text:
# wavenet

Wavelet network function for nonlinear ARX and Hammerstein-Wiener models

## Description

A `wavenet` object implements a wavelet network function, and is a nonlinear mapping function for estimating nonlinear ARX and Nonlinear Hammerstein-Weiner models. The mapping function, which is also referred to as a nonlinearity, uses a combination of linear weights, an offset and a nonlinear function to compute its output. The nonlinear function contains wavelet unit functions that operate on a radial combination of inputs.

Mathematically, a wavenet network is a function that maps m inputs X(t) = [x(t1),x2(t),…,xm(t)]T to a scalar output y(t) using the following relationship:

`$y\left(t\right)={y}_{0}+{\left(Χ\left(t\right)-\overline{X}\right)}^{T}PL+W\left(Χ\left(t\right)\right)+S\left(Χ\left(t\right)\right)$`

Here:

• X(t) is an m-by-1 vector of inputs, or regressors, with mean $\overline{Χ}$.

• y0 is the output offset, a scalar.

• P is an m-by-p projection matrix, where m is the number of regressors and is p is the number of linear weights. m must be greater than or equal to p.

• L is a p-by-1 vector of weights.

• W(X) and S(X) together constitute the nonlinear function of the wavelet network. W(X) is a sum of dilated and translated wavelets while S(X) is a sum of dilated and translated scaling functions (also known as scalelets). The total number of wavelet dw and scaling functions ds is referred to as the number of units of the network.

For definitions of the wavelet function term W(X) and the scaling function term S(X), see More About.

Use `wavenet` as the value of the `OutputFcn` property of an `idnlarx` model or the `InputNonlinearity` and `OutputLinearity` properties of an `idnlhw` object. For example, specify `wavenet` when you estimate an `idnlarx` model with the following command.

`sys = nlarx(data,regressors,wavenet)`
When `nlarx` estimates the model, it essentially estimates the parameters of the `wavenet` function.

You can configure the `wavenet` function to disable components and fix parameters. To omit the linear component, set `LinearFcn.Use` to `false`. To omit the offset, set `Offset.Use` to `false`. To specify known values for the linear function and the offset, set their `Value` attributes directly and set the corresponding `Free` attributes to `False`. Use `evaluate` to compute the output of the function for a given vector of inputs.

## Creation

### Syntax

``W = wavenet``
``W = wavenet(numUnits)``
``W = wavenet(numUnits,UseLinearFcn)``
``W = wavenet(numUnits,UseLinearFcn,UseOffset)``

### Description

example

````W = wavenet` creates a `wavenet` object `W`, for which the function computes the number of units automatically during model estimation. ```

example

````W = wavenet(numUnits)` specifies the number of units `numUnits`. This syntax includes an option that allows you to interactively assess the relationship between the number of units and unexplained variance.```

example

````W = wavenet(numUnits,UseLinearFcn)` specifies whether the function uses a linear function as a subcomponent.```

example

````W = wavenet(numUnits,UseLinearFcn,UseOffset)` specifies whether the function uses an offset term.```

### Input Arguments

expand all

Number of units, specified as the string or character vector that represents `'auto'` or `'interactive'`, or as a positive integer. `numUnits` determines the number of wavelets or scaling functions, or, if both elements are present, the combined number of wavelets and scaling functions. Typically, the wavelet network contains either wavelets or scaling functions, but not both. Specify `numUnits` as one of the following values:

• `'auto'` — The software determines the number of units automatically during model estimation.

• `'interactive'` — During model estimation, the software displays an interactive bar plot that relates unexplained variance to the number of units. Click on a bar to view the achievable fit to the estimation data for the selected number of units. A blue bar indicates the optimal choice, based on the generalized cross-validation (GCV) criterion. A general rule for the selection of the number of units is to use the smallest number of units that capture most of the variance.

• Positive integer — The software uses the specified value directly.

This argument sets the `W.NonlinearFcn.NumberOfUnits` property.

Option to use the linear function subcomponent, specified as `true` or `false`. This argument sets the value of the `W.LinearFcn.Use` property.

Option to use an offset term, specified as `true` or `false`. This argument sets the value of the `W.Offset.Use` property.

## Properties

expand all

Input signal information for signals used for estimation, specified as vectors of m property-specific values, where m is the number of input signals. The `Input` properties for each input signal are as follows:

• `Name` — Names of the input signals, specified as a 1-by-m string or character array, where m is the number of inputs

• `Mean` — Mean of the input signals, specified as a numeric scalar

• `Range` — Ranges of the input signals, specified as a 2-by-m numeric array that contains the minimum and maximum values

Output signal information, specified as property-specific values. The `Output` properties are as follows:

• `Name` — Name of the output signal, specified as a string or a character array

• `Mean` — Mean of the output signal, specified as a numeric scalar

• `Range` — Range of the output signal, specified as a 2-by-1 numeric array that contains the minimum and maximum values

Parameters of the linear function, specified as follows:

• `Use` — Option to use the linear function in the wavelet network, specified as a scalar logical. The default value is `true`. For an example of setting this option, see Exclude Linear Term from Wavelet Network Mapping Object.

• `Value` — Linear weights that compose L', specified as a 1-by-p vector.

• `InputProjection` — Input projection matrix P, specified as an m-by-p matrix, that transforms the input vector of length m into a vector of length p. For Hammerstein-Wiener models, `InputProjection` is equal to `1`.

• `Free` — Option to update entries of `Value` during estimation, specified as a 1-by-p logical vector. The software honors the `Free` specification only if the starting value of `Value` is finite. The default value is `true`.

• `Minimum` — Minimum bound on `Value`, specified as a 1-p vector. If `Minimum` is specified with a finite value and the starting value of `Value` is finite, then the software enforces that minimum bound during model estimation.

• `Maximum` — Maximum bound on `Value`, specified as a 1-p vector. If `Maximum` is specified with a finite value and the starting value of `Value` is finite, then the software enforces that maximum bound during model estimation.

• `SelectedInputIndex` — Indices of `wavenet` inputs (see `Input.Name`) that are used as inputs to the linear function, specified as an 1-by-nr integer vector, where nr is the number of inputs. For nonlinear ARX models, the `RegressorUsage` property determines these indices. For Hammerstein-Wiener models, `SelectedInputIndex` is always `1`.

Parameters of the offset term, specified as follows:

• `Use` — Option to use the offset in the wavelet network, specified as a scalar logical. The default value is `true`.

• `Value` — Offset value, specified as a scalar.

• `Free` — Option to update `Value` during estimation, specified as a scalar logical. The software honors the `Free` specification of `false` only if the value of `Value` is finite. The default value is `true`.

• `Minimum` — Minimum bound on `Value`, specified as a numeric scalar or `–Inf`. If `Minimum` is specified with a finite value and the value of `Value` is finite, then the software enforces that minimum bound during model estimation. The default value is `-Inf`.

• `Maximum` — Maximum bound on `Value`, specified as a numeric scalar or `Inf`. If `Maximum` is specified with a finite value and the starting value of `Value` is finite, then the software enforces that maximum bound during model estimation. The default value is `Inf`.

Parameters of the nonlinear function, specified as follows:

• `NumberOfUnits` — Number of units, specified as `'auto'`, `'interactive'`, or a positive integer. `NumberOfUnits` determines the number of wavelets or scaling functions, or, if both elements are present, the combined number of wavelets and scaling functions. Typically, the wavelet network contains either wavelets or scaling functions, but not both. The options for `NumberOfUnits` are as follows:

• `'auto'` — The software determines the number of units automatically during model estimation.

• `'interactive'` — During model estimation, the software displays an interactive bar plot that relates unexplained variance to the number of units. Click on a bar to view the achievable fit to the estimation data for the selected number of units. A blue bar indicates the optimal choice, based on the generalized cross-validation (GCV) criterion. A general rule for the selection of the number of units is to use the smallest number of units that capture most of the variance.

• Positive integer — The software uses the specified value directly.

• `Structure` — Advanced options that control the structure of the wavelet and scaling functions, specified as in the following table.

PropertyDescriptionDefault
`FinestCell`Minimum number of data points in the smallest cell, specified as `'auto'` or a positive integer. A cell is the area covered by the part of a wavelet that is significantly nonzero. The default setting of `'auto'` specifies that the software determines this value during estimation.`'auto'`
`MinimumCells`Minimum number of cells in the partition, specified as a positive integer.`16`
`MaximumCells`Maximum number of cells in the partition, specified as a positive integer.`16`
`MaximumLevels`Maximum number of wavelet levels, specified as a positive integer. `10`
`DilationStep`Dilation step size, specified as a positive integer.`2`
`TranslationStep`Translation step size, specified as a positive integer.`1`

• `Parameters` — Parameters of `wavenet`, specified as in the following table.

Field NameDescriptionDefault
`InputProjection `

Projection matrix Q, specified as an m-by-q matrix. Q transforms the detrended input vector $\left(X-\overline{X}\right)$ of length m into a vector of length q. Typically, Q has the same dimensions as the linear projection matrix P. In this case, q is equal to p, which is the number of linear weights.

For Hammerstein-Wiener models, `InputProjection ` is equal to `1`.

`[]`
`ScalingCoefficient`

Scaling function coefficients si, specified as a ds-by-1 vector.

`[]`
`ScalingTranslation`

Scaling translation matrix, specified as a ds-by-q matrix of scaling translation row vectors ei.

`[]`
`ScalingDilation`

Scaling function dilation coefficients di, specified as an ds-by-1 vector.

`[]`
`WaveletCoefficient`

Wavelet function coefficients wi, specified as a dw-by-1 vector.

`[]`
`WaveletTranslation`

Wavelet translation matrix, ei, specified as a dw-by-q matrix of wavelet translation row vectors ci.

`[]`
`WaveletDilation`

Wavelet dilation coefficients bi, specified as an dw-by-1 vector.

`[]`

• `Free` — Option to estimate parameters, specified as a logical scalar. If all the parameters have finite values, such as when the `wavenet` object corresponds to a previously estimated model, then setting `Free` to `false` causes the parameters of the nonlinear functions W(X) and S(X) to remain unchanged during estimation. The default value is `true`.

• `SelectedInputIndex` — Indices of `wavenet` inputs (see `Input.Name`) that are used as inputs to the nonlinear function, specified as an 1-by-nr integer vector, where nr is the number of inputs. For nonlinear ARX models, the `RegressorUsage` property determines these indices. For Hammerstein-Wiener models, `SelectedInputIndex` is always `1`.

## Examples

collapse all

`MO = wavenet;`

View the `wavenet` object.

`disp(MO)`
```Wavelet Network Nonlinear Function: Wavelet network with number of units chosen automatically. Linear Function: uninitialized Output Offset: uninitialized Input: [1×1 idpack.Channel] Output: [1×1 idpack.Channel] LinearFcn: [1×1 nlident.internal.UseProjectedLinearFcn] NonlinearFcn: [1×1 nlident.internal.WavenetFcn] Offset: [1×1 nlident.internal.ChooseableOffset] ```

Create the `wavenet` mapping object `MO`.

`MO = wavenet;`

Exclude the linear term from `MO`.

`MO.LinearFcn.Use = false;`

View the `wavenet` object.

`disp(MO)`
```Wavelet Network Nonlinear Function: Wavelet network with number of units chosen automatically. Linear Function: not in use Output Offset: uninitialized Input: [1×1 idpack.Channel] Output: [1×1 idpack.Channel] LinearFcn: [1×1 nlident.internal.UseProjectedLinearFcn] NonlinearFcn: [1×1 nlident.internal.WavenetFcn] Offset: [1×1 nlident.internal.ChooseableOffset] ```

`load twotankdata y u;`

Create an `iddata` object from the estimation data.

`z = iddata(y,u,0.2);`

Create a wavelet network mapping object with five units.

`MO = wavenet(5);`

Estimate the nonlinear ARX model.

`sys = nlarx(z,[4 4 1],MO)`
```sys = Nonlinear ARX model with 1 output and 1 input Inputs: u1 Outputs: y1 Regressors: Linear regressors in variables y1, u1 List of all regressors Output function: Wavelet Network with 5 units Sample time: 0.2 seconds Status: Estimated using NLARX on time domain data "z". Fit to estimation data: 96.8% (prediction focus) FPE: 3.553e-05, MSE: 3.515e-05 ```

`load motorizedcamera;`

Create an `iddata` object.

`z = iddata(y,u,0.02,'Name','Motorized Camera','TimeUnit','s');`

`z` is an `iddata` object with six inputs and two outputs.

Specify the model orders and delays.

`Orders = [ones(2,6),ones(2,6),ones(2,6)];`

Specify the same nonlinearity estimator for each input channel.

`InputNL = wavenet;`

Specify different nonlinearity estimators for each output channel.

` OutputNL = [deadzone,wavenet];`

Estimate the Hammerstein-Wiener model.

`sys = nlhw(z,Orders,InputNL,OutputNL);`

To see the shape of the estimated input and output nonlinearities, plot the nonlinearities.

`plot(sys)`

Click on the input and output nonlinearity blocks on the top of the plot to see the nonlinearities.

`load iddata7 z7;`

Specify `wavenet` for the model output function. Configure the `wavenet` object to have a fixed offset value of 1 and to use five units in the nonlinear component.

```w = wavenet; w.Offset.Value = 1; w.Offset.Free = false; w.NonlinearFcn.NumberOfUnits = 5;```

Specify a linear model regressor set using a lag array that produces four consecutive output regressors and five consecutive input regressors.

`reg = linearRegressor({'y1','u1'},{1:4,0:4});`

Estimate the nonlinear ARX model.

`sys = nlarx(z7,reg,w);`

Examine the postestimation properties of the output function.

`disp(sys.OutputFcn)`
```Wavelet Network Inputs: y1(t-1), y1(t-2), y1(t-3), y1(t-4), u1(t), u1(t-1), u1(t-2), u1(t-3), u1(t-4) Output: y1 Nonlinear Function: Wavelet network with 5 units. Linear Function: initialized to [-1.12 0.469 1.25 0.556 -0.81 -0.261 -0.074 0.711 1.15] Output Offset: fixed to 1 Input: [1×1 idpack.Channel] Output: [1×1 idpack.Channel] LinearFcn: [1×1 nlident.internal.UseProjectedLinearFcn] NonlinearFcn: [1×1 nlident.internal.WavenetFcn] Offset: [1×1 nlident.internal.ChooseableOffset] ```
`disp(sys.OutputFcn.Input)`
``` Channel with properties: Name: [1×9 string] Mean: [0.0795 0.0848 0.1082 0.1134 0.0253 0.0253 0.0202 0.0202 0.0202] Range: [2×9 double] ```
`disp(sys.OutputFcn.NonlinearFcn)`
``` WavenetFcn with properties: NumberOfUnits: 5 Structure: [1×1 nlident.internal.WavenetStructure] Parameters: [1×1 nlident.internal.WavenetFcnParameters] Free: 1 SelectedInputIndex: [1 2 3 4 5 6 7 8 9] ```

`load throttledata`

Specify `wavenet` for the model output nonlinearity and set the arguments for `NumUnits` to `5` and `UseLinearFcn` and `UseOffset` to `false`.

`w = wavenet(5,false,false);`

An alternative method for removing the linear function and offset is to use dot notation after creating the nonlinearity.

```w.LinearFcn.Use = false; w.Offset.Use = false;```

Estimate the model, using an `order` specification of `[4 4 1]`.

`sys = nlhw(ThrottleData,[4 4 1],[],w);`

Compare the simulated model response with the estimation data.

`compare(ThrottleData,sys);`

expand all

## Algorithms

You can use `wavenet` in both nonlinear ARX and Hammerstein-Wiener models. The algorithms for estimating `wavenet` parameters depend on which model you are estimating.

• In a nonlinear ARX model, `wavenet` uses either a noniterative or an iterative technique for predicting the parameters, depending on option settings in `nlarxOptions`.

• If the `Focus` option is set to `'prediction'`, then `wavenet` uses a fast noniterative technique to estimate parameters [1]. Successive refinements after the first estimation use an iterative algorithm.

• If the `Focus` option is set to `'simulation'`, then `wavenet` uses an iterative technique to estimate parameters.

• To always use either an iterative or a noniterative algorithm, specify the `IterativeWavenet` property of `nlarxOptions` as `'on'` or `'off'`, respectively.

• In a Hammerstein-Wiener model, `wavenet` uses iterative minimization to determine the parameters.

## Compatibility Considerations

expand all

Not recommended starting in R2021a

## References

[1] Qinghua Zhang. “Using Wavelet Network in Nonparametric Estimation.” IEEE Transactions on Neural Networks 8, no. 2 (March 1997): 227–36. https://doi.org/10.1109/72.557660.


text:
# Constrained Text Generation with AI

I was discussing how AI text generation, such as ChatGPT, might end up getting used in computer games. So far, designers are fairly reluctant to adopt the technology. One of the key problems is that you just can’t control the output enough. Language models will break character or respond in inappropriate and toxic ways. Finding a good solution to this is a huge research field, and not likely to get cracked soon.

For the foreseeable future, AI in games is much more likely to be used offline – assets and dialog generation generated up front, so it can be vetted before being integrated into the game.

But it got me thinking, can we vet the AI’s output in advance, but still get the benefits of intelligent decision making at runtime? It turns out, we can! I doubt it’ll be useful in every circumstance, but I can certainly see uses for it, like chatbots, games.

# VoronatorSharp

I’ve relased a new library, VoronatorSharp.

VoronatorSharp is a C# library that computes Voronoi diagrams. The Voronoi diagram for a collection of points is the polygons that enclose the areas nearest each of those sites.

Voronoi diagrams have applications in a number of areas such as computer graphics.

This library features:

• Computes Voronoi diagrams and Delaunay triangulations.
• Voronoi polygons can be clipped to a rectangular area.
• Uses a n log(n) sweephull algorithm.
• The implementation attempts to minimize memory allocations.
• Integrates with Unity or can be be used standalone.
• Uses robust orientation code.
• Handles Voronoi diagrams with only 1 or 2 points, and collinear points.

# Mosaic Paint

As a side-project of a side-project, I’ve made a little painting program. It’s like a normal paint program, only you paint on a tile grid instead of pixels. You can create mosaic and stained-glass style images.

Try it out!

# Chiseled Paths Revisited

Back in 2017, I described a method of random path generation called Chiseling. It gives very nice wiggly paths, but I was never satisifed with the performance. I later revisited it, and found a faster algorithm, but it was a bit complicated to implement.

I’m pleased to say that I think I’ve finally found a way of implementing it that is both fast and simple.

# Varia 1.0 released

Announcing Varia, a new Unity asset for adding small random variations into your games.

Spice up your levels, remix your gameplay, and make your assets go further for you. It’s FREE!

Get it here

# Infinite Modifying in Blocks

I’m going to share with you a technique I’ve found for doing lazy, reliable, deterministic, constant-time infinite generation of tile based levels using Wave Function Collapse (WFC). But first, let’s cover some background, Modifying in Blocks, and lazy chunk based infinite generation.

# Tessera: A Practical System for Extended WaveFunctionCollapse

I’ve been working a lot on Tessera. I presented a paper at the most recent PCG Workshop of FDG, where I explain how Tessera makes WaveFunctionCollapse somewhat less daunting, and go into some of the details of its features.

That may not be news for users of the software, but here I explain how things work, and what parts work well / I’m especially proud of.

Paper

# Junkbot Arena

I entered the GMTK Jam again. This year, I was in a larger team, working together on the theme Joined Together.

You can play it on itch.io.

# For Keep’s Sake!

I did another game jam. This time, I made For Keep’s Sake!, for PROCJAM 2020. It’s not really a game, it’s just a toy procedural thing / tech demo. Still, I had fun making it and I hope you enjoy.

# Lucky Fluke

This year I decided to enter the 48 hour GMTK Jam. I teamed up with the excellent Praeto and jhicks to make a little shooter based on the theme: Out of Control

format: plain


text:
# 16.13: The Free Energy

In the previous section, we were careful to differentiate between the entropy change occurring in the reaction system ΔSsys, on the one hand, and the entropy change occurring in the surroundings, ΔSsurr, given by –ΔH/T, on the other. By doing this we were able to get a real insight into what controls the direction of a reaction and why. In terms of calculations, though, it is a nuisance having to look up both entropy and enthalpy data in order to determine the direction of a reaction. For reasons of convenience, therefore, chemists usually combine the entropy and the enthalpy into a new function called the Gibbs free energy, or more simply the free energy, which is given the symbol G. If free-energy tables are available, they are all that is needed to predict the direction of a reaction at the temperature for which the tables apply.

In order to introduce free energy, let us start with the inequality

$$-\frac{\Delta H}{T}+ {\Delta S}_{sys} > 0$$

This inequality must be true if a reaction occurring at constant pressure in surroundings at constant temperature is to be spontaneous. It is convenient to multiply this inequality by T; it then becomes

$$-\Delta H + T \Delta S > 0$$

(From now on we will abandon the subscript "sys".) If –ΔH + T ΔS is greater than zero, it follows that multiplying it by –1 produces a quantity which is less than zero, that is,

$$\Delta H - T \Delta S < 0 \label{3}$$

This latest inequality can be expressed very neatly in terms of the free energy G, which is defined by the equation

$$G=H-TS$$

When a chemical reaction occurs at constant temperature, the free energy will change from an initial value of G, given by $$G_{1}=H_{1}=TS_{1}$$

to a final value

$$G_{2}=H_{2}-TS_{2}$$ The change in free energy ΔG will thus be $$\Delta G = G_{2} - G_{1} = H_{2} - H_{1} - T(S_{2}-S_{1})$$

or

$$\Delta G = \Delta H - T\Delta S$$

Feeding this result back into inequality $$\ref{3}$$ gives the result

$$\Delta G = \Delta H - T \Delta S <0$$

$$\Delta G < 0 \label{10}$$

This very important and useful result tells us that when a spontaneous chemical reaction occurs (at constant temperature and pressure), the free-energy change is negative. In other words a spontaneous change corresponds to a decrease in the free energy of the system.

If we have available the necessary free-energy data in the form of tables, it is now quite easy to determine whether a reaction is spontaneous or not. We merely calculate ΔG for the reaction using the tables. If ΔG turns out to be positive, the reaction is nonspontaneous, but if it turns out to be negative, then by virtue of Eq. $$\ref{10}$$ we can conclude that it is spontaneous. Data on free energy are usually presented in the form of a table of values of standard free energies of formation. The standard free energy of formation of a substance is defined as the free-energy change which results when 1 mol of substance is prepared from its elements at the standard pressure of 1 atm and a given temperature, usually 298 K. It is given the symbol ΔGf°. A table of values of ΔGf° (298 K) for a limited number of substances is given in the following table.

Table $$\PageIndex{1}$$ Some Standard Free Energies of Formation at 298.15 K (25°C)

 Compound ΔGfo /kJ mol-1 Compound ΔGfo /kJ mol-1 AgCl(s) -109.789 H2O(g) -228.572 AgN3(s) 591.0 H2O(l) -237.129 Ag2O(s) -11.2 H2O2(l) -120.35 Al2O3(s) -1582.3 H2S(g) -33.56 Br2(l) 0.0 HgO(s) -58.539 Br2(g) 3.110 I2(s) 0.0 CaO(s) -604.03 I2(g) 19.327 CaCO3(s) -1128.79 KCl(s) -409.14 C--graphite 0.0 KBr(s) -380.66 C--diamond 2.9 MgO(s) -569.43 CH4(g) -50.72 MgH2(s) 76.1 C2H2(g) 209.2 NH3(g) -16.45 C2H4(g) 68.15 NO(g) 86.55 C2H6(g) -32.82 NO2(g) 51.31 C6H6(l) 124.5 N2O4(g) 97.89 CO(g) -137.168 NF3(g) -83.2 CO2(g) -394.359 NaCl(s) -384.138 CuO(s) -129.7 NaBr(s) -348.983 Fe2O3(s) -742.2 O3(g) 163.2 HBr(g) -53.45 SO2(g) -300.194 HCl(g) -95.299 SO3(g) -371.06 HI(g) 1.7 ZnO(s) -318.3

This table is used in exactly the same way as a table of standard enthalpies of formation. This type of table enables us to find ΔG values for any reaction occurring at 298 K and 1 atm pressure, provided only that all the substances involved in the reaction appear in the table. The two following examples illustrate such usage.

Example $$\PageIndex{1}$$: Spontaneous Reactions

Determine whether the following reaction is spontaneous or not:

$\ce{4NH3(g) + 5 O2(g) → 4NO(g) + 6H2O(l)}\qquad 1 \text{ atm, 298K}$

Solution Following exactly the same rules used for standard enthalpies of formation, we have

$$\Delta G_{m}^{\circ} = \Sigma \Delta G_{f}^{\circ}\text{ (products)} - \Sigma \Delta G_{f}^{\circ} \text{ (reactants)}$$

$$\qquad = \ce{4 \Delta G_{f}^{\circ}(NO) + 6 \Delta G_{f}^{\circ}(H2O) - 4\Delta G_{f}^{\circ}(NH3) - 5\Delta G_{f}^{\circ}(O2)}$$

Inserting values from the table of free energies of formation, we then find

$$\Delta G_{m}^{\circ} = [4 \times 86.7 + 6 \times (-273.3) - 4 \times (-16.7) - 5 \times 0.0]\frac{ \text{kJ }}{\text{mol}}$$

$$\qquad = -1010\frac{\text{ kJ}}{\text{ mol}}$$

Since $$\Delta G_{m}^{\circ}$$ is very negative, we conclude that this reaction is spontaneous.

The reaction of NH3 with O2 is very slow, so that when NH3 is released into the air, no noticeable reaction occurs. In the presence of a catalyst, though, NH3 burns with a yellowish flame in O2. This reaction is very important industrially, since the NO produced from it can be reacted further with O2 and H2O to form HNO3:

$$\ce{2NO + \frac{3}{2}O2 + H2O→2HNO3}$$

Nitric acid, HNO3 is used mainly in the manufacture of nitrate fertilizers but also in the manufacture of explosives.

Example $$\PageIndex{2}$$: Spontaneous Reactions

Determine whether the following reaction is spontaneous or not:

$\ce{2NO(g) + 2CO(g) → 2CO2(g) + N2 (g)}\qquad 1 \text{ atm, 298K}$

Solution Following previous procedure we have

$$(\Delta G_{m}^{\circ} = (-2\times 394.4 + 0.0 - 2 \times 86.7 + 2 \times 137.3)\frac{\text{ kJ}}{\text{ mol}}$$

$$\qquad = 687.6\frac{ \text{ kJ}}{\text{ mol}}$$

The reaction is thus spontaneous.

This example is an excellent illustration of how useful thermodynamics can be. Since both NO and CO are air pollutants produced by the internal-combustion engine, this reaction provides a possible way of eliminating both of them in one reaction, killing two birds with one stone. A thee-way catalytic converter is able to perform the equivalent of this reaction. The reduction step coverts NOx to O2 and N2. Then, in the oxidation step, CO and O2 are converted to CO2. If ΔGm° had turned out be +695 kJ mol–1, the reaction would be nonspontaneous and there would be no point at all in developing such a device.[1]

We quite often encounter situations in which we need to know the value of ΔGm° for a reaction at a temperature other than 298 K. Although extensive thermodynamic tables covering a large range of temperatures are available, we can also obtain approximate values for ΔG from the relationship

$$\Delta G_{m}^{\circ}=\Delta H_{m}^{\circ}-T\Delta S_{m}^{\circ}$$

If we assume, as we did previously, that neither ΔHm° nor ΔSm° varies much as the temperature changes from 298 K to the temperature in question, we can then use the values of ΔHm°(298 K) obtained from the Table of Some Standard Enthalpies of Formation at 25°C and ΔSm°(298 K) obtained from the Table of Standard Molar Entropies to calculate ΔGm° for the temperature in question.

Example $$\PageIndex{3}$$: Spontaneous at Different Temperatures

Using the enthalpy values and the entropy values, calculate ΔHm° and ΔSm° for the reaction

$\ce{CH4(g) + H2O(g) → 3 H2(g) + CO(g)} \qquad 1 \text{ atm}$

Calculate an approximate value for $$\Delta G_{m}^{º}$$ for this reaction at 600 and 1200 K and determine whether the reaction is spontaneous at either temperature.

Solution From the tables we find

$$\Delta H_{m}^{\circ}(298 \text{ K})= 3\Delta H_{f}^{\circ}(\text{H}_{2})+\Delta H_{f}^{\circ}\text{(CO)} - \Delta H_{f}^{º}( \text{CH}_{4}) - \Delta H_{f}^{\circ}(\text{H}_{2}\text{O})$$

$$\qquad = (3 \times 0.0 - 110.6 + 74.8 + 241.8) \frac{\text{ kJ}}{\text{ mol}} = +206.1\frac{\text{kJ}}{\text{ mol}}$$

and similarly

$$\Delta S_{m}^{\circ}(298K) = (3 \times 130.6 + 197.6 - 187.9 - 188.7)\frac{\text{ J}}{\text{ mol K}} = +212.8\frac{\text{ J}}{\text{ mol K}}$$

At 600 K we estimate

$$\Delta G_{m}^{\circ}=\Delta H^{\circ}(298 \text{ K}) - T\Delta S^{\circ}(298 \text{ K})$$

$$\qquad =206.1\frac{ \text{ kJ}}{\text{ mol}} - 600 \times 212.8\frac{\text{ J}}{\text{ mol}}$$

$$\qquad = (206.1 - 127.7)\frac{\text{kJ}}{\text{ mol}} = +78.4\frac{\text{ kJ}}{\text{ mol}}$$

Since $$\Delta G$$ is positive, the reaction is not spontaneous at this temperature

At 1200 K by contrast

$$\Delta G_{m}^{\circ}=206.1\frac{\text{ kJ}}{\text{ mol}} - 1200 \times 212.8\frac{\text{ J}}{\text{ mol}}$$

$$\qquad = (206.1 - 255.4)\frac{\text{ kJ}}{\text{ mol}} = -49.3\frac{\text{ kJ}}{\text{ mol}}$$

At this higher temperature, therefore, the reaction is spontaneous.

From more extensive tables we find that accurate values of the free-energy change are $$\Delta G_{m}^{\circ}(600 \text{ K}) = +72.6\frac{\text{ kJ}}{\text{ mol}}$$ and $$\Delta G_{m}^{\circ}(1200 \text{ K})=-77.7\frac{\text{ kJ} }{\text{ mol}}$$. Our approximate value at 1200 K is thus about 50 percent in error. Nevertheless it predicts the right sign for $$\Delta G$$, a result which is adequate for most purposes.

1. Baird, C., Cann, M. Environmental Chemistry. 3rd edition. 2005. W. H. Freeman and Company. 83-85.


text:
# Determining beta distribution parameters $\alpha$ and $\beta$ from two arbitrary points (quantiles)

Suppose I have two points $(p_1,x_1)$ and $(p_2,x_2)$ where $p_i$ is a probability on the beta CDF and $x_i$ is a value on that same CDF. How would I go about determining the beta distribution shape parameters $\alpha$ and $\beta$ with only these two points?

To clarify, I'm assuming I already know the lower and upper bounds of the distribution L and U.

• By definition a Beta distribution has bounds $0$ and $1$, so apparently you are referring to a scaled, recentered Beta. No matter: what is of import is how you obtained the numbers $p_1, p_2, x_1, x_2$. Are these given theoretically (that is, exactly), or have one or more of them been measured with some possibility of error? In all cases you will need to resort to numerical methods, but which methods are appropriate to use and how the output is interpreted depends on these distinctions. – whuber Aug 20 '14 at 13:57
• @whuber Apologies, I am referring to a scaled, recentered beta. The points would specified exactly. I had thought this might require numerical methods, but I wasn't sure and wanted to check if there might be an analytic solution. – gregor Aug 20 '14 at 14:06

### Solution

The transformation

$$(p, x) \to (p, (x-L)/(U-L))$$

converts these points to ones on CDFs for a Beta$(\alpha,\beta)$ distribution. Assuming this has been done (so we don't need to change the notation), the problem is to find $\alpha$ and $\beta$ for which

$$F(\alpha, \beta; x_i) = p_i, i = 1, 2$$

where the Beta CDF equals

$$F(\alpha,\beta; x) = \frac{\Gamma(\alpha+\beta)}{\Gamma(\alpha)\Gamma(\beta)}\int_0^x t^{\alpha-1}(1-t)^{\beta-1} dt.$$

This is a nice function of $\alpha \gt 0$ and $\beta \gt 0$: it is differentiable in those arguments and not too expensive to evaluate. However, there exists no closed-form general solution, so numerical methods must be used.

### Implementation Tips

Beware: when both $x_i$ are at the same tail of the distribution, or when either is close to $0$ or $1$, finding a reliable solution can be problematic. Techniques that are helpful in this circumstance are

1. Reparameterize the distributions to avoid enforcing the "hard" constraints $\alpha\ge 0, \beta \ge 0$. One that works is to use the logarithms of these parameters.

2. Optimize a measure of the relative error. A good way to do this for a CDF is to use the squared difference of the logits of the values: that is, replace the $p_i$ by $\text{logit}(p_i) = \log(p_i/(1-p_i))$ and fit $\text{logit}(F(\alpha,\beta;x_i))$ to these values by minimizing the sum of squared differences.

3. Either begin with a very good estimate of the parameters or--as experimentation shows--overestimate them. (This may be less necessary when following guideline #2.)

### Examples

Illustrating these methods is the following sample code using the nlm minimizer in R. It produces perfect fits even in the first case, which is numerically challenging because the $x_i$ are small and far out into the same tail. The output includes plots of the true CDFs (in black) on which are overlaid the fits (in red). The points on the plots show the two $(x_i, p_i)$ pairs.

This solution can fail in more extreme circumstances: obtaining a close estimate of the correct parameters can help assure success.

#
# Logistic transformation of the Beta CDF.
#
f.beta <- function(alpha, beta, x, lower=0, upper=1) {
p <- pbeta((x-lower)/(upper-lower), alpha, beta)
log(p/(1-p))
}
#
# Sums of squares.
#
delta <- function(fit, actual) sum((fit-actual)^2)
#
# The objective function handles the transformed parameters theta and
# uses f.beta and delta to fit the values and measure their discrepancies.
#
objective <- function(theta, x, prob, ...) {
ab <- exp(theta) # Parameters are the *logs* of alpha and beta
fit <- f.beta(ab[1], ab[2], x, ...)
return (delta(fit, prob))
}
#
# Solve two problems.
#
par(mfrow=c(1,2))
alpha <- 15; beta <- 22 # The true parameters
for (x in list(c(1e-3, 2e-3), c(1/3, 2/3))) {
x.p <- f.beta(alpha, beta, x)        # The correct values of the p_i
start <- log(c(1e1, 1e1))            # A good guess is useful here
sol <- nlm(objective, start, x=x, prob=x.p, lower=0, upper=1,
parms <- exp(sol$estimate) # Estimates of alpha and beta # # Display the actual and estimated values. # print(rbind(Actual=c(alpha=alpha, beta=beta), Fit=parms)) # # Plot the true and estimated CDFs. # curve(pbeta(x, alpha, beta), 0, 1, n=1001, lwd=2) curve(pbeta(x, parms[1], parms[2]), n=1001, add=TRUE, col="Red") points(x, pbeta(x, alpha, beta)) }  • @parvin You shouldn't be making any changes at all. As explained at the outset of this answer, the first thing my solution does is transform a scaled, shifted Beta variable into a standard Beta variable. In the code, the default parameters for l.beta (namely, lower=0 and upper=1) are for a standard Beta. – whuber Apr 10 '17 at 13:48 • @parvin Do it in three steps. 1: Initialize the quantiles and the logits of the probabilities (as described in the text of this answer): x <- c(.3, .8); x.p <- (function(p) log(p/(1-p)))(c(0.025, 0.975)). 2: Solve: start <- log(c(1e1, 1e1)); sol <- nlm(objective, start, x=x, prob=x.p, lower=0, upper=1, typsize=c(1,1), fscale=1e-12, gradtol=1e-12); parms <- exp(sol$estimate). 3: Check: qbeta(p = c(.025, .975), parms[1], parms[2]). The output will be "[1] 0.3 0.8", confirming the solution. Be sure to inspect sol$code to confirm convergence. – whuber Apr 10 '17 at 14:18 • @parvin I just gave you complete, working code. It will execute almost instantaneously if you have first run the example code in my answer. If you have further questions about how to use R, might I suggest you inquire on Stack Overflow? – whuber Apr 10 '17 at 15:07 • Dear whuber, Thank you very much, very thorough answer, as always. I was wondering (and I can post a question if my question would have a possible answer) though if given some empirical information about the (quantiles, mean, and variance), we can find the$\alpha~ and ~\beta$for a reasonably comparable beta-distribution that would have the similar quantiles, mean, and variance as provided by the empirical information? – rnorouzian Apr 16 '17 at 15:08 • @Jan The log is useless when$p_i$is close to$1.$Moreover, the logit treats probabilities symmetrically in the sense that its derivative at$p$is the same as its derivative at$1-p$and the Beta family is similarly symmetric in the sense that whenever$F$is a Beta distribution, so is the function$x\to 1-F(1-x).\$ Although the logarithm alone might work, both these characteristics suggest the logit will be even better and it's scarcely any more expensive to compute. – whuber May 28 at 12:30


text:
# Afteroffice

Wiki

### Site Tools

faq:email:how_to_increase_your_email_numberpage

# Differences

This shows you the differences between two versions of the page.

 faq:email:how_to_increase_your_email_numberpage [2016/06/17 10:04]leohoo created faq:email:how_to_increase_your_email_numberpage [2016/06/17 10:07] (current)leohoo 2016/06/17 10:07 leohoo 2016/06/17 10:04 leohoo created 2016/06/17 10:07 leohoo 2016/06/17 10:04 leohoo created Line 5: Line 5: - Login to your Vo account. - Login to your Vo account. - - Go to **Email**. \\ + - Go to **Email**. \\ {{:faq:email:1.png?nolink|}} - - Click on **Folder Setting** and select to **Setting** \\ + - Click on **Folder Setting** and select to **Setting** \\ {{:faq:email:2.png?nolink|}} - - You may now select to show how many messages in a page \\ + - You may now select to show how many messages in a page \\ {{:faq:email:3.png?nolink|}} - Press Update once you've done the setting - Press Update once you've done the setting


text:
# Permutations of Identical Objects (Part 1)

So far we’ve talked about permutations of objects which were distinct. Things change when some (or all) of the objects to be arranged are identical.

Suppose we have to arrange 5 balls in a row of which 3 are of the same color, and the other two are of different colors. How many different arrangements are possible?

Let’s designate five boxes, each of which is to be filled by one ball.

First, we’ll place the identical balls in any three of the five boxes. This can be done in 5C3 ways. Here’s one of them.

Next, in the remaining two boxes, we’ll place the remaining two balls. This can be done in 2! ways.

or

Therefore the total number of arrangements will be 5C3 x 2! = 5!/3! = 20.

Now let’s say 2 of the 5 balls are of the same color and the other 3 are of different colors. How many different arrangements are possible?

Similar to the method used above, we’ll first place the identical balls in any 2 of the 5 boxes, in 5C2 ways. One of the arrangement is given below.

Now in the remaining three boxes, the remaining three balls can be placed in 3! ways.

Therefore the total number of arrangements will be 5C2 x 3! = 5!/2! = 60.

We could also have placed the different colored balls first. This can be done by first selecting any three boxes, (in 5C3 ways), and then placing the balls in the boxes (3! ways).

After we’ve placed these three balls, the remaining two balls will be filled with the two identical balls (which can be done in only one way).

The answer remains the same (5C3 x 3!) x 1 = 5!/2! = 60

Do you see a pattern? Had the 5 balls been all of different colors, the total number of arrangements would have been 5!. When 3 of the balls were identical, the answer changed to 5!/3!, and when 2 of them were identical, the answer was 5!/2!. Can we arrive at a formula or a generalisation?

Suppose there are n objects, to be arranged in a row, of which p objects are identical, and the remaining are distinct. How many arrangements are possible?

In this case we have n boxes, each to be filled with one ball. We’ll first select any p boxes out of the n boxes, in nCp ways. Now we’ll place the identical balls in the selected boxes, one in each. We’re now left with n – p boxes and n – p balls, which can be placed in the boxes in (n – p)! ways.

Therefore the total number of ways is nCp (n – p)! or n!/p!

## Lesson Summary

1. The number of ways to arrange n objects in a row, of which exactly p objects are identical, is n!/p!

I’ll pause here, and take a few more cases involving identical objects in the next part of the lesson. See you there.


text:
Theory:

In many scientific applications, it may need to measure the higher than $$42$$$$°C$$ and lesser than $$35$$$$°C$$. In such cases, clinical thermometers can't be used, and the need for laboratory thermometers arise. Laboratory or Lab thermometers are the instruments used to measure the temperatures for scientific research in schools and labs.
Laboratory or Lab thermometers are the instruments used to measure the temperatures for scientific research in schools and labs.
Laboratory thermometer

Lab thermometers are designed to measure substances' temperatures and also find the boiling point and freezing point.

Experimental setup to measure the temperature

In industries, it is used to measure the temperature higher than what clinical thermometers can do.

Structure of the laboratory thermometer:
• Compared to clinical thermometers, lab thermometers have a long narrow tube (stem) and bulb.
• Laboratory thermometers do not have a kink.
Temperature scale in laboratory thermometer:
• It has only the Celsius scale ranging from $$−$$$$10$$$$°C$$ to $$110$$$$°C$$.
Important!
Precautions to be followed while using a laboratory thermometer:
• Do not tilt (bend) the lab thermometer while doing the temperature measurement. Place it upright.
• Record the readings only when the substances from all the sides have surrounded the bulb.
• Make sure that the bulb is not be in contact with the bottom or sides of the container.
• While doing the measurements, do not move the thermometer.
Differences between clinical and laboratory thermometers:

 Parameter to be compared Clinical thermometer Laboratory thermometer Application Clinical (Hospitals). Scientific Research and Laboratories Uses It is used to measure the human body temperature. It is used to determine the boiling point and freezing point of the substances. Range $$35$$$$°C$$ to $$42$$$$°C$$ / $$94$$$$°F$$ to $$108$$$$°F$$ $$10$$$$°C$$ to $$110$$$$°C$$ Structure Mercury level does not fall on its own, as there is a kink near the bulb, which stops the mercury from returning into the bulb Mercury level falls on its own as no kink is present. Working We can read the temperature after removing the thermometer from the armpit or mouth. Temperature is read while keeping the thermometer in the temperature source, e.g. a liquid or any other thing. Restoration Jerks are given to lower the mercury level. No need to give a jerk to lower the mercury level.


text:
# Probability density for velocity in mechanical energy

To be sure my basic physics isn't rusty...

Consider a 2D bowled shaped classical potential well within which a classical particle of mass m is rolling. In this system the conservation of energy holds so the particle of mass m would roll from one end to another-indefinitely.

Because conservation of energy holds, we expect the mechanical energy to be

$E=T + U = \frac{1}{2}mv^{2}-mgh$

where $v$ is the velocity of the particle

$g$ is the gravitational acceleration

and

$h$ is the heigh relative to the ground.

In classical physics, the maximum velocity of the particle occurs when the particle is at $r=\left ( x,h=0 \right )$ and the minimum velocity occurs when the particle is at some position $r=\left ( x,h \right ) \exists h$ on both end of the well such that its kinetic energy T is 0 and potential energy U is at maximum.

Again, this follows from the conservation of energy:

$\Delta T= - \Delta U$

Now, I would like to construct a mathematical equation describing the probability of finding this particle of mass m as a function of its velocity. Intuitively, the greater the velocity of the particle at some point the lower the probability to find the particle and the smaller its velocity is the higher the probability to find the particle.

Solving $E=T + U = \frac{1}{2}mv^{2}-mgh$ for v:

$v=\sqrt{\frac{2 \left ( E+mgh \right ) }{m}}$

If we want to explictly determine the probability of finding the particle as a function of its velocity, we should expect the probability density as a function of velocity to be of the form

$P=P\left ( v \right ) \propto \frac{1}{v}$

which comports to our common sense intuition.

How can I go about constructing a more explicit and informative equation that would enable to me determine the probability of finding the particle as a function of its velocity?

Any help is appreciated.

• Your particle isn't rolling, it's sliding. It needs a $\frac{1}{2}I\omega^2$ term to complicated things. – JEB Nov 2 '17 at 1:32
• Nitpick: the sign of the potential energy U is off: U increases with increasing h, while v decreases comeasurately. – Cosmas Zachos Nov 2 '17 at 14:23

I assume you are only interested in 2d motion in the (x,h) plane, so you are taking vanishing angular momentum, which would only complicate the problem.

Your essential error is that the "intuitive" form you have is wrong--it would make sense as a probability density in arclength, but not in v. That is, if you can review for the much simpler classical oscillator, the system spends more time at some xs or vs than in others, in general disproportionately so: consider t(x) or t(v).

For a half-period τ/2, the infinitesimal probability of the marble with v in the interval dv is
$$\frac {2dt}{\tau}=\frac{2}{\tau} \frac{dv}{\dot{v}}=P(v)dv ~,$$ that is, you need $\dot{v}$ as a function of v and E which is definitely a function of the shape of the bowl. The process flows linearly in time, but nonlinearly w.r.t. functions of the time, such as x(t), v(t), etc, and must be adjusted by the corresponding Jacobian determinants in the measure.

I will set up the problem for a parabolic bowl, $h=kx^2$, based on this answer, but won't pursue the general bowl shape case -- maybe there is a slick solution. $$T= \frac{m}{2}(\dot{x}^2 + \dot{h}^2) = \frac{m}{2} v^2= \frac{m}{2}(\dot{x}^2 + (2kx\dot{x})^2)=\frac{m}{2}\dot{x}^2(1 + 4k^2x^2) , ~~~~~~U= mgh =mgkx^2.$$ h has been eliminated. The Euler-Lagrange equation of motion reduces to
$$(1+4k^2x^2)\ddot{x}+4k^2\dot{x}^2x+2gkx=0 .$$

Since $E=\frac{m}{2} v^2+ mgkx^2$, and $$\frac{d}{dt} v^2= 2v \dot{v}=2 \dot{x} \ddot{x}(1 + 4k^2x^2) + 8k^2 x \dot{x}^3\\ = -4gkx\dot{x}=-4gkv\frac{x}{\sqrt{1+4k^2x^2}},$$ all you have to do is eliminate x in favor of v and E, to find $\dot{v}$ as a function of v and E, $$\dot{v}=2gk~/\sqrt{4k^2+mgk/(E-mv^2/2)}~.$$ As t goes from 0 to τ/4, v goes from 0 to $\sqrt{2mE}$.

I doubt if what you're trying to achieve is possible without defining the shape of the well.

One well behaved system is the parabolic potential well, for which:

$$h\propto x^2$$

And thus:

$$U(x)=kx^2$$

That can be Classically treated or (for very small systems) we can use the Schrödinger equation (here time-independent and in the $x$-dimension only):

$$\Big[-\frac{\hbar}{2m}\nabla^2+U(x)\Big]\Psi(x)=E\Psi(x)$$

The wave functions $\Psi_n(x)$ and energy levels $E_n$ are well known and on display in the link, as it is the case of the Quantum Harmonic Oscillator. (A full derivation can be found here).

Find the velocity by dividing the momentum operator by mass $m$:

$$\hat{v}=-\frac{i}{m}\hbar \nabla$$

Without defining $U(x)$, no precise quantum information can be obtained because the Schrödinger equation cannot be solved.


text:
# What is "code" in "toric code"?

+ 7 like - 0 dislike
113 views

When I first heard people talking about using Kitaev's toric code to do topological quantum computation, I was thinking how many lines does the toric code have. Then I was told that the "code" really represents quantum states. Later, I understood that the "code" is the degenerate ground subspace of a gapped Hamiltonian. But then I was corrected by people from quantum information who pointed out that code is a subspace of the Hilbert space of a quantum system, but code is also more than a subspace.

So now I am wondering what is "code"?

This post imported from StackExchange Physics at 2014-04-05 17:30 (UCT), posted by SE-user Xiao-Gang Wen
There is a link now provided by the editing. paragraph 2.2.1 seems to be using the definition of "code" as "The toric code is the simplest topological lattice model that supports Abelian anyons." I guess the word "code" is used as in "encode", a code encodes a specific model?

This post imported from StackExchange Physics at 2014-04-05 17:30 (UCT), posted by SE-user anna v
Here we have yet another difinition of "code": "code" is a quantum qubit model. This is very different from "code" is a subspace.

This post imported from StackExchange Physics at 2014-04-05 17:30 (UCT), posted by SE-user Xiao-Gang Wen
@anna - In my opinion this question is trying to imply subspace is logically similar to a qbit model and therefore mathematically predictable.

This post imported from StackExchange Physics at 2014-04-05 17:30 (UCT), posted by SE-user Argus

+ 8 like - 0 dislike

Let me try to give you the answer in just the right amount of generality. A quantum code is just a short way to say a quantum error-correcting code. It is a special embedding of one vector space into another larger one that satisfies some additional properties. If we start with a Hilbert space $H$, then a code is a decomposition into $H = (A \otimes B) \oplus C$. The quantum information is encoded into system $A$. In the event that $B$ is trivial, then indeed this is just a subspace of $H$. When $B$ is nontrivial, we say call it a subsystem code. Let's specialize to the case of $n$ qubits, so that $H = (\mathbb{C}^2)^{\otimes n}$, and it is easiest to imagine that the dimensions of $A$, $B$, and $C$ are all powers of 2, though of course this discussion could be generalized.

Let $P$ be the orthogonal projector onto $A\otimes B$, and let $\mathcal{E}$ be an arbitrary quantum channel, i.e. a completely positive trace preserving linear map. We say that $\mathcal{E}$ is recoverable if there exists another quantum channel $\mathcal{R}$ such that for all states $\rho_A \otimes \rho_B$, we have $$\mathcal{R}\circ\mathcal{E}(\rho_A \otimes \rho_B) = \rho_A \otimes \rho'_B,$$ where $\rho'_B$ is arbitrary. This says that for any state which is supported on $A\otimes B$ and is initially separable, we can reverse the effects of $\mathcal{E}$ up to a change on system $B$.

Fortunately, there are simpler equivalent conditions that one can check instead. For example, an equivalent condition can be stated in terms of the Kraus operators $E_j$ for the channel $\mathcal{E}$. The subsystem $A$ is correctable for $\mathcal{E}(\rho) = \sum_j E_j \rho E_j^\dagger$ if an only if for all $i,j$, there exists a $g^{ij}_B$ on subsystem $B$ such that $$P E_i^\dagger E_j P = 1\hspace{-3pt}\mathrm{l}_A \otimes g^{ij}_B.$$ You can interpret this condition as saying that no error process associated to the channel $\mathcal{E}$ can gain any information about subsystem $A$.

Consider error channels which consist of Kraus operators that, when expanded in the Pauli basis, only have support on at most $d$ of the $n$ qubits in our Hilbert space. If every such channel is correctable for subsystem $A$, then we say our code has distance $d$. The largest such $d$ is called the distance of the code. For the toric code, this is the linear size of the lattice.

This post imported from StackExchange Physics at 2014-04-05 17:30 (UCT), posted by SE-user Steve Flammia
answered Jun 4, 2012 by (110 points)

Thanks for the detailed description of "code". According your description, "code" is a subspace, but "code" also has something more. It is still not very clear what is "code". If "code" is subspace + something, then what is this "something". You explained why code is important for error correction in quantum computation, which is very nice. But do we have a straight forward definition of "code"?

This post imported from StackExchange Physics at 2014-04-05 17:30 (UCT), posted by SE-user Xiao-Gang Wen

A code is simply the decomposition $H = (A \otimes B)\oplus C$. By itself, this is too general to be interesting. Therefore, people only emphasize that something is a code when it has additional properties. For example, people call it the "toric code" because it can correct quantum errors. The simple 2D ferromagnetic Ising model is also a code... but it only encodes a single classical bit, and corrects no quantum errors. So you will never hear people talk about the "Ising code". Sorry if the answer is disappointing, but it is really just that decomposition!

This post imported from StackExchange Physics at 2014-04-05 17:30 (UCT), posted by SE-user Steve Flammia

Now I see: "code" is like a piece of a drawing, it may be an art, or it may be not. (BTW I do like your answer very much.)

+ 1 like - 0 dislike

In general a "code" in quantum information is a collection of "codewords". One takes a (relatively large) number of physical qubits and considers only a limited number of states (i.e. a low-dimensional subspace) out of the full Hilbert space (formally, the code is the subspace). For stabilizer codes, all of these states are ground states of some gapped hamiltonian. Because there is a good deal of redundancy, the system is more robust against errors and decoherence.

Perhaps a clearer example would be the repetition code. Say you have six qubits, but you restrict yourself to the subspace spanned by $$\{|000,000\rangle,|000,111\rangle,|111,000\rangle,|111,111\rangle\}.$$ You can then think of these long combinations as "codewords" for the logical states $$\{|00\rangle,|01\rangle,|10\rangle,|11\rangle\},$$ but they can still be recognized if any given qubit suffers some error.

This post imported from StackExchange Physics at 2014-04-05 17:30 (UCT), posted by SE-user Emilio Pisanty
answered Jun 3, 2012 by (520 points)
Thanks for the intuitive and pictorial explain of code. But I still like to know what is "code" exactly. If "code" is subspace + something, then what is this "something". Or maybe the "code" is just a subspace with nothing more (?).

This post imported from StackExchange Physics at 2014-04-05 17:30 (UCT), posted by SE-user Xiao-Gang Wen

 Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead. To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL. Please consult the FAQ for as to how to format your post. This is the answer box; if you want to write a comment instead, please use the 'add comment' button. Live preview (may slow down editor)   Preview Your name to display (optional): Email me at this address if my answer is selected or commented on: Privacy: Your email address will only be used for sending these notifications. Anti-spam verification: If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:p$\hbar$y$\varnothing$icsOverflowThen drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds). To avoid this verification in future, please log in or register.


text:
# How can I set my server to only accept requests from my own client app? (similar to SSL Client Certificates)

I'd like to have my server APIs only accept requests from my own app, to prevent other "rogue" clients of my service.

As i understand it, the way to do this would be with a "client certificate" that the app sends, and that the web server is configured to verify.

However, I'm hosting my app in Heroku, and I believe it's not possible to do that, so I'm looking for something as good as possible that would allow me to achieve this.

I thought that maybe I could have a key pair, where the client uses a private key to sign a certain agreed-upon token (plus some random salt, so that the encrypted string is always different), and the server uses the public key to verify the token (and rejects duplicate salts to prevent replay). Or maybe the client signs the whole request with its private key, or something like that.

The idea would be that even if someone manages to get around our SSL pinning (with something like iOS kill switch, potentially) and inspect our traffic and figure out how our API works, they still can't call us unless they reverse engineer the binary to extract that certificate / private key. I understand that it's possible to do that, I'm just trying to put up as many barriers as possible.

What are good ways of doing this?

Thanks!
Daniel

• If you can't use SSL client certs then do some additional crypto on top of SSL. – user42178 Feb 17 '15 at 13:03
• You can build a ssl-like process. But you shouldn't encrypt all data with asymmetric encryption because its slow. Hardcode servers public key to your app, create a random crypto string and after encrypting it with servers public key, send it to server. On the serverside you can decrypt the key that your client sent and start encrypting the data with this key since both client and server know it. But use SSL even you have your own encryption layer – Batuhan Feb 17 '15 at 13:25
• SSL was deprecated over a decade ago, I sure hope you aren't using SSL. TLSv1 or later is the only acceptable secure transport layer. – rook Feb 17 '15 at 14:46
• @Rook I'm probably using TLS. Whatever's "the default"? I bought a certificate and gave it to Heroku. Sorry, but I'm a n00b at the details of this. – Daniel Magliola Feb 18 '15 at 14:13

This type of problem lends itself to Cargo-Cult Security type "solutions".

In the real world there is no possible mechanism that can prevent a rogue client from connecting to your service. A VPN is a proven security system that allows trusted clients access to a trusted network, but the internet is inherently untrustworthy. The attacker will have access to any secret embedded in your app, or stored in app memory, TLS client certificates rely upon a secret.

When designing a web service never forget: "The client is the attacker, and can never be trusted." If you have made this mistake, then you need to go back to the drawing board.

• I understand this, but my intention is to make it as hard / annoying as possible to raise the "minimum motivation level" needed to actually do this. My server is secure and you can't do anything nasty to it from the outside (that I know of), but I still don't want people making their own clients. So far, if I don't check anything on the server, you don't need to touch the app binary to extract any secrets. Forcing an attacker to do so is one more hurdle, one more hoop, that will hopefully dissuade them. – Daniel Magliola Feb 18 '15 at 10:06
• @Daniel Magliola The only one you are fooling with cargo-cult security is yourself. – rook Feb 18 '15 at 13:44
• @DanielMagliola that's DRM, and will always eventually fail – Natanael Mar 20 '15 at 14:34
• DRM and code obfuscation will indeed never stop a motivated attacker, but if his objective is just to make it more annoying to create a custom client, it nevertheless is the valid approach. – Dillinur Apr 30 '15 at 12:27

Note

This answer is only applicable under the stated assumptions. I have made them based upon the explicit wording of the question, which explicitly allows for a known attack vector to not be mitigated.

Security is a relative balance between the value of loss should an asset be compromised, and the effort (incl. cost etc.) that an adversary is willing to make to achieve such compromise. It is the author's prerogative to decide upon such a balance as they have the full picture regarding stakeholders.

Assumptions

The threat you are attempting to mitigate is one of an adversary who can read / tamper with their own communications, impersonate the client, but not reverse engineer the contents of the binary (either due to a lack of technical capability, or a lack of willingness).

TL;DR

HMAC(message | nonce, key) along with the client message / nonce "in the clear" (over TLS, but without any further encryption).

Your question is one of authentication, but you appear to be attempting to solve it with encryption (yes there is some crossover in certain circumstances, but separating the two will make the answer easier).

If a secret key (not an asymmetric private key; just a sufficiently large, cryptographically secure, random number) is stored in the binary (as you were proposing with a public/private key-pair) then it is not revealed by knowledge of the HMAC/plaintext pair.

Your server is also knowledgeable of the key, computes the HMAC for the message received, and discards any client communications that are invalid. The nonce is provided by the server to the client before it sends the message, and is unique. It acts to protect against replays of intercepted messages.

Caveat

As noted earlier and in other answers / comments, one may still obtain the key from the binary. For those who are interested there is a really cool technique that calculates the entropy for all regions of the binary, and then maps the linear position to a Hilbert curve. Machine code regions will have a relatively lower entropy than 'key' regions. Chris Domas demonstrates this in one of his videos; possibly his TED talk although I can't remember (watch the TED video either way).

• again, that merely moves the client secret around - a malicious user would still be able to find it and use it for his own bogus app. – AviD Apr 30 '15 at 17:46
• I agree. However, as I stated in the paragraph regarding assumptions, this is a risk that the author is explicitly willing to take. Security is a relative balance between the value of loss should an asset be compromised, and the effort (incl. cost etc.) that an adversary is willing to make to achieve such compromise. It is the author's prerogative to make such a balance as they have the full picture regarding stakeholders. I will update my answer accordingly. – Arran Schlosberg Apr 30 '15 at 22:07

You can go with any of the tunneling mechanism to accept the particular IP's in the server side or else simply configure your firewall to accept the list of trusted clients.

• Unfortunately, my client is a mobile app, so I can't whitelist IPs... Any other ideas? – Daniel Magliola Feb 18 '15 at 10:02
• In case you can try for google oAuth mechanism or OTP to client as banks doing. – user45475 Feb 18 '15 at 20:27

Use OAuth2.0 . It not only authorize the user, but also client application with client_id and client_key properties.

• What does prevent an application from spoofing those attributes? – Dillinur Apr 30 '15 at 12:28
• I am not sure but maybe you can store them into local db in the client app with encryption in development time. In run time, the app gets the data an sends to server in oauth post body. In the server side you can know from which server does the request come from..According to the credentials, you can send token to client.. And if you use ssl, then no network sniffer catch it. – yeulucay May 8 '15 at 8:46
• "store them into local db in the client app" - Then I just copy the local db from the client app to my clone app. "with encryption in development time" - if your app can decrypt the data, so can my clone app. Whatever information I need to do that can be extracted from your app. If your app can not decrypt the data, then my app doesn't need to be able to do that either. – Philipp Jul 26 at 8:29


text:
# Scheduling 12 teams competing at 6 different events

I have a seemingly simple question. There are 12 teams competing in 6 different events. Each event is seeing two teams compete. Is there a way to arrange the schedule so that no two teams meet twice and no teams repeat an event.

Thanks.

Edit: Round 1: All 6 events happen at the same time. Round 2: All 6 events happen at the same time. And so on until Round 6.

-
Sure-don't play any games. More seriously, do you want each team to play 6 games, in which case they will only meet 6 other teams? It should be easy-just start making a chart. –  Ross Millikan May 18 '12 at 18:08
I once spent some hours writing up code for solving this exact problem (but with more teams) for a summer camp. Suddenly a guy walked in the door, handed me a hand-made solution, said nothing and left. –  utdiscant May 18 '12 at 18:13
Yes, each team only meets 6 other teams. I tried to make some chart but the constraints become very difficult to fulfill. The reason for such difficulty has to do with the number 6. If there were 14 teams competing in 7 events it would be much easier: it suffices to set up the teams in two groups of 7 and rotate them any which way through the 7 (prime number) events. –  Minh May 18 '12 at 18:27
This is reminiscent of en.wikipedia.org/wiki/Kirkman's_schoolgirl_problem –  deoxygerbe May 18 '12 at 19:00

A solution to the specific problem is here:

Event 1     Event 2     Event 3     Event 4     Event 5     Event 6
1  - 2      11 - 1      1  - 3      6  - 1      10 - 1      1  - 9
3  - 4      2  - 3      4  - 2      2  - 11     2  - 9      10 - 2
5  - 6      4  - 5      5  - 7      7  - 4      3  - 11     4  - 8
7  - 8      6  - 7      8  - 6      3  - 10     4  - 6      7  - 3
9  - 10     8  - 9      10 - 11     9  - 5      8  - 5      11 - 5
11 - 12     12 - 10     9  - 12     12 - 8      7  - 12     12 - 6

which came from the following webpage: http://www.crowsdarts.com/roundrobin/sched12.html

-
I realize my query wasn't specific enough. I made an edit. The above solution doesn't quite work. –  Minh May 18 '12 at 18:47
@Minh: What doesn't work? Maybe you want to label each column "Round 1" instead of Event 1? –  Phira May 18 '12 at 19:27
@Phira: Say you label each column "Round x", then you have to label each row "Event y". Then you don't want any team repeating an event. –  Minh May 18 '12 at 19:31

This can be solved generally for events of two teams where the number of events is half the number of teams and the number of rounds is one less than the number of teams.

Represent a schedule as an edge-colored complete graph. Let the vertices correspond to teams, edges correspond to an event, and colors coorespond to a round.

The graph is laid out with one vertex in the center and the remainder equally spaced in a circle around the center vertex. Each "spoke" (edge from center vertex to an outer vertex) and edges perpendicular to it share a color. In other words, a spoke from the center to an outer vertex, $v$, shares a color with edges on the vertices $n$ to the right and $n$ to left of $v$, for $0<n<\frac{t}{2}$ where $t$ is the number of teams.

Therefore, for the specific case in the question, we have the following edge-colored complete graph.

Since this problem only asks for the first 6 rounds, we can use the first 6 rounds generated by the graph.

        Color   Event 1    2     3     4     5     6
Round 1 (Black)     (A-B) (C-L) (D-K) (E-J) (F-I) (G-H)
Round 2 (Red)       (A-C) (B-D) (E-L) (F-K) (G-J) (H-I)
Round 3 (Yellow)    (A-D) (B-F) (C-E) (G-L) (H-K) (I-J)
Round 4 (Blue)      (A-E) (B-H) (C-G) (D-F) (I-L) (J-K)
Round 5 (Green)     (A-F) (B-J) (C-I) (D-H) (E-G) (K-L)
Round 6 (Orange)    (A-G) (B-L) (C-K) (D-J) (E-I) (F-H)

-


text:
These instructions explain how to compile VLFeat from sources. While this is necessary in order to develop or modify VLFeat, using the pre-compiled binaries will work in most other cases.

VLFeat is largely self-contained and hence easy to compile. While certain features such as multi-core computation and vector instruction support may require specific compilers, most compilers and environments should be capable of producing fully functional version of the library. Compiling MATLAB or Octave support requires the corresponding applications to be installed too.


text:
I have the blueprints. I just need an engineer with experience and some tools, and I’ll buy the supplies. [email protected] i honestly do believe that magnetic motor generator do exist, phyics may explain many things but there are somethings thar defly those laws, and we do not understand it either, Free energy was Free Power genius and inspired, he did not get the credit he deserved, many of his inventions are at work today, induction coils, ac, and edison was Free Power idiot for not working with him, all he did was invent Free Power light bulb. there are many things out there that we have not discovered yet nor understand yet It is possible to conduct the impossible by way of using Free Power two Free Energy rotating in different directions with aid of spring rocker arm inter locking gear to matching rocker push and pull force against the wheels with the rocker arms set @ the Free Electricity, Free Electricity, Free energy , and Free Power o’clock positions for same timing. No further information allowed that this point. It will cause Free Power hell lot of more loss jobs if its brought out. So its best leaving it shelved until the right time. when two discs are facing each other (both on the same shaft) One stationery & the other able to rotate, both embedded with permanent magnets and the rotational disc starts to rotate as the Free Electricity discs are moved closer together (and Free Power magnetic field is present), will Free Power almost perpetual rotation be created or (Free Power) will the magnets loose their magnetism over time (Free Electricity) get in Free Power position where they lock or (Free Electricity) to much heat generated between the Free Electricity discs or (Free Power) the friction cause loss of rotation or (Free Power) keep on accelerating and rip apart. We can have powerful magnets producing energy easily.
I might have to play with it and see. Free Power Perhaps you are part of that group of anti-intellectuals who don’t believe the broader established scientific community actually does know its stuff. Ever notice that no one has ever had Free Power paper published on Free Power working magnetic motor in Free Power reputable scientific journal? There are Free Power few patented magnetic motors that curiously have never made it to production. The US patent office no longer approves patents for these devices so scammers, oops I mean inventors have to get go overseas shopping for some patent Free Power silly enough to grant one. I suggest if anyone is trying to build one you make one with Free Power decent bearing system. The wobbly system being shown on these recent videos is rubbish. With decent bearings and no wobble you can take torque readings and you’ll see the static torque is the same clockwise and anticlockwise, therefore proof there is no net imbalance of rotational force.
Not Free Power lot to be gained there. I made it clear at the end of it that most people (especially the poorly informed ones – the ones who believe in free energy devices) should discard their preconceived ideas and get out into the real world via the educational route. “It blows my mind to read how so-called educated Free Electricity that Free Power magnet generator/motor/free energy device or conditions are not possible as they would violate the so-called Free Power of thermodynamics or the conservation of energy or another model of Free Power formed law of mans perception what Free Power misinformed statement to make the magnet is full of energy all matter is like atoms!!”
Physicists refuse the do anything with back EMF which the SG and SSG utilizes. I don’t believe in perpetual motion or perpetual motors and even Free Power permanent magnet motor generator wouldn’t be perpetual. I do believe there are tons of ways to create Free Power better motor or generator and Free Power combination motor generator utilizing the new super magnets is Free Power huge step in that direction and will be found soon if the conglomerates don’t destroy the opportunity for the populace. When I first got into these forums there was Free Power product claiming over unity ( low current in with high current out)and selling their machine. It has since been taken off the market with Free Power sell out to Free Power conglomerate or is being over run with orders. I don’t know! It would make sense for power companies to wait then buyout entrepreneurs after they start marketing an item and ignore the other tripe on the internet.. Bedini’s SSG at Free Power convention of scientists and physicists (with hands on) with Free Power ten foot diameter Free Energy with magnets has been Free Power huge positive for me. Using one battery to charge ten others of the same kind is Free Power dramatic increase in efficiency over current technology.
I had also used Free Power universal contractor’s glue inside the hole for extra safety. You don’t need to worry about this on the outside sections. Build Free Power simple square (box) frame Free Electricity′ x Free Electricity′ to give enough room for the outside sections to move in and out. The “depth” or length of it will depend on how many wheels you have in it. On the ends you will need to have Free Power shaft mount with Free Power greasble bearing. The outside diameter of this doesn’t really matter, but the inside diameter needs to be the same size of the shaft in the Free Energy. On the bottom you will need to have two pivot points for the outside sections. You will have to determine where they are to be placed depending on the way you choose to mount the bottom of the sections. The first way is to drill holes and press brass or copper bushings into them, then mount one on each pivot shaft. (That is what I did and it worked well.) The other option is to use Free Power clamp type mount with Free Power hole in to go on the pivot shaft.
In most cases of interest there are internal degrees of freedom and processes, such as chemical reactions and phase transitions, which create entropy. Even for homogeneous “bulk” materials, the free energy functions depend on the (often suppressed) composition, as do all proper thermodynamic potentials (extensive functions), including the internal energy.
The torque readings will give the same results. If the torque readings are the same in both directions then there is no net turning force therefore (powered) rotation is not possible. Of course it is fun to build the models and observe and test all of this. Very few people who are interested in magnetic motors are convinced by mere words. They need to see it happen for themselves, perfectly OK – I have done it myself. Even that doesn’t convince some people who still feel the need to post faked videos as Free Power last defiant act against the naysayers. Sorry Free Power, i should have asked this in my last post. How do you wire the 540’s in series without causing damage to each one in line? And no i have not seen the big pma kits. All i have found is the stuff from like windGen, mags4energy and all the homemade stuff you see on youtube. I have built three pma’s on the order of those but they don’t work very good. Where can i find the big ones? Free Power you know what the 540 max watts is? Hey Free Power, learn new things all the time. Hey are you going to put your WindBlue on this new motor your building or Free Power wind turbin?

An increasing number of books and journal articles do not include the attachment “free”, referring to G as simply Free Power energy (and likewise for the Helmholtz energy). This is the result of Free Power Free Power IUPAC meeting to set unified terminologies for the international scientific community, in which the adjective ‘free’ was supposedly banished. [Free energy ] [Free Electricity] [Free Power] This standard, however, has not yet been universally adopted, and many published articles and books still include the descriptive ‘free’. Get free electricity here.
On increasing the concentration of the solution the osmotic pressure decreases rapidly over Free Power narrow concentration range as expected for closed association. The arrow indicates the cmc. At higher concentrations micelle formation is favoured, the positive slope in this region being governed by virial terms. Similar shaped curves were obtained for other temperatures. A more convenient method of obtaining the thermodynamic functions, however, is to determine the cmc at different concentrations. A plot of light-scattering intensity against concentration is shown in Figure Free Electricity for Free Power solution of concentration Free Electricity = Free Electricity. Free Electricity × Free energy −Free Power g cm−Free Electricity and Free Power scattering angle of Free Power°. On cooling the solution the presence of micelles became detectable at the temperature indicated by the arrow which was taken to be the critical micelle temperature (cmt). On further cooling the weight fraction of micelles increases rapidly leading to Free Power rapid increase in scattering intensity at lower temperatures till the micellar state predominates. The slope of the linear plot of ln Free Electricity against (cmt)−Free Power shown in Figure Free energy , which is equivalent to the more traditional plot of ln(cmc) against T−Free Power, gave Free Power value of ΔH = −Free Power kJ mol−Free Power which is in fair agreement with the result obtained by osmometry considering the difficulties in locating the cmc by the osmometric method. Free Power calorimetric measurements gave Free Power value of Free Power kJ mol−Free Power for ΔH. Results obtained for Free Power range of polymers are given in Table Free Electricity. Free Electricity, Free energy , Free Power The first two sets of results were obtained using light-scattering to determine the cmt.
The solution to infinite energy is explained in the bible. But i will not reveal it since it could change our civilization forever. Transportation and space travel all together. My company will reveal it to thw public when its ready. My only hint to you is the basic element that was missing. Its what we experience in Free Power everyday matter. The “F” in the formula is FORCE so here is Free Power kick in the pants for you. “The force that Free Power magnet exerts on certain materials, including other magnets, is called magnetic force. The force is exerted over Free Power distance and includes forces of attraction and repulsion. Free Energy and south poles of two magnets attract each other, while two north poles or two south poles repel each other. ” What say to that? No, you don’t get more out of it than you put in. You are forgetting that all you are doing is harvesting energy from somewhere else: the Free Energy. You cannot create energy. Impossible. All you can do is convert energy. Solar panels convert energy from the Free Energy into electricity. Every second of every day, the Free Energy slowly is running out of fuel.
I looked at what you have for your motor so far and it’s going to be big. Here is my e-mail if you want to send those diagrams, if you know how to do it. [email protected] My name is Free energy MacInnes from Orangeville, On. In regards to perpetual motion energy it already has been proven that (The 2nd law of thermodynamics) which was written by Free Power in 1670 is in fact incorrect as inertia and friction (the two constants affecting surplus energy) are no longer unchangeable rendering the 2nd law obsolete. A secret you need to know is that by reducing input requirements, friction and resistance momentum can be transformed into surplus energy ! Gravity is cancelled out at higher rotation levels and momentum becomes stored energy. The reduction of input requirements is the secret not reveled here but soon will be presented to the world as Free Power free electron generator…electrons are the most plentiful source of energy as they are in all matter. Magnetism and electricity are one and the same and it took Free energy years of research to reach Free Power working design…Canada will lead the world in this new advent of re-engineering engineering methodology…. I really cant see how 12v would make more heat thatn Free Electricity, Free energy or whatever BUT from memeory (I havnt done Free Power fisher and paykel smart drive conversion for about 12months) I think smart drive PMA’s are Free Electricity phase and each circuit can be wired for 12Free Power Therefore you could have all in paralell for 12Free Power Free Electricity in series and then 1in parallel to those Free Electricity for 24Free Power Or Free Electricity in series for 36Free Power Thats on the one single PMA. Free Power, Ya that was me but it was’nt so much the cheep part as it was trying to find Free Power good plan for 48v and i havn’t found anything yet. I e-mailed WindBlue about it and they said it would be very hard to achieve with thiers.
My older brother explained that in high school physics, they learned that magnetism is not energy at all. Never was, never will be. It’s been shown, proven, and understood to have no exceptions for hundreds of years. Something that O. U. should learn but refuses to. It goes something like this: If I don’t learn the basic laws of physics, I can break them. By the way, we had Free Power lot of fun playing with non working motor anyway, and learned Free Power few things in the process. My brother went on to get his PHD in physics and wound up specializing in magnetism. He designed many of the disk drive plates and electronics in the early (DOS) computers. bnjroo Harvey1 Thanks for the reply! I’m afraid there is an endless list of swindlers and suckers out there. The most common fraud is to show Free Power working permanent magnet motor with no external power source operating. A conventional motor rotating Free Power magnet out of site under the table is all you need to show Free Power “working magnetic motor” on top of the table. How could I know this? Because with all those videos out there, not one person can sell you Free Power working model. Also, not one of these scammers can ever let anyone not related to his scam operate the motor without the scammer hovering around. The believers are victims of something called “Confirmation Bias”. Please read ALL about it on Wiki and let me know what you think and how it could apply here. This trap has ensnared some very smart people. Harvey1 bnjroo Free Energy two books! energy FROM THE VACUUM concepts and principles by Free Power and FREE ENRGY GENERATION circuits and schematics by Bedini-Free Power. Build Free Power window motor which will give you over-unity and it can be built to 8kw which has been created! NOTHING IS IMPOSSIBLE! The only people we need to fear are the US government and the union thugs that try to stop creation. Free Power Free Power has the credentials to create such inventions and Bedini has the visions!
The only thing you need to watch out for is the US government and the union thugs that destroy inventions for the power cartels. Both will try to destroy your ingenuity! Both are criminal elements! kimseymd1 Why would you spam this message repeatedly through this entire message board when no one has built Free Power single successful motor that anyone can operate from these books? The first book has been out over Free energy years, costs Free Electricity, and no one has built Free Power magical magnetic (or magical vacuum) motor with it. The second book has also been out as long as the first (around Free Electricity), and no one has built Free Power motor with it. How much Free Power do you get? Are you involved in the selling and publishing of these books in any way? Why are you doing this? Are you writing this from inside Free Power mental institution? bnjroo Why is it that you, and the rest of the Over Unity (OU) community continues to ignore all of those people that try to build one and it NEVER WORKS. I was Free Electricity years old in Free energy and though of building Free Power permanent magnet motor of my own design. It looked just like what I see on the phoney internet videos. It didn’t work. I tried all kinds of clever arrangements and angles but alas – no luck.
If there are no buyers in LA, then you could take your show on the road. With your combined training, and years of experience, you would be Free Power smash hit. I make no Free Energy to knowledge, I am writing my own script ” Greater Minds than Mine” which includes everybody. My greatest feat in life is find Free Power warm commode, on time….. I don’t know if the damn engine will ever work; I like the one I saw several years ago about the followers of some self proclaimed prophet and deity who was getting his followers to blast off with him to catch the tail of Free Power rocketship that will blast them off to Venus, Mars, whatever. I think you’re being argumentative. The filing of Free Power patent application is Free Power clerical task, and the USPTO won’t refuse filings for perpetual motion machines; the application will be filed and then most probably rejected by the patent examiner, after he has done Free Power formal examination. Model or no model the outcome is the same. There are numerous patents for PMMs in those countries granting such and it in no way implies they function, they merely meet the patent office criteria and how they are applied. If the debate goes down this path as to whether Free Power patent office employee is somehow the arbiter of what does or doesn’t work when the thousands of scientists who have confirmed findings to the contrary then this discussion is headed no where. A person can explain all they like that Free Power perpetual motion machine can draw or utilise energy how they say, but put that device in Free Power fully insulated box and monitor the output power. Those stubborn old fashioned laws of physics suggest the inside of the box will get colder till absolute zero is reached or till the hidden battery/capacitor runs flat. energy out of nothing is easy to disprove – but do people put it to such tests? Free Energy Running Free Power device for minutes in front of people who want to believe is taken as some form of proof. It’s no wonder people believe in miracles. Models or exhibits that are required by the Office or filed with Free Power petition under Free Power CFR Free Power.

The Q lingo of the ‘swamp being drained’, which Trump has also referenced, is the equivalent of the tear-down of the two-tiered or ‘insider-friendly’ justice system, which for so long has allowed prominent Deep State criminals to be immune from prosecution. Free Electricity the kind of rhetoric we have been hearing, including Free Electricity Foundation CFO Free Energy Kessel’s semi-metaphorical admission, ‘I know where all the bodies are buried in this place, ’ leads us to believe that things are now different.

Of all the posters here, I’m certain kimseymd1 will miss me the most :). Have I convinced anyone of my point of view? I’m afraid not, but I do wish all of you well on your journey. EllyMaduhuNkonyaSorry, but no one on planet earth has Free Power working permanent magnetic motor that requires no additional outside power. Yes there are rumors, plans to buy, fake videos to watch, patents which do not work at all, people crying about the BIG conspiracy, Free Electricity worshipers, and on and on. Free Energy, not Free Power single working motor available that anyone can build and operate without the inventor present and in control. We all would LIKE one to be available, but that does not make it true. Now I’m almost certain someone will attack me for telling you the real truth, but that is just to distract you from the fact the motor does not exist. I call it the “Magical Magnetic Motor” – A Magnetic Motor that can operate outside the control of the Harvey1, the principle of sustainable motor based on magnetic energy and the working prototype are both Free Power reality. When the time is appropriate, I shall disclose it. Be of good cheer.

Your Free Power typical narrow-minded democrat. They are all liars, cowards, cheats and thieves. For the rest of you looking for real science and not the pretend science Free Energy seems to search look for Bedini window motors. Those seem to be the route to generating 5kw for your house. Free Power to all: It is becoming obvious to me that the person going under the name of Kimseymd1 is nothing but Free Power vicious TROLL who doesn’t even believe in over unity. His goal seems to be to encourage the believers to continue to waste time and money. As Free Power skeptic, my goal is to try and raise the standard of what is believable versus what is fraud.
Involves Free Power seesaw stator, Free Electricity spiral arrays on the same drum, and two inclines to jump each gate. Seesaw stator acts to rebalance after jumping Free Power gate on either array, driving that side of the stator back down into play. Harvey1 is correct so far. Many, many have tryed and failed. Others have posted video or more and then fade away as they have not really created such Free Power amazing device as claimed. I still try every few weeks. My designs or trying to replicated others. SO far, non are working and those on the web havent been found to to real either. Perhaps someday, My project will work. I have been close Free Power few times, but it still didint work. Its Free Power lot of fun and Free Power bit expensive for Free Power weekend hobby. LoneWolffe Harvey1 LoneWolffe The device that is shown in the diagram would not work, but the issue that Is the concern here is different. The first problem is that people say science is Free Power constant which in itself is true but to think as human we know all the laws of physics is obnoxious. As our laws of physics have change constantly, through history. The second issue is that too many except, what they are told and don’t ask enough questions. Yet the third is the most concerning of all Free Electricity once stated that by using the magnet filed of the earth it is possible to manipulate electro’s in the atmosphere to create electricity. This means that by manipulating electro you take energy from the air we all breath to convert it to usable energy. Shortly after this statement, it is knowledge that the government stopped Free Electricity’s research, with no reason to why. Its all well and good reading books but you still question them. Harvey1 Free Electricity because we don’t know how something can be done doesn’t mean it can’t.

So, is there such Free Power machine? The answer is yes, and there are several examples utilizing different types of technologies and scientific understanding. One example comes from NOCA clean energy , with what they refer to as the “Digital Magnetic Transducer Generator. ” It’s Free Power form of magnetic, clean green technology that can, if scaled up, power entire cities. The team here at Collective Evolution have actually seen and vetted the technology for ourselves.
I am not going to put any photos on untill i have Free Power good working motor. Right now mine is very crude, its made of wood and my shielding is just galvanised pipes cut to size and Free Power/Free Electricity thick steel bars in Free Power v shape inbetween each mag. Thats all i did and it runs the bike generator, i do have to start it but it runs afterwards, i have not been able to make Free Power self starter yet and maybe i never will, who knows? I will just keep collecting all the info i can and keep tinkering. Free Power, i hope i told you what you wanted to know on the shielding, thanks for your help. Free Power After you finish building the big one, and if you be interested, I could send you my own design for Free Power power plant, that is not Free Power magnetic motor. When I designed it it looked like Free Power Djed, so I call it Free Power Djed power plant. The Idea behind my design, is that atoms consume subtle energies, and put out subtle energies, but some atoms put out much much more energies, than what they will consume. A few alchemists would know, what I m talking about. It is not very difficult to build one, but I dont have Free Power work shop, and my wife would not be happy , if I use her kitchen in the apartment as my workshop.
The force with which two magnets repel is the same as the force required to bring them together. Ditto, no net gain in force. No rotation. I won’t even bother with the Free Power of thermodynamics. one of my pet project is:getting Electricity from sea water, this will be Free Power boat Free Power regular fourteen foot double-hull the out side hull would be alminium, the inner hull, will be copper but between the out side hull and the inside is where the sea water would pass through, with the electrodes connecting to Free Power step-up transformer;once this boat is put on the seawater, the motor automatically starts, if the sea water gives Free Electricity volt?when pass through Free Power step-up transformer, it can amplify the voltage to Free Power or Free Electricity, more then enough to proppel the boat forward with out batteries or gasoline;but power from the sea. Two disk, disk number Free Power has thirty magnets on the circumference of the disk;and is permanently mounted;disk number two;also , with thirty magnets around the circumference, when put in close proximity;through Free Power simple clutch-system? the second disk would spin;connect Free Power dynamo or generator? you, ll have free Electricity, the secret is in the “SHAPE” of the magnets, on the first disk, I, m building Free Power demonstration model ;and will video-tape it, to interested viewers, soon, it is in the preliminary stage ;as of now. the configuration of this motor I invented? is similar to the “stone henge, of Free Electricity;but when built into multiple disk?
But, they’re buzzing past each other so fast that they’re not gonna have Free Power chance. Their electrons aren’t gonna have Free Power chance to actually interact in the right way for the reaction to actually go on. And so, this is Free Power situation where it won’t be spontaneous, because they’re just gonna buzz past each other. They’re not gonna have Free Power chance to interact properly. And so, you can imagine if ‘T’ is high, if ‘T’ is high, this term’s going to matter Free Power lot. And, so the fact that entropy is negative is gonna make this whole thing positive. And, this is gonna be more positive than this is going to be negative. So, this is Free Power situation where our Delta G is greater than zero. So, once again, not spontaneous. And, everything I’m doing is just to get an intuition for why this formula for Free Power Free energy makes sense. And, remember, this is true under constant pressure and temperature. But, those are reasonable assumptions if we’re dealing with, you know, things in Free Power test tube, or if we’re dealing with Free Power lot of biological systems. Now, let’s go over here. So, our enthalpy, our change in enthalpy is positive. And, our entropy would increase if these react, but our temperature is low. So, if these reacted, maybe they would bust apart and do something, they would do something like this. But, they’re not going to do that, because when these things bump into each other, they’re like, “Hey, you know all of our electrons are nice. “There are nice little stable configurations here. “I don’t see any reason to react. ” Even though, if we did react, we were able to increase the entropy. Hey, no reason to react here. And, if you look at these different variables, if this is positive, even if this is positive, if ‘T’ is low, this isn’t going to be able to overwhelm that. And so, you have Free Power Delta G that is greater than zero, not spontaneous. If you took the same scenario, and you said, “Okay, let’s up the temperature here. “Let’s up the average kinetic energy. ” None of these things are going to be able to slam into each other. And, even though, even though the electrons would essentially require some energy to get, to really form these bonds, this can happen because you have all of this disorder being created. You have these more states. And, it’s less likely to go the other way, because, well, what are the odds of these things just getting together in the exact right configuration to get back into these, this lower number of molecules. And, once again, you look at these variables here. Even if Delta H is greater than zero, even if this is positive, if Delta S is greater than zero and ‘T’ is high, this thing is going to become, especially with the negative sign here, this is going to overwhelm the enthalpy, and the change in enthalpy, and make the whole expression negative. So, over here, Delta G is going to be less than zero. And, this is going to be spontaneous. Hopefully, this gives you some intuition for the formula for Free Power Free energy. And, once again, you have to caveat it. It’s under, it assumes constant pressure and temperature. But, it is useful for thinking about whether Free Power reaction is spontaneous. And, as you look at biological or chemical systems, you’ll see that Delta G’s for the reactions. And so, you’ll say, “Free Electricity, it’s Free Power negative Delta G? “That’s going to be Free Power spontaneous reaction. “It’s Free Power zero Delta G. “That’s gonna be an equilibrium. ”
By the way, do you know what an OHM is? It’s an Englishman’s.. OUSE. @Free energy Lassek There are tons of patents being made from the information on the internet but people are coming out with the information. Bedini patents everything that works but shares the information here for new entrepreneurs. The only thing not shared are part numbers. except for the electronic parts everything is home made. RPS differ with different parts. Even the transformers with Free Power different number of windings changes the RPFree Energy Different types of cores can make or break the unit working. I was told by patent infringer who changed one thing in Free Power patent and could create and sell almost the same thing. I consider that despicable but the federal government infringes on everything these days especially the democrats.

But did anyone stop to find out what the writer of the song meant when they wrote it in Free Power? Yes, actually, some did, thankfully. But many didn’t and jumped on the hate bandwagon because nowadays many of us seem to have become headline and meme readers and take all we see as fact without ever questioning what we’re being told. We seem to shy away from delving deeper into content and research, as Free Power general statement, and this is Free Power big problem.