initialized before solution can be computed" end if end if; _dat := eval(_dtbl[_i], 2); _dtbl[4] := _i; try _src := `dsolve/numeric/SC/IVPrun`(_dat, _xout) catch: userinfo(2, `dsolve/debug`, print(`Exception in solnproc:`, [lastexception][2 .. -1])); error  end try; if _dat[17] <> _dtbl[1][17] then _dtbl[1][17] := _dat[17]; _dtbl[1][10] := _dat[10] end if; if _src = 0 and 100 < _dat[4][9] then _val := _dat[3][1][_nv+1, 8] else _val := _dat[11][_dat[4][20], 0] end if; if _src <> 0 or _dat[4][9] <= 0 then _dtbl[1][5][1] := _xout else _dtbl[1][5][1] := _val end if; if _i = 3 and _val < _xout then Rounding := -infinity; if _dat[4][9] = 1 then error "cannot evaluate the solution further right of %1, probably a singularity", evalf[8](_val) elif _dat[4][9] = 2 then error "cannot evaluate the solution further right of %1, maxfun limit exceeded (see ?dsolve,maxfun for details)", evalf[8](_val) elif _dat[4][9] = 3 then if _dat[4][25] = 3 then error "cannot evaluate the solution past the initial point, problem may be initially singular or improperly set up" else error "cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up" end if elif _dat[4][9] = 4 then error "cannot evaluate the solution further right of %1, accuracy goal cannot be achieved with specified 'minstep'", evalf[8](_val) elif _dat[4][9] = 5 then error "cannot evaluate the solution further right of %1, too many step failures, tolerances may be too loose for problem", evalf[8](_val) elif _dat[4][9] = 6 then error "cannot evaluate the solution further right of %1, cannot downgrade delay storage for problems with delay derivative order > 1, try increasing delaypts", evalf[8](_val) elif _dat[4][9] = 10 then error "cannot evaluate the solution further right of %1, interrupt requested", evalf[8](_val) elif 100 < _dat[4][9] then if _dat[4][9]-100 = _nv+1 then error "constraint projection failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-100 = _nv+2 then error "index-1 and derivative evaluation failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-100 = _nv+3 then error "maximum number of event iterations reached (%1) at t=%2", round(_dat[3][1][_nv+1, 3]), evalf[8](_val) else if _Env_dsolve_nowarnstop <> true then `dsolve/numeric/warning`(StringTools:-FormatMessage("cannot evaluate the solution further right of %1, event #%2 triggered a halt", evalf[8](_val), round(_dat[3][1][_dat[4][9]-100, 1]))) end if; Rounding := 'nearest'; _xout := _val end if else error "cannot evaluate the solution further right of %1", evalf[8](_val) end if elif _i = 2 and _xout < _val then Rounding := infinity; if _dat[4][9] = 1 then error "cannot evaluate the solution further left of %1, probably a singularity", evalf[8](_val) elif _dat[4][9] = 2 then error "cannot evaluate the solution further left of %1, maxfun limit exceeded (see ?dsolve,maxfun for details)", evalf[8](_val) elif _dat[4][9] = 3 then if _dat[4][25] = 3 then error "cannot evaluate the solution past the initial point, problem may be initially singular or improperly set up" else error "cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up" end if elif _dat[4][9] = 4 then error "cannot evaluate the solution further left of %1, accuracy goal cannot be achieved with specified 'minstep'", evalf[8](_val) elif _dat[4][9] = 5 then error "cannot evaluate the solution further left of %1, too many step failures, tolerances may be too loose for problem", evalf[8](_val) elif _dat[4][9] = 6 then error "cannot evaluate the solution further left of %1, cannot downgrade delay storage for problems with delay derivative order > 1, try increasing delaypts", evalf[8](_val) elif _dat[4][9] = 10 then error "cannot evaluate the solution further right of %1, interrupt requested", evalf[8](_val) elif 100 < _dat[4][9] then if _dat[4][9]-100 = _nv+1 then error "constraint projection failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-100 = _nv+2 then error "index-1 and derivative evaluation failure on event at t=%1", evalf[8](_val) elif _dat[4][9]-100 = _nv+3 then error "maximum number of event iterations reached (%1) at t=%2", round(_dat[3][1][_nv+1, 3]), evalf[8](_val) else if _Env_dsolve_nowarnstop <> true then `dsolve/numeric/warning`(StringTools:-FormatMessage("cannot evaluate the solution further left of %1, event #%2 triggered a halt", evalf[8](_val), round(_dat[3][1][_dat[4][9]-100, 1]))) end if; Rounding := 'nearest'; _xout := _val end if else error "cannot evaluate the solution further left of %1", evalf[8](_val) end if end if; if _EnvInFsolve = true then _dig := _dat[4][26]; if type(_EnvDSNumericSaveDigits, 'posint') then _dat[4][26] := _EnvDSNumericSaveDigits else _dat[4][26] := Digits end if; _Env_dsolve_SC_native := true; if _dat[4][25] = 1 then _i := 1; _dat[4][25] := 2 else _i := _dat[4][25] end if; _val := `dsolve/numeric/SC/IVPval`(_dat, _xout, _src); _dat[4][25] := _i; _dat[4][26] := _dig; [_xout, seq(_val[_vmap[_i]], _i = 1 .. _n-_ne)] else Digits := _dat[4][26]; _val := `dsolve/numeric/SC/IVPval`(eval(_dat, 2), _xout, _src); [_xout, seq(_val[_vmap[_i]], _i = 1 .. _n-_ne)] end if end proc, (2) = Array(0..0, {}), (3) = [t, ACII(t), Central(t), Depot(t), EGFR(t), PAKT(t), PERK(t), PMEK(t), PPi3k(t), PRaf(t), PRas(t), Pmyc(t), SPC(t)], (4) = []}); _vars := _dat[3]; _pars := map(rhs, _dat[4]); _n := nops(_vars)-1; _solnproc := _dat[1]; if not type(_xout, 'numeric') then if member(x_rkf45, ["start", 'start', "method", 'method', "left", 'left', "right", 'right', "leftdata", "rightdata", "enginedata", "eventstop", 'eventstop', "eventclear", 'eventclear', "eventstatus", 'eventstatus', "eventcount", 'eventcount', "laxtol", 'laxtol', "numfun", 'numfun', NULL]) then _res := _solnproc(convert(x_rkf45, 'string')); if 1 < nops([_res]) then return _res elif type(_res, 'array') then return eval(_res, 1) elif _res <> "procname" then return _res end if elif member(x_rkf45, ["last", 'last', "initial", 'initial', "parameters", 'parameters', "initial_and_parameters", 'initial_and_parameters', NULL]) then _xout := convert(x_rkf45, 'string'); _res := _solnproc(_xout); if _xout = "parameters" then return [seq(_pars[_i] = _res[_i], _i = 1 .. nops(_pars))] elif _xout = "initial_and_parameters" then return [seq(_vars[_i+1] = [_res][1][_i+1], _i = 0 .. _n), seq(_pars[_i] = [_res][2][_i], _i = 1 .. nops(_pars))] else return [seq(_vars[_i+1] = _res[_i+1], _i = 0 .. _n)] end if elif type(_xout, `=`) and member(lhs(_xout), ["initial", 'initial', "parameters", 'parameters', "initial_and_parameters", 'initial_and_parameters', NULL]) then _xout := convert(lhs(x_rkf45), 'string') = rhs(x_rkf45); if type(rhs(_xout), 'list') then _res := _solnproc(_xout) else error "initial and/or parameter values must be specified in a list" end if; if lhs(_xout) = "initial" then return [seq(_vars[_i+1] = _res[_i+1], _i = 0 .. _n)] elif lhs(_xout) = "parameters" then return [seq(_pars[_i] = _res[_i], _i = 1 .. nops(_pars))] else return [seq(_vars[_i+1] = [_res][1][_i+1], _i = 0 .. _n), seq(_pars[_i] = [_res][2][_i], _i = 1 .. nops(_pars))] end if elif type(_xout, `=`) and member(lhs(_xout), ["eventdisable", 'eventdisable', "eventenable", 'eventenable', "eventfired", 'eventfired', "direction", 'direction', NULL]) then return _solnproc(convert(lhs(x_rkf45), 'string') = rhs(x_rkf45)) elif _xout = "solnprocedure" then return eval(_solnproc) elif _xout = "sysvars" then return _vars end if; if procname <> unknown then return ('procname')(x_rkf45) else _ndsol := 1; _ndsol := _ndsol; _ndsol := pointto(_dat[2][0]); return ('_ndsol')(x_rkf45) end if end if; try _res := _solnproc(_xout); [seq(_vars[_i+1] = _res[_i+1], _i = 0 .. _n)] catch: error  end try end proc

(2.1)

plots:-odeplot(soln, [t, Depot(t)], t = 0 .. 10); plots:-odeplot(soln, [t, Central(t)], t = 0 .. 10); plots:-odeplot(soln, [t, PAKT(t)], t = 0 .. 10); plots:-odeplot(soln, [t, PERK(t)], t = 0 .. 10); plots:-odeplot(soln, [t, PMEK(t)], t = 0 .. 10); plots:-odeplot(soln, [t, PRaf(t)], t = 0 .. 10); plots:-odeplot(soln, [t, Pmyc(t)], t = 0 .. 10); plots:-odeplot(soln, [t, SPC(t)], t = 0 .. 10); plots:-odeplot(soln, [t, ACII(t)], t = 0 .. 10)

 

 

 

 

 

 

 

 

 

``

Download ode.mw

3 4 5 6 7 8 9 Last Page 5 of 118