What is Minimization: Definition and 96 Discussions
In automata theory (a branch of theoretical computer science), DFA minimization is the task of transforming a given deterministic finite automaton (DFA) into an equivalent DFA that has a minimum number of states. Here, two DFAs are called equivalent if they recognize the same regular language. Several different algorithms accomplishing this task are known and described in standard textbooks on automata theory.
My interest is on number 11.
In my approach;
##v= xyz##
##1000=xyz##
##z= \dfrac{1000}{xy}##
Surface area: ##f(x,y)= 2( xy+yz+xz)##
##f(x,y)= 2\left( xy+\dfrac{1000}{x} + \dfrac{1000}{y}\right)##
##f_{x} = 2y -\dfrac{2000}{x^2} = 0##...
Hello,
I'm facing a practical optimization problem for which I don't know whether a standard approach exists or not.
I would have liked to rephrase the problem in a more general way, for the sake of "good math", but I'm afraid I would leave out some details that might be relevant. So, I'm going...
so this is the question , I have to minimize this DFA
this is How I did it
but when I checked for answers , this is what it was, can someone please explain to me what mistake I made? I have been wondering about this for past 2 days
Hi, I don't understand what does it mean that at equilibrium the proper thermodynamic potential of the system is minimized.
For example on the book Herbert B. Callen - Thermodynamics and an Introduction to Thermostatistics it is written:
Helmholtz Potential Minimum Principle. The equilibrium...
Hi,
I was reading through some notes on standard problems and their corresponding dual problems. I came across the L2 norm minimization for an equality constraint, and then I thought how one might formulate the dual problem if we had an L1-norm instead.
Question:
Consider the following...
a) ONLY
The common way to solve this problem is minimizing the two-variable equation after using the substitution ##z^2=1/(xy)##. Yet I wondered if it is possible to optimize the distance equation with three varibles. So I wrote the following equations:
Distance:
$$f(x,y,z)=s^2=x^2+y^2+z^2$$...
Hallo at all!
I'm learning statistic in python and I have a problem to show you.
I have this parametric function:
$$P(S|t, \gamma, \beta)=\langle s(t) \rangle
\left( \frac{\gamma-\beta}{\gamma\langle
s(t) \rangle -\beta}\right)^2\left( 1- \frac{\gamma-\beta}{\gamma\langle
s(t) \rangle...
Thanks in advance for any insight!
Following Pathria's discussion of phase transitions, I'm getting tripped up on the discussion of Landau's theory. Pathria begins with a zero-field free energy ##\psi = A/NkT## where ##A## is the Helmholtz free energy.
He proceeds to characterize the...
Homework Statement
Given a Hilbert space $$V = \left\{ f\in L_2[0,1] | \int_0^1 f(x)\, dx = 0\right\},B(f,g) = \langle f,g\rangle,l(f) = \int_0^1 x f(x) \, dx$$ find the minimum of $$B(u,u)+2l(u)$$.
Homework Equations
In my text I found a variational theorem stating this minimization problem...
Homework Statement
Homework Equations
Minimum/Maximum occurs when the first derivative=0
The Attempt at a Solution
$$Q=\sqrt{\frac{2(K+pQ)}{h}}~\rightarrow~Q=\frac{2}{h}(KM+pM)$$
##Q'=0~## gives no sense result
What is the exact difference between energy minimization and equilibration in a molecular dynamics simulation since both brings the system to the local energy minima?
Given the following expressions:
and that ## \bf{B}_s = \nabla \times \bf{A}_s ##
how does one solve for the following expressions given in (12) and (13)?
I've attempted doing so and derive the following expressions (where the hat indicates a unit vector):
## bV = \bf{ \hat{V}} \cdot...
Homework Statement
company manufactures paper cups that are designed to hold 8 fluid ounces
each. The cups are in the shape of a frustum of a right circular cone (so the top and
bottom of the cup are circles, not necessarily of the same size, and the side profile is
that of a...
Cryptography is based on reason-result chains like hash functions: which are inexpensive to propagate in the intended direction, but seem hard to reverse. However, decomposing them into satisfaction of simple (direction-agnostic) relations like 3-SAT clauses, may bring a danger of existence of...
If $a^2b^2+b^2c^2+c^2a^2-69abc=2016$, then, what can be said about the least value of $\min(a, b ,c)$?
This problem is unyielding to the major inequalities like AM-GM, Cauchy-Schwarz, etc. I also tried relating it to $x^3+y^3+z^3-3xyz=(x+y+z)(\sum_{cyc}x^2+\sum_{cyc}xy)$, but of no use. Any...
Hi to everyone,
I'm trying to plot a 3D graph on MATLAB but I do not know how.
The function that I want to plot is: y=fminbnd(@(x) wei(x,shape,scale,tw,tf),x0,x1).
I would like to plot the minimization of the function wei (y) in function of the shape and the scale.
Wei is a function that I...
Homework Statement
I have to prove some things on the Weber-Ferma problem. Here is the assignment :
We want to find a point $$x$$ in the plane whose sum of weighted
distances from a given set of fixed points $$y_1, ...,y_m$$ is minimized.
1-Show that there exist a global mimimum to the...
Hi, I would like to know if the inequality sign plays any role to the following optimization problem:
minimize f0(x)
subject to f1(x)>=0
where both f0(x) and f1(x) are convex. The standard form of these problems require a constraint such as: f1(x)<=0, but i am interested in the opposite...
Hi,
I need to minimize, with respect to \hat{y}(x), the following function:
\tilde{J}_x = \mathbb{E}_{p(x,y)}[(\hat{y}(x)-y)^2] + \nu \mathbb{E}_{p(x,y)}[(\hat{y}(x)-y)tr(\nabla_x^2\hat{y}(x))] + \nu \mathbb{E}_{p(x,y)}[||\nabla_x\hat{y}(x)||^2],
where x is a vector and y a scalar.
I found this...
ƒ(ß)=.5sec(ß) + √[1+(sec2(ß)/4)+tan(ß)/√(2)]
Without graphing it or using calculus find the minimum. I already know the answer but want to know how to do it. It s at π/12 and is something like 1.5.
First off this is NOT a homework problem. I already know the answer is something like 1.5 at π/12...
Hi, I have an mathematics assignment to do, and I wonder if the topic I have chosen is doable for me. I want to minimize the surface area of a cobbler cocktail shaker, and until now my plan was to get the curve equation for the side of it, and get the area equation from surface of revolution...
Homework Statement
Two light sources of identical strength are placed 8 m apart. An object is to be placed at a point P on a line ℓ parallel to the line joining the light sources and at a distance d meters from it (see the figure). We want to locate P on ℓ so that the intensity of illumination...
Hi, I'm learning python and I'm just trying to minimize a function of many variables, but I have some problems with my code.
import numpy as np
import scipy.optimize as op
from scipy.optimize import minimize
table1_np = np.genfromtxt('Data/tabla1.txt', usecols=0)
#--------------------------...
Hello,
For my master thesis I'm looking at the Two-Higgs-Doublet-Modell at finite Temperature and I'm searching for the Minimum values of the two VEVs of the Doublets. Therefore i have my Potential with Input Parameters v1 and v2 in which I want to minimize the Potential and a Vector with User...
In a trivial optimization problem, when seeking the value of x2 that minimizes y(x2)/(x2-x1), the solution is graphically given by the tangent line shown in the figure.
I'm having a lot of difficulty understanding why this is true, i.e., the logical steps behind the equivalence supporting the...
Typically in problems involving binary classification (i.e. radar detection, medical testing), one will try to find a binary classification scheme that minimizes the total probability of error.
For example, consider a radar detection system where a signal is corrupted with noise, so that if the...
Homework Statement
This is actually an Applied Project in the text, and overall is quite a large problem, so I won't post the entire thing, as there are lots of equations and steps where the text guides me by saying "show that...this thing...then...show that this other thing..."
What I need...
If we study model fit on a nonlinear regression model $Y_i=f(z_i,\theta)+\epsilon_i$, $i=1,...,n$, and in the Gauss-Newton method, the update on the parameter $\theta$ from step $t$ to $t+1$ is to minimize the ￼sum of squares...
I'm trying to find a increasing postive function \phi (x) that minimizes the following integral for x in [0, L]:
\int_0^L A \frac{ d ^2 \phi (x) } {dx^2}+ (B +C cos( \phi (x)) ^2 \mbox{d}x
with A and B real positve numbers and
\phi (0) =0
\phi ' (L) =0
When I use the the Lagrange...
I'm trying to find a function for x in [0, L] that minimizes this:
\int_0^{L} A \phi(x) \frac{ d \phi(x) }{dx} + B cos(\phi(x))\ d\mbox{x}
For real (given) positve numbers A and B.
with
\phi(0) = 0
\phi(x) is an increasing positve function.
Can somebody point me in the right direction?
Homework Statement
http://i.imgur.com/VYPECuW.png?1 (f1: f2: f3: f1*f2: f1*f3: f2*f3: f1*f2*f3: is what's written near tables)
I need to minimize the functions (sum of minterms: f1 0, 1, 2, 4, 5, 11, 15; f2 0, 2, 4, 13, 15; f3 0, 1, 3, 4, 5, 7, 13, 15) using K-tables... This is what they show...
Several theories try and explain consciousness from a quantum perspective. Most notoriously the Penrose-Hameroff Orch OR hypothesis comes to mind, but there are others by Henry Stapp, Giuseppi Vitiello, and Gustav Bernroider to name a few. The consciousness philosopher David Chalmers has...
Homework Statement
f(x) is the function we want to minimize. Beyond being real-valued, there are no other conditions on it. (I'm surprised it's not at least continuous, but the book doesn't say that's a condition.) We choose the next x^k through the relation x^k = x^{k-1} + \alpha_{k}d^k. We...
Homework Statement
Minimize the function f(x,y) = \sqrt{x^2 + y^2} subject to x + y \leq 0. Show that the function MP(z) is not differentiable at z = 0.
Homework EquationsThe Attempt at a Solution
I haven't gotten anywhere because I don't understand why the solution isn't trivial, i.e. (0,0)...
Hello,
I am using the x squared minimization method to compute two parametres in a function let's say (A,B) which correspondes to the minimum value of x^2. Now if i want to make a contour plot of A,B (A=x axis and B=y axis) for the values of x^2-x^2_(minimum)=1σ=2.3 what is the proper way...
I would like to find a FORTRAN subroutine or a good way to minimize function numerically.So basically my function has 20 variables and I am able to provide analytic form of the first and the second derivative of the function. Basically what I want is: have the form of the function of 20...
Write out the minimal Product of Sums (POS) equation with the following Karnaugh Map. Just need someone to check my work please. I am questioning my self on my grouping. Did I group correctly or should I have grouped the bottom left 0 and D versus the 0 in the group of 8? Thanks for your time...
The question is : If the vector space C[1,1] of continuous real valued functions on the interval [1,1] is equipped with the inner product defined by (f,g)=^{1}_{-1} \intf(x)g(x)dx
Find the linear polynomial g(t) nearest to f(t) = e^t?
So I understand the solution will be given by...
In MATLAB, I am using fmincon to solve a minimization problem with nonlinear constraints. The problem is that, it is giving me a wrong answer, a point that is not a minimizer (not even close), and that is not within the tolerance. I made sure to use a feasible initial point.
However, when I...
Hello, :)
I would like to minimize and find the zeros of the function F(S,P)=trace(S-SP’(A+ PSP’)^-1PS) in respect to S and P.
S is symmetric square matrix.
P is a rectangular matrix
Could you help me?
Thank you very much
All the best
GoodSpirit
Homework Statement
A system is to be operated 5000 hours per year, where
Total Cost (for 5 years) = Acquisition cost + Spares cost + Downtime cost
System acquisition cost is related to MTBF, θ, as follows:
CA(θ) = 685.2917e0.003779θ
The average cost of a spare item is $1,000 and the...
Homework Statement
If I said minimize the cost function
|a-2b| + |-3a-b|
subject to
2a + b <= 6
a,b >= 0
We can all see it's 0,0 but if I want to apply the simplex algorithm to it, how do I reformulate the problem into something I can use
Homework Equations
The Attempt at...
I've got a question that I don't know how to solve. The question is:
We want to produce a tent, without a bottom part, which has two rectangular sides and two gables in the form of two isosceles triangles with the base against the ground. Determine the height of the tent, which has volyme V and...
Homework Statement
Use the result (6.41) of Problem 6.1 to prove that the geodesic (shortest path) between two given points on a sphere is a great circle. [Hint: The integrand f(ψ,ψ',θ) in (6.41) is independent of ψ, so the Euler-Lagrange equation reduces to ∂f/ψ' = c, a constant. This gives...