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How to download and install Matlab 2014a (New Version

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How to minimize computing time of nonlinear system observability analysis? (Using Matlab)

Hello,
I'm trying to ger the observability of a nonlinear system of 12 ODEs, I'm working just with the 12 states as symbolic variables in Matlab (I have access to 2014a, 2015 and 2016 versions). So far I have the Jacobi matrix (which was computed in separated columns and each one took hours), but when I try to check the rank of this matrix (or from a part of it, e.i. dO13=[dOx1 dOx2 dOx3]) all it does is that Matlab stops working or even the whole computer gets slower or stops working (I'm working on a laptop with Core i5 and 8 GB RAM and in two desktop Core i7 16GB RAM).
I think this is because of the weight of the terms of the derivates which makes it heavier and harder to process, I looked up for a way to lower the weight of the symbolic variables (when I type 'whos' in the command window it says it's 112 bytes) or to assign them a type of variable but I haven't been able to make this work. Is there anything else I can do?

Thanks so much

Here's the code I'm working with:

syms x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 D=78000; B1=0; B2=1; B3=1; B3N=0; %% Healthy patient parameters: VG=1.88; k1=0.065; k2= 0.079; VI= 0.05; m1=0.190; m2=0.484; m4=0.194; m5=0.0304; m6=0.6471; HEb=0.6; kmax=0.0558; kmin=0.0080; kabs=0.057; kgri=0.0558; f1=675.8079; a=0.00013; b=0.82; c=0.00236; d=0.010; kp1=2.70; kp2=0.0021; kp3=0.009; kp4=0.0618; ki=0.0079; Fcns=1; Vm0=2.50; Vmx=0.047; Km0=225.59; Kmx=0; p2u=0.0331; ke1=0.0005; ke2=339; K=2.30; alpha=0.050; beta=0.11; gamma=0.5; BW=78; Ib=25; Sb= 1.85; Gb= 90; h=Gb; estabilidad del sistema %% STRUCTURE: A=[(-kp2 -(B1*ke1) - k1) k2 0 0 0 (-kp3) 0 0 f1*kabs/BW 0 (-kp4) 0; k1 (-k2) 0 0 0 0 0 0 0 0 0 0; 0 0 (-m1) m2 0 0 0 0 0 0 (gamma) 0; 0 0 m1 (-(m2 + m4)) 0 0 0 0 0 0 0 0; 0 0 0 (ki/VI) (-ki) 0 0 0 0 0 0 0; 0 0 0 0 ki (-ki) 0 0 0 0 0 0; 0 0 0 0 0 0 (-kgri) 0 0 0 0 0; 0 0 0 0 0 0 kgri (-kmax) 0 0 0 0; 0 0 0 0 0 0 0 kmax (-kabs) 0 0 0; 0 0 0 p2u/VI 0 0 0 0 0 (-p2u) 0 0; B2*(K*(-kp2 - (B1*ke1) - k1))/VG (B2*K*k2)/VG 0 0 0 (-B2*K*kp3)/VG 0 0 ((B2*K*f1*kabs)/BW)/VG 0 (-gamma - ((B2*K*kp4)/VG)) 1; (B3*alpha*beta)/VG 0 0 0 0 0 0 0 0 0 0 (-alpha)]; Beta= [kp1 - Fcns + (B1*ke1*ke2); 0; 0; 0; 0; 0; 0; 0; 0; (-p2u*Ib); B2*(K*((kp1 - Fcns + (B1*(ke1*ke2)))/VG)) + Sb; (-B3*alpha*beta *h) - (B3N*alpha*Sb)]; B=[0 0 0; -1 0 0; 0 -1 0; 0 0 0; 0 0 0; 0 0 0; 0 0 0; 0 0 (-(kmax-kmin)/2); 0 0 (kmax-kmin)/2; 0 0 0; 0 0 0; 0 0 0]; g=[((Vm0 + (Vmx*x10))*x2)/((Km0 + (Kmx*x10)) + x2); (((-m5*gamma *m1*x11) + (m6*m1))/(1-(-m5*gamma*x11 + m6)))*x3; (tanh((5/(2*D*(1-b))) * (x7 + x8 - (b*D))) - tanh((5/(2*D*c))*(x7 + x8 - (c*D))))*x8]; % Phi= [0; 0; 0; 0; 0; 0; Di; 0; 0; 0; 0; 0]; X=[x1; x2; x3; x4; x5; x6; x7; x8; x9; x10; x11; x12]; f= (A*X) + Beta + B*g; C=[(1/VG) 0 0 0 0 0 0 0 0 0 0 0]; y= C*X; h= y; %% NONLINEAR SYSTEM OBSERVABILITY: % Lie derivatives: Lf= [diff(h,x1) diff(h,x2) diff(h,x3) diff(h,x4) diff(h,x5) diff(h,x6) diff(h,x7) diff(h,x8) diff(h,x9) diff(h,x10) diff(h,x11) diff(h,x12)]; Lfh= Lf*f; Lf2= [diff(Lfh,x1) diff(Lfh,x2) diff(Lfh,x3) diff(Lfh,x4) diff(Lfh,x5) diff(Lfh,x6) diff(Lfh,x7) diff(Lfh,x8) diff(Lfh,x9) diff(Lfh,x10) diff(Lfh,x11) diff(Lfh,x12)]; Lf2h= Lf2*f; Lf3= [diff(Lf2h,x1) diff(Lf2h,x2) diff(Lf2h,x3) diff(Lf2h,x4) diff(Lf2h,x5) diff(Lf2h,x6) diff(Lf2h,x7) diff(Lf2h,x8) diff(Lf2h,x9) diff(Lf2h,x10) diff(Lf2h,x11) diff(Lf2h,x12)]; Lf3h= Lf3*f; Lf4= [diff(Lf3h,x1) diff(Lf3h,x2) diff(Lf3h,x3) diff(Lf3h,x4) diff(Lf3h,x5) diff(Lf3h,x6) diff(Lf3h,x7) diff(Lf3h,x8) diff(Lf3h,x9) diff(Lf3h,x10) diff(Lf3h,x11) diff(Lf3h,x12)]; Lf4h= Lf4*f; Lf5= [diff(Lf4h,x1) diff(Lf4h,x2) diff(Lf4h,x3) diff(Lf4h,x4) diff(Lf4h,x5) diff(Lf4h,x6) diff(Lf4h,x7) diff(Lf4h,x8) diff(Lf4h,x9) diff(Lf4h,x10) diff(Lf4h,x11) diff(Lf4h,x12)]; Lf5h= Lf5*f; Lf6= [diff(Lf5h,x1) diff(Lf5h,x2) diff(Lf5h,x3) diff(Lf5h,x4) diff(Lf5h,x5) diff(Lf5h,x6) diff(Lf5h,x7) diff(Lf5h,x8) diff(Lf5h,x9) diff(Lf5h,x10) diff(Lf5h,x11) diff(Lf5h,x12)]; Lf6h= Lf6*f; Lf7= [diff(Lf6h,x1) diff(Lf6h,x2) diff(Lf6h,x3) diff(Lf6h,x4) diff(Lf6h,x5) diff(Lf6h,x6) diff(Lf6h,x7) diff(Lf6h,x8) diff(Lf6h,x9) diff(Lf6h,x10) diff(Lf6h,x11) diff(Lf6h,x12)]; Lf7h= Lf7*f; Lf8= [diff(Lf7h,x1) diff(Lf7h,x2) diff(Lf7h,x3) diff(Lf7h,x4) diff(Lf7h,x5) diff(Lf7h,x6) diff(Lf7h,x7) diff(Lf7h,x8) diff(Lf7h,x9) diff(Lf7h,x10) diff(Lf7h,x11) diff(Lf7h,x12)]; Lf8h= Lf8*f; Lf9= [diff(Lf8h,x1) diff(Lf8h,x2) diff(Lf8h,x3) diff(Lf8h,x4) diff(Lf8h,x5) diff(Lf8h,x6) diff(Lf8h,x7) diff(Lf8h,x8) diff(Lf8h,x9) diff(Lf8h,x10) diff(Lf8h,x11) diff(Lf8h,x12)]; Lf9h= Lf9*f; Lf10= [diff(Lf9h,x1) diff(Lf9h,x2) diff(Lf9h,x3) diff(Lf9h,x4) diff(Lf9h,x5) diff(Lf9h,x6) diff(Lf9h,x7) diff(Lf9h,x8) diff(Lf9h,x9) diff(Lf9h,x10) diff(Lf9h,x11) diff(Lf9h,x12)]; Lf10h= Lf10*f; Lf11= [diff(Lf10h,x1) diff(Lf10h,x2) diff(Lf10h,x3) diff(Lf10h,x4) diff(Lf10h,x5) diff(Lf10h,x6) diff(Lf10h,x7) diff(Lf10h,x8) diff(Lf10h,x9) diff(Lf10h,x10) diff(Lf10h,x11) diff(Lf10h,x12)]; Lf11h= Lf11*f; %% OBSERVATION SPACE MATRIZ: O=[h; Lfh; Lf2h; Lf3h; Lf4h; Lf5h; Lf6h; Lf7h; Lf8h; Lf9h; Lf10h; Lf11h]; %% JACOBI MATRIZ: dO=[diff(O(1,:),x1), diff(O(1,:),x2), diff(O(1,:),x3), diff(O(1,:),x4) diff(O(1,:),x5) diff(O(1,:),x6) diff(O(1,:),x7) diff(O(1,:),x8) diff(O(1,:),x9) diff(O(1,:),x10) diff(O(1,:),x11) diff(O(1,:),x12); diff(O(2,:),x1), diff(O(2,:),x2), diff(O(2,:),x3), diff(O(2,:),x4) diff(O(2,:),x5) diff(O(2,:),x6) diff(O(2,:),x7) diff(O(2,:),x8) diff(O(2,:),x9) diff(O(2,:),x10) diff(O(2,:),x11) diff(O(2,:),x12); diff(O(3,:),x1), diff(O(3,:),x2), diff(O(3,:),x3), diff(O(3,:),x4) diff(O(3,:),x5) diff(O(3,:),x6) diff(O(3,:),x7) diff(O(3,:),x8) diff(O(3,:),x9) diff(O(3,:),x10) diff(O(3,:),x11) diff(O(3,:),x12); diff(O(4,:),x1), diff(O(4,:),x2), diff(O(4,:),x3), diff(O(4,:),x4) diff(O(4,:),x5) diff(O(4,:),x6) diff(O(4,:),x7) diff(O(4,:),x8) diff(O(4,:),x9) diff(O(4,:),x10) diff(O(4,:),x11) diff(O(4,:),x12); diff(O(5,:),x1), diff(O(5,:),x2), diff(O(5,:),x3), diff(O(5,:),x4) diff(O(5,:),x5) diff(O(5,:),x6) diff(O(5,:),x7) diff(O(5,:),x8) diff(O(5,:),x9) diff(O(5,:),x10) diff(O(5,:),x11) diff(O(5,:),x12); diff(O(6,:),x1), diff(O(6,:),x2), diff(O(6,:),x3), diff(O(6,:),x4) diff(O(6,:),x5) diff(O(6,:),x6) diff(O(6,:),x7) diff(O(6,:),x8) diff(O(6,:),x9) diff(O(6,:),x10) diff(O(6,:),x11) diff(O(6,:),x12); diff(O(7,:),x1), diff(O(7,:),x2), diff(O(7,:),x3), diff(O(7,:),x4) diff(O(7,:),x5) diff(O(7,:),x6) diff(O(7,:),x7) diff(O(7,:),x8) diff(O(7,:),x9) diff(O(7,:),x10) diff(O(7,:),x11) diff(O(7,:),x12); diff(O(8,:),x1), diff(O(8,:),x2), diff(O(8,:),x3), diff(O(8,:),x4) diff(O(8,:),x5) diff(O(8,:),x6) diff(O(8,:),x7) diff(O(8,:),x8) diff(O(8,:),x9) diff(O(8,:),x10) diff(O(8,:),x11) diff(O(8,:),x12); diff(O(9,:),x1), diff(O(9,:),x2), diff(O(9,:),x3), diff(O(9,:),x4) diff(O(9,:),x5) diff(O(9,:),x6) diff(O(9,:),x7) diff(O(9,:),x8) diff(O(9,:),x9) diff(O(9,:),x10) diff(O(9,:),x11) diff(O(9,:),x12); diff(O(10,:),x1), diff(O(10,:),x2), diff(O(10,:),x3), diff(O(10,:),x4) diff(O(10,:),x5) diff(O(10,:),x6) diff(O(10,:),x7) diff(O(10,:),x8) diff(O(10,:),x9) diff(O(10,:),x10) diff(O(10,:),x11) diff(O(10,:),x12); diff(O(11,:),x1), diff(O(11,:),x2), diff(O(11,:),x3), diff(O(11,:),x4) diff(O(11,:),x5) diff(O(11,:),x6) diff(O(11,:),x7) diff(O(11,:),x8) diff(O(11,:),x9) diff(O(11,:),x10) diff(O(11,:),x11) diff(O(11,:),x12); diff(O(12,:),x1), diff(O(12,:),x2), diff(O(12,:),x3), diff(O(12,:),x4) diff(O(12,:),x5) diff(O(12,:),x6) diff(O(12,:),x7) diff(O(12,:),x8) diff(O(12,:),x9) diff(O(12,:),x10) diff(O(12,:),x11) diff(O(12,:),x12)]; %% RANK OF THE JACOBI MATRIZ: rdO=rank(dO) %% RE-CHECK IN CASE OF SMALL NUMBERS: EscO= rref(dO) rank(EscO) 
submitted by HelloMyNameIs_28 to ControlTheory

6

I'm participating in a Neural Engineering Hackathon this weekend. Give me your best ideas!

We have all weekend to create a cool device, game, software, etc. related to neural engineering. I imagine most of the control signals will be from EMG, not EEG though. Anyone have some cool ideas that could be completed in a weekend of solid work? Thanks!
Some tools we have available to us:
Arduino UNO + components/sensors/connectors
Rapid Protoboards
Intel Galileo Board
Measuring tape, ducts tape, notebooks, batteries, 8Gb flash drive, krazy glue, superglue,
Computer with software:
Adobe Suite (Photoshop,Illustrator,In-Design,Bridge)
Matlab 2014a
MS Office
Visual Studios 2013
SolidWorks 2014
Blender
Unity
Gimp
We also have 3D printers and some other equipment that hasn't been revealed to us yet.
submitted by dadboat1 to neuroscience