## 2d – Calculate the position at given speed and acceleration at a given time

I am attending a Pixar class at the Khan Academy and encountering a simulation of a double spring at a certain time step. I understand how it works and why it behaves that way, but I want to know if the math is actually correct. What interests me are the following lines:

``````    // mass 1 speed
mass1VelocityY = mass1VelocityY + mass1AccelerationY * timeStep;
mass1VelocityX = mass1VelocityX + mass1AccelerationX * timeStep;

// ground 1 position
mass1PositionY = mass1PositionY + mass1VelocityY * timeStep;
mass1PositionX = mass1PositionX + mass1VelocityX * timeStep;
``````

So we first calculate the speed and add a fraction of the calculated acceleration to it. Then we calculate the position and add a fraction of the calculated speed to it. So we build the final position in time `T` by summing `T / time step` Intermediate positions.

Given the formula for the shift `s = ut + 0.5at ^ 2` from where:

s = displacement
u = initial speed
a = acceleration
t = time

If I use the values: s = 0, u = 0, a = 1, t = 2, I get `s = 2`, This means that if I start from zero and build up the speed with an acceleration of 1 m / s / s, I will end up at position 2 with a speed of 2 m / s.

Now, if I try to follow the same logic, but split that result into 20 steps`(2 / 0.1 - t = 2 time step = 0.1)`If you summarize the results of all these intermediate steps as in this code, I get another result: `s = 0.55 at t = 1` and `s = 2.1 at t = 2`,

My initial intuition is that, because in the code we multiply timeStep twice with the acceleration in the code, this leads to a potentiation and the progression is no longer linear and smaller steps get smaller values ​​at the beginning. So I have 3 questions:

1) Did I understand what the code is doing right?

2) Is what the code does the most correct / accurate method of calculating the displacement?

3) I really want to understand these concepts. So if you have any other advice or know something that might be helpful to me, please let me know.

## Parallelization – acceleration of tensor contractions and multiplication

Consider a tensor $$T in mathbb {R} ^ {N times N times N times M}$$ and two vectors $$x, y in mathbb {R} ^ N$$, I want to calculate that $$N times M$$ Vector defined by $$X_ {ij} = operatorname {tr} (x ^ top T _ {:,:, i, j} y) = operatorname {tr} _ {12} (yx ^ top T)$$ efficient.

I tried it in two ways:

``````TCtable[x_, T_, y_] : = Parallel table[Module[{Tslice},
Tslice = T[[;; , ;; , i, j]];
Tr[x[Transpose].Tslice.y]], {i, 1, length[x]}, {j, 1, last[Dimensions[T]]}];

TCTRACE[x_, T_, y_] : = TensorContract[y.x[Transpose].T, {1, 2}];
``````

My tensors have the very nice property of that $$T _ {:,:, i, j}$$ is very economical for everyone $$i, j$$ (So ​​I represent my tensor in Mathematica as a sparse array).

With $$N = 500, M = 3$$ The parallel table method takes about 1 second, while the explicit tensor multiplication and partial tracking takes about 20 seconds. Are there other clever ways to speed things up? I would like to calculate this for many different tensors and vectors of the same size. So, if there's a way to compile the code or amortize the complexity, that would be great too!

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## real analysis – convergence acceleration of a series using optimal parameters

One way to speed up the convergence of a series is to turn it into a faster series using optimal parameters. Examples of this approach can be found in this article. I have obtained a generalization of this method to express a series with two other independent variables:

If $$| frac {x} {x + y} | <1$$, Then,

$$sum_ {n = 1} ^ { infty} a_nx ^ n = big ( frac {y} {x + y} big) ^ {r + 1} sum_ {n = 0} ^ { infty} Big ( frac {x} {x + y} Big) ^ {n} sum_ {k = 0} ^ {n} {n + r select k + r} a_k y ^ k$$

This expresses a power series in the LHS as two independent variables $$y$$ and $$r$$ This feature can be theoretically optimized to accelerate the convergence of the series.

question: How to choose the optimum $$y$$ and $$r$$ so that the RHS converges fastest?

Note: Asked this in MSE, but got no answers in a week. Post it here and delete it from MSE to avoid duplicates.

## Algorithms – Understand the linear acceleration set and how strong it is

The linear acceleration set says this for every constant $$c$$You can choose the language $$c$$ faster It does not mean that you can make it faster by a non-constant function.

The acceleration set works by defining a new Turing machine that writes $$c$$ Character of the old Turing machine in a single tape cell, and customize the transient function to simulate in a single step everything that the original machine did between entering and leaving the individual $$c$$-Zeichenblock. If $$c$$ Since this is a constant, it does not depend on the input. You only have to calculate the new machine once and use it for the input you want. But if you want $$c$$ To have a non-constant function, you have to find out what the new machine is each time you run it. This takes an exponentially long time because exponentially many are possible $$c$$Token blocks for which you need to find out the transfer function.

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## Windows 7 – Disable the annoying acceleration for the volume keys

I have volume keys on my keyboard to increase or decrease the volume. This ad will appear when I change the volume: https://i.imgur.com/9EGglRq.png

Each key changes the volume by 2% per single press. If I press the raise key ten times quickly, the volume will increase by 20%. But as far as the removal of the button is concerned – I have reduced the volume by 50%! It starts slowly, at 2% per 1 press, but eventually the percentage rises above 10% per single press. I wanted to reduce the volume by about 20%, but got too low a sound or was even muted. Now it gets very annoying for me!

Does anyone know how to lower the volume when the acceleration decreases?

## android studio – Emulator: Emulator: ERROR: The x86 emulation currently requires hardware acceleration! and Emulator: Operation terminated with exit code 1

I can not virtualize my mobile devices in Android Studio

https://stackoverflow.com/questions/29136173/emulator-error-x86-emulation-currently-erquires-hardware-acceleration

The first was to see if the hardware acceleration was installed and so it was

2) I went to the SDK directory C: Users % USERNAME% AppData Local Android sdk extras intel Hardware_Accelerated_Execution_Manager and run the file intelhaxm-android.exe

but it tells me that virtualization is disabled

Virtualization appears activated

If someone can help me, I would appreciate it very much. I just bought a new computer with an Intel processor and was very excited because I thought it would be easy to virtualize

## Startup acceleration Ubuntu 18.04

I also have the same issue that I have been looking for a lot, but I can find anything to fix it (I have processor = Intel Core i3, RAM = 4G, Swap = 9G) and my boot info is:

```~\$ systemd analysis
Startup completed in 10.299s (kernel) + 49.706s (user space) = 1min 6ms
graphics.target reached 49,694s in user space
```

and graphical analysis

```~\$ systemd-analysis critical-chain graphical.target
The time after activating or starting the device is printed after the "@" mark.
The time taken for the device to start up is printed after the "+" sign.

graphical.target @ 49.694s
Ultmulti-user.target @ 49.693s
└─mysql.service @ 39.610s + 10.082s
Worknetwork.target @ 39.607s
└─wpa_supplicant.service @ 34.142s + 5.464s
└─dbus.service @ 28.807s
└─Basic.target @ 28.749s
└─sockets.target @ 28.749s
└─snapd.socket @ 28,747s + 1 ms
└─sysinit.target @ 28.719s
└─systemd-timesyncd.service @ 28.477s + 240ms
└─systemd-tmpfiles-setup.service @ 27.622s + 716ms
└─systemd-journal-flush.service @ 5,195s + 22,426s
└─systemd-remount-fs.service @ 4.389s + 803ms
└─systemd-journald.socket @ 4.354s
└─system.slice @ 4.354s
└─-.slice @ 4.334s
```

## Time complexity – Definition of acceleration for Amdahl's law

Suppose I have an algorithm C that runs in time T, which decomposes into two "subalgorithms" A and B that run in time p * T and (1-p).T, so the algorithm C needs the time pT + (1-p) * T.

Suppose I have another algorithm C & # 39; that calculates the same thing as the algorithm C that is in time T & # 39; running, where two sub-algorithms A & # 39; and B & # 39; Similar to A and B s.t. p & # 39; * T & # 39; + (1-p & # 39;) * T & # 39; = T & # 39;

I would like to measure the "partial acceleration" of the p-part A of C as in Amdahl's law. Must I

1. have the subalgorithm A & # 39; to compute exactly the same as A or
2. can I have another subalgorithm A & # 39; that computes more than A.

In Case 2, can I still use the ratio of execution times from A to A? As acceleration with ratio p?

Suppose I can not do 1. because I do not have such a subalgorithm A # 2. How can I then measure the execution times of A & # 39; and A if p and p are different?