This specific instance of the problem affects users of the dd-wrt firmware.  In my case, I am using build 24461 of the firmware.  The solution is to run the following commands on the router (either with ssh or telnet):

swconfig dev eth0 set enable_vlan 1
swconfig dev eth0 set apply

I’ve since put this in the startup commands that the router will execute, so these settings will stay even after a router reboot.

For some routers, it might be eth1 instead of eth0.  It depends on which network interface is assigned to the WAN.  This can be check in the router page under Setup > Networking.

Link to forum post: http://www.dd-wrt.com/phpBB2/viewtopic.php?t=152738&postdays=0&postorder=asc&start=0

The Deutsches Museum is one of the largest museums I’ve been to. There were so many topics on technology that the museum had. They had the usual topics on flight, ship building, engines, etc., but they had even more exhibits on classical mechanics, electromagnetism, chemistry, nuclear physics, mining, semiconductors, computers, cartography, microsystems, space exploration, printing, etc.

There was even a cool demonstration of arc lightning.

The section of space exploration was quite interesting too, but it wasn’t as big as the exhibit at the Smithsonian Museum of Flight.

The clean room exhibit reminded me a little bit of the type of work I did during my internship at Bosch.

Of course in any exhibit on computers, there has to be a computer from Remington Rand.

Here is the experimental apparatus that was used to discover nuclear fission.

The stuff I looked at was only scratching the surface of the museum. I pretty much skipped entire sections like time keeping, wind turbines, bridge building, among other things. I was there for four hours too and I didn’t even look at any one section in a lot of detail. To see everything, one would have to spend days here.

Link to photo album here

• Intel Core i3-370M Processor (2.4 GHz)
• Nvidia G310M Graphics Engine with 1 GB DDR3 Dedicated VRAM and Optimus Technology
• 4 GB of DDR3 1066MHz DRAM (2 GB x 2 slots)
• Intel Wireless 802.11 b/g/n + WiDi
• 500 GB Hard Drive (5400 RPM)
• Windows 7 Home Premium (64 bit) Operating System (which I upgraded to Pro)
• 13.3-Inch HD (1366×768) LED Display
• HDMI Port
• USB 3.0 port
• Bluetooth
• 8 cell 5600 mAh battery

The one thing it doesn’t have that I realized just now is that the computer doesn’t have an optical drive. I didn’t know that before. I guess I assumed that all computers except for netbooks have them. It’s not really a big deal though.Since my laptop kind of died on me earlier, there weren’t many things I could do to solve the problem. I pretty much only had three options: get my laptop repaired, buy/borrow a monitor for the duration of my stay, or buy a new laptop.

Repairing my laptop was definitely the first thing I tried. I researched on how to fix it, but I couldn’t even get the screws out to even peek at the insides. Right now, I still think that the problem inside the computer is just a loose connection. Unfortunately, I can’t confirm that. I could let Dell fix the computer, but my warranty expired a long time ago. I also bought the computer from Canada and would have to go through lots of red tape just to get it repaired by Dell Europe.

The next thing I tried was to find someone who had an extra monitor I could borrow. Since all my friends in Germany are all interns or thesis students, they all had only a laptop and not an extra display. Although, I did manage to borrow one for like a week until I had to return it. I could have bought a new monitor, but then it would have been really been difficult to bring home a 20 something inch screen (if I’m buying a monitor to keep then I wouldn’t buy anything smaller). I didn’t feel like buying a cheap one and just leaving it behind when I leave Germany either.

In the end, I ended up buying a new laptop (with much financial assistance from my parents). I figure my old laptop is getting old anyways (2007), and for the past year and a half it had been failing to keep up with my intense computer usage habits. When I return to Vancouver, I’ll get this laptop repaired and then my parents could use it (or my brother if he decides that he needs to bring a laptop somewhere).

After almost four years of using my Inspiron 1520, its age finally caught up with it and its light literally went out.  The backlight refuses to turn on now.  I came back from Berlin last Monday and found my computer in this state.  I left it off during that time too.  During this time, I had trouble doing any blogging and uploading any photos.

Google told me that the problem lay with either a loose connection, the inverter or the lamp.  I tried to check this out myself and open the computer case, but the screws refused to budge.  People online somehow got theirs open, but I couldn’t.

Unfortunately, my warranty expired so I’d have to pay to get this computer fixed.  I looked at my options on the Dell site and the North American Dell Support refused to help me and kept referring me to the European side even though I bought my computer in Canada (I really don’t know what these guys at the call centers are doing).  After about three calls to the support line, I finally found someone helpful and she told me that I had to change my laptop registration such that it showed a European location before I could get it fixed.  An alternative option would have been to send the computer back to Canada to get it fixed.

What I did instead was just buy a new laptop.  My laptop is already super old and already can’t really keep up with my tasks anyway, so I suppose it’s time for an upgrade.  What surprised me was that laptops in Germany (from their Best Buy/Future Shop equivalents anyway) cost so much more than in North America.  In fact, it was cheaper for me to buy my computer in Canada and get my parents to ship it to me rather than buying it locally.  I’m sure there are cheaper places, but I don’t exactly know how to look through all these German websites.  Another added advantage in buying from Canada is that I’d have a computer with the US Keyboard layout rather than the German one.  And in the future when my laptop needs repairs, it’ll be easy.

In the meantime, I’m using a 17 inch LCD screen that I borrowed from a friend.  This will suffice until my new computer arrives.  No more shining a lamp at my computer screen and squinting my eyes to see the screen anymore.  I also don’t need to be using my phone to go on the internet at home either.

• Introduction
• Motivation
• Newton’s Method
• Steepest Descent Method
• Limitation
• Sources

Introduction

In many sciences, the problem of non-linear optimization appears quite often.  What happens if they’re non-linear?  Sometimes, the system of equations remains easy to solve even given non-linearity, but other times, the possibility of solving the problem analytically may not exist if the algebra gets too complicated.  The solution lies in using numerical methods (approximations).  Here, I present two common methods: Newton’s Method, and the Steepest Descent Method. 

Each method has its own limitations and the choice of which method to use depends on the problem.  These methods involve using iterative computation in order to reach a solution.  Luckily, computers can prove useful in providing solutions very quickly due to its quick processing power for numerical computation.

In order to understand some of the concepts and terms used in this article, the reader has knowledge in multivariable calculus.  Also, equations in picture form made the line spacing look funny, so I’m going to do my best write the equations as text.  I should also point out that I couldn’t write the vector arrow on top of the variables in text form so vectors are written in bold.

Motivation

In calculus, the idea of optimization involves taking the derivative of the function and equating it to zero.  In multivariable calculus, the same idea applies except, we set all the partial derivatives to zero and solve the system.

So in general, if we are given a function:

ƒ(x), where x = [x₁, x₂, … x_n]^T

The maximum or minimum can be found by taking a partial derivative with respect to the vector x.  This gives the following equations:

∂ƒ/dx₁ = 0

∂ƒ/dx₂ = 0

…

∂ƒ/dx_n = 0

A short-hand way of expressing the above equations is by using the gradient vector, giving∇ƒ(x) = 0.  By definition, the gradient is defined by:

∇ƒ(x) = [∂ƒ/dx₁, ∂ƒ/dx₂, … , ∂ƒ/dx_n].

An analytical solution is not always possible, hence the motivation for approximating the solution using numerical methods.

Newton’s Method

In general, this method is written below.  Explanation of each step will follow.

1. Given the equations to solve, derive equations for the approximating line or plane, depending on whether the problem is 2D, 3D, nD, etc.
2. Using the linearized equations, solve the system of equations
3. Using the results from step 2, generate new equations for a new approximating line or plane, and repeat step 2.

This method also involves starting with a guess, denoted by a variable with a subscript of 0.  A guess is required, because this is the starting point for this method.  Using this guess, each successive solution should converge (more on that later).

Step 1

In order to solve the equations ∇ƒ(x) = 0 (see Motivation for more information), we can apply multivariate Newton’s method to approximate the solution.  Like the single-variate (two-dimensional) version, a linear approximation is required.  However, instead of having an approximation in the form of a line, the approximation is a plane instead.

2D (line): ƒ(x) ≈ ƒ(x₀) + ƒ’(x₀)(x – x₀)

3D (plane): ƒ(x, y) ≈ ƒ(x₀, y₀) + ƒ_x(x₀, y₀)(x – x₀) + ƒ_y(x₀, y₀)(y – y₀)

nD (nD plane): ƒ(x) ≈ ƒ(x₀) + ∇ƒ(x₀)(x – x₀)

Since we are trying to optimize, we have the partial derivatives of the function we are trying to optimize, but in order to apply Newton’s Method, we need a linear approximation of the partial derivatives.  This means that in order to approximate the partial derivatives, we need to take another derivative in order to get the slopes of the approximating planes.  If that description didn’t make sense, try the following.  For an equation with two independent variables, there will be two equations for the partial derivatives, one for x and one for y.  Taking partial derivatives from each of those equations again will give the slopes of the plane that approximate the first partial derivative.  So if we have two independent variables, we end up getting four equations: ƒ_xx, ƒ_xy,ƒ_yy, and ƒ_yx (ƒ_xy and ƒ_yx should be the same).  In general, for n partial derivatives, we would have n² equations if we took another set of derivatives.  The approximations for both of the partial derivatives would be:

ƒ_x(x, y) ≈ ƒ_x(x₀, y₀) + ƒ_xx(x₀, y₀)(x – x₀) + ƒ_xy(x₀, y₀)(y – y₀)

ƒ_y(x, y) ≈ ƒ_y(x₀, y₀) + ƒ_yy(x₀, y₀)(x – x₀) + ƒ_yx(x₀, y₀)(y – y₀)

Plug in the values for the second derivatives, and the values from the initial guess (the x y values and what function value you get using those values).

Step 2

Although the equations generated from step 1 is yet another system of equations, the main difference is that the equations from step 1 are linear.  This means that the system can be solved analytically.  Solve for the solution of the system using row reduction methods, or other methods.  The solution from solving the system will be the values used for the next iteration and will replace the guessed values.  The solution may or may not be close to the actual solution.  More iterations need to be done to see if the answer changes with each iteration.  Usually if the guess is really far away, then it takes a lot of iterations to get it really close.  However, sometimes, a bad guess may cause the solution to diverge, meaning that the solution will be further and further off.

Step 3

Generate new equations for the approximating planes using the solution from step 2.  Using these equations, go back to step 2 and solve it again.  This method is super tedious if done on paper.  Matlab can help, but then again, Matlab can do the entire approximation with just a few commands, but not everyone has access to it unfortunately.

Hopefully after a few iterations, the solution stops changing.  When that happens, you can substitute the final solution back into the original equation to see if it works!

Steepest Descent Method

Here is the general method:

1. Find the direction of the maximum or minimum directional derivative
2. Follow it until a maximum or minimum is reached

Newton’s Method is sufficient in a lot of cases, but sometimes it may be too hard to go beyond first derivatives.  This main idea of this method is to use the first derivative and follow the direction in which the function gets larger/smaller.  A fundamental concept used in this method is the directional derivative.  Since in 3D (or higher dimensions), we are not restricted to movement along the x axis.  This means we could move in any random direction, and in each direction the rate of change is going to be different.  To calculate the max or min, we need to calculate where the directional derivative is largest or smallest.  Just like a boulder rolling down the steepest slope on the hill.

Starting with a guess, we can find out the value of the function at the point and the direction to travel in.  Take a step in that direction and see how the value of the function changed.  Keep doing that until a max or min is reached.

Step 1

The definition of the directional derivative is the dot product of the gradient and the unit vector specifying the direction.  Here is the definition of the directional derivative:

D_uƒ = ∇ƒ(x)·u

Since the definition involves a dot product, it is true that if the two vectors are orthogonal, the resulting dot product is zero.  The direction that this derivative is in is called the level direction.  But if the two vectors are parallel, we get the highest value of the directional derivative.  For a vector that is parallel in the same direction, the directional derivative will be a maximum, but if the vector is antiparallel (parallel but both pointing opposite ways), the directional derivative will be a minimum.

Since the maximum value of the directional derivative is parallel to the gradient, we can calculate the unit vector of the gradient and use it as the unit vector u.  In order to get the minimum, simply flip the direction of the vector by multiplying it by –1.

u = ∇ƒ(x)/|∇ƒ(x)|

Although not necessarily required, substituting this value into the definition of the directional derivative, and doing some simplification with algebra, the maximum and minimum directional derivative is given by:

Max D_uƒ = |∇ƒ(x)|

Min D_uƒ = -|∇ƒ(x)|

Using the initial guess, calculate the direction of to travel in at that point.

Step 2

Knowing the direction to travel choose a desired step size “h”.  This means that if the equation will be traversed in a particular direction, we need to know exactly how far to go.  Choosing smaller step sizes gives better computational accuracy but increases computation time.

To get to the maximum, use the direction for the maximum directional derivative.  To get the minimum, use the direction for the smallest directional derivative.

Starting with a guess, calculate the function value at that point.  Then take a step in the direction given by Step 1 using the step size.  The variable “u” here is a component of the unit vector

x_n+1 = x_n + u_xh

y_n+1 = y_n + u_yh

At this new value, calculate the function value again.  Keep repeating this until the maximum or minimum is reached.

Limitation

The approximation is generally only as good as the initial guess.  Sometimes, a bad guess can lead to a solution that never converges.  In that case, a different value must be used in order to find a converging solution.  For example, if we have a fourth order polynomial function, a local extreme will exist.  As x approaches –∞ or ∞, y will do the same.  If I use the steepest descent and give a bad guess, my solution will go to ∞ instead of the local extreme.

Sources

1. Calculus by Gilbert Strang
2. Applied Regression Analysis by Norman Draper and Harry Smith

Switching the Language for Windows

To do this, go to the Control Panel and open the Regional and Language Options.  This might be hard to do when Windows is in a different language so just look for the icon that has a globe on it.  Depending on the version of Windows, switching the language may not be possible.  And also, different versions of Windows put these buttons in different places within the Language Options.  Click around the tabs, and there should be a drop down box for you to change the language.  Once that’s done, restart the computer.

Switching the Language for Office

Hopefully switching the language for Windows worked, because it would really help for this part, although it isn’t necessary.  Not every version of Office supports changing languages.  It depends on the version that was installed.  Go to the Start Menu, find Microsoft Office, and then Microsoft Office Tools.  Under there, there should be an icon for Language Settings.  The icon has a globe and an A on it under Windows 7.  Open it and change the language.

Virus & Spyware Removal

Best Buy: Apparently they charge a whopping $249 for in home or in office service and $189 for online service or in store support.  This package includes:

Looking at each of these items are the list, these are all things that people could do themselves for free if people took the time to learn.  Some of these tasks take only a few minutes to do.  For example, malware removal just takes a few clicks on the antivirus and the rest is just waiting for results.  Updating the system just requires getting Windows Update to look for them.  Actually, Windows will even tell you that you need to update.  It is just that a lot of people ignore it or disable automatic updates.  Backing up the files on the computer only requires moving files from the computer to an external storage device with a simple drag and drop.  The time consuming part isn’t moving the files, but is actually thinking of what files need to be backed up.  Geek Squad can’t help with that.  Anybody that knows how to use a computer should be able to do that.  And if people don’t have access to external storage, their friends most likely do.

The rest of these services provide little detail about the extent of their service.  Formatting the computer solves most software issues, but a fix like that is quite brute force and not extensive at all.  On the other hand, an extensive fix means determining which piece of hardware or software is responsible for the problem.  Say that the client gets a blue screen or that Explorer is crashing repeatedly.  Solving this problem requires knowing what people do on the computer.  But the problem is that some people are not even aware of what they did (whether directly or indirectly) to cause the computer to behave a certain way.  These computer problems make formatting an attractive repair option.  Again, this fix takes only a few clicks, and the rest is just letting the computer do what those clicks told it to do.

A few minutes worth of work to save over a hundred dollars.  Even if someone is new to computers, a quick Google search will show solutions to these problems catered to beginners.  Sounds like a bargain to me.

Security and Performance

Here are more crazy computer repairs/maintenance services that Best Buy offers.  A little more reasonable this time.

Yet again, Best Buy charges people for easy fixes (see the first nine included services on the list).  They are all quick things that people can do on the computer if they put the time in (see pseudo-rant in the previous section).  One thing here that people that I can see people would pay for is physically setting up the computer, but people should not have to.  It is really not that hard.  In grade 3, my mother set up the computer all by herself, and she had never touched a computer in her life before.  It was mostly typewriters back then.  Organizing the wires and cables is an even less daunting task than setting up the computer.  It merely involves taking wires and cables together, wrapping them together and putting them neatly against the wall so it doesn’t look ugly.  Some would say that organizing the wires isn’t even necessary because people don’t even see the mess of wires behind the computer even if it was there.  The next thing on the list seems like a good idea at first, teaching people how to use a computer.  But realistically speaking, people will always forget.  Like many stereotypical middle aged and older people, no matter how many times they are taught to do something on the computer, they will inevitably forget.  The last three things on the list are a joke.  Simply knowing how to read will allow one to complete those tasks.  People do not need to pay so much to get a computer fixed.

Wireless Networking

Here are more things that people pay for at Best Buy.

Three words for people who pay for this.  Read the manual.  Reading the manual for the router not only teaches people how to hook it up, it also tells people how to set up your entire network complete with enabling the router’s security features.  They don’t even have to purchase an upgrade to install an additional device!  The manual explains how.  All that is required, is pretty much plug in the cable in the spot that the manual says and it will work.  Taking thirty minutes to read the manual to connect to the Internet can help save you $169.  Even better deal than switching to Geico for car insurance!

Conclusion

Getting a computer fixed from Best Buy looks like a huge money grab.  Best Buy’s site featured even more computer services that people could purchase, but I didn’t go through it all.  They are all very similar.  They all offer solutions that literally cost people nothing if they took the time to learn.  Aside from the people that are just not very knowledgeable with computers, maybe some people are just lazy and would rather throw money at a problem to make it go away.

Source: http://www.bestbuy.ca/en-CA/category/computers-networking/28857.aspx?path=3aa9e4f25b9e89f41bd934261dff9881en01

Warning: After doing this, I’ve lost all contact with my router even with the IP of the router changed.  This is probably because my router is acting as a switch.  The only way that I’ve found to access the router page is to reset the router.  This is probably due to the fact that my router is a piece of junk and I don’t know if this is something consistent among all routers.

1. Change the IP of the router to something else that is unused in the network (I changed mine to 192.168.0.254)
2. Disable the DHCP client on the router
3. Plug the ethernet cable from the wall/modem to one of the LAN ports on the router (Don’t use the WAN port anymore)
4. Plug ethernet cables from each computer to any free LAN port on the router
5. Release/renew IP’s on all computers

Note: Do not use the WAN port since the DHCP functionality has been disabled.

Despite the drawback of not being able to access the router afterward, I now have all my computers networked.  Some people on forums had solutions on retaining access to the router, but those methods didn’t work for me.

However, this poses a problem for syncing the desktop folder.  I wasn’t going to move everything on my desktop to the dropbox folder because that would mean I wouldn’t be able to see these files on the desktop anymore.  Also, if I did put a symlink in my user folder, network shares would be broken since other computers cant follow symlinks when using network access.  I couldn’t go back to putting a symlink in the Dropbox directory due to the problem that I just had.  So what I did was use LiveMesh.  LiveMesh has the ability to follow symlinks while the program is running.  Now I put up a symlink for my Desktop in my Documents folder and now the program just syncs that.  For some reason, LiveMesh can’t sync the Desktop folder directly.

I might just ditch Dropbox altogether so I can do all my file syncing using LiveMesh.

However, LC won’t tell you that your Warcraft III port is blocked.  Google a port scanner tool and have it scan your Warcraft port (default 6112).  Also make sure that the LC config file has the same port that you forwarded.  The game port that you set in-game have no bearing on the LC port.  The only requirement is that it must be different than the LC port, but that port number is not important for hosting games.

The last issue is quite obscure.  I ran into an issue where one of my friends couldn’t join my game, but everybody else could.  Warcraft simply gave him a gray screen.  I immediately thought that it was a problem on their end and not mine.  However, upon closer inspection, it appears that if I set my LC hosting port to default, everybody can join.  The reason I didn’t use the default port is because someone else was using the 6112 port and I couldn’t forward the same port on multiple computers.  I don’t really know why that is, but it works beautifully.