Sometimes I get an idea that I think may be worth something, maybe not much, but something. But then I forget it. Better write it down, here.

2010-09-06

Efficient two-dimensional convolution with arbitrary rotationally symmetric kernels. A 2-d Gaussian kernel has the nice property that a rotationally symmetric kernel is achieved by successive horizontal and vertical convolutions. This makes 2-d convolution with Gaussian kernels very cheap, and “Gaussian blur” has thus become, partially for this reason, a popular operation in image processing. No other kernel with this property exists when the kernel is limited to real numbers, as the kernel function must satisfy . But, if one allows the kernel to consist of complex numbers, then an appropriately phased version of the Gaussian kernel also satisfies the condition. The condition may be broken down into a magnitude condition and a phase condition that must both be satisfied. The magnitude condition reads , meaning that the kernel must have a Gaussian function as its magnitude function. Because in multiplication of complex numbers the phases are summed, the phase (argument) condition reads , with the shorthand . The only family of functions to satisfy this is . So now we would be able to write such phased Gaussian functions. The actual idea: The output from different kernels from the phased Gaussian family could be combined by a complex-weighted sum to create approximations of arbitrary rotationally symmetric kernels. At the end one could either use the magnitude or the real or imaginary part of the sum as the real number output.

2010-05-18

A theory on how molecules inside a cell manage to be in the part of the cell where they are needed. If macromolecules A and B bind to each other and B and C also bind to each other, and the two binding reactions need not compete with one another, then obviously A and C will also end up close together, via B. This must be a very common way to create a tight organization between macromolecules. But what about when a more loose organization is required, let’s say when the rather freely diffusing tRNA’s are needed where translation takes place. It seems unlikely that the contents of a cell would be an inefficient homogeneous porridge of macromolecules. Perhaps affinities between macromolecules brings about organization. To describe the affinities between N species of macromolecules, one would need at least an N x N triangular matrix of affinity constants. It would be interesting to simulate such a system, and to see if compartmentalization takes place by itself without boundaries. If a macromolecule of an unknown purpose is found to have affinity to several components of a cellular process, then the guess can be made that it probably contributes to the process somehow. These affinities probably wouldn’t need to be very strong. Some types of metabolic and transport systems could perhaps be shown to be more effective in an internally organized cell.

2010-04-07

A directional microphone that is a 3D configuration of multiple omnidirectional microphone elements. The signals from the different elements are made to be in phase by using digital delay lines. The microphone can also be made resistant to turbulences caused by wind by temporarily muting the affected elements, and by surrounding each with a chassis that protects it against wind from a certain direction. The direction would be different for each element.

2010-02-24

A method for training artificial neural networks to generate missing data within a variable context. As the idea is hard to put in a single sentence, I will use an example:

An image may have missing pixels (let’s say, under a smudge). How can one restore the missing pixels, knowing only the surrounding pixels? One approach would be a “generator” neural network that, given the surrounding pixels as input, generates the missing pixels.

But how to train such a network? One can’t expect the network to exactly produce the missing pixels. Imagine, for example, that the missing data is a patch of grass. One could teach the network with a bunch of images of lawns, with portions removed. The teacher knows the data that is missing, and could score the network according to the root mean square difference (RMSD) between the generated patch of grass and the original data. The problem is that if the generator encounters an image that is not part of the training set, it would be impossible for the neural network to put all the leaves, especially in the middle of the patch, in exactly the right places. The lowest RMSD error would probably be achieved by the network filling the middle area of the patch with a solid color that is the average of the color of pixels in typical images of grass. If the network tried to generate grass that looks convincing to a human and as such fulfills its purpose, there would be an unfortunate penalty by the RMSD metric.

My idea is this (see figure below): Train simultaneously with the generator a classifier network that is given, in random or alternating sequence, generated and original data. The classifier then has to guess, in the context of the surrounding image context, whether the input is original (1) or generated (0). The generator network is simultaneously trying to get a high score (1) from the classifier. The outcome, hopefully, is that both networks start out really simple, and progress towards generating and recognizing more and more advanced features, approaching and possibly defeating human’s ability to discern between the generated data and the original. If multiple training samples are considered for each score, then RMSD is the correct error metric to use, as this will encourage the classifier network to output probabilities.

2010-02-18

A graphic design methodology that projects a 2D pattern of silhouettes as objects onto a 3D landscape and renders the scene using 3D methods. For example, a set of squares is turned into a city of facades on a landscape, perhaps even with perspective.

2010-01-27

Exact coordinates for computer aided design (CAD). If a CAD program stores coordinates internally as floating point, then movement of objects such as rotations will accumulate error in the inexact numerical coordinates. This could result in two points not coinciding when they should, if they were subjected to different transformations. Perhaps the only way to avoid this would be to store the coordinates exactly, including things like square roots and such in a formula type of an expression. When possible, the expression would be simplified. For example sqrt(2)*sqrt(2) would become 2. The drawback is that everything would become slower.

2010-01-13

Terminator yeast for carbonation of bottled beverages. Carbonation of bottled beverages by yeast has the problem that the yeast will use up all the sugar, and usually it would be good to leave at least some sweetness. So, engineer a yeast that stops fermenting after, let’s say, a number of growth cycles. Additionally, to reduce the amount of sediment, the yeast could be made to waste energy instead of using it for growth. The trigger of this could be related to growth cycles. The best would be detection of pressure, stopping the metabolism of the yeast when there is enough pressure in the bottle. A mechanism for pressure sensing could perhaps be evolved by switching between different food sources and by signaling the switch beforehand by a pressure change. Alternatively the trigger could be CO concentration. Reading a bit on the topic, some researchers have produced cold-sensitive strains of baker’s yeast by using nystatin, which presumably kills growing yeast cells.

2009-10-04

Singing brakes for bicycles. By etching sound wave patterns into the rim, the rim brake could be made to produce tones, maybe even arbitrary sounds.

2009-09-12

This is intended as an artistic effect, not actual labeling of pills. Uh, sounds like such an obvious idea that someone probably already used it.

2009-08-30

Create genetically manipulated trees with branches in line and only on two sides, to get more knotless lumber

• Does the tree twist and loose the polarity? Now this is a possibility.
• How to do it? Should look into developmental biology.
• Does the tree get enough light? The branches can branch also horizontally so it wouldn’t be just a flat tree. And even if it’s a flat tree it gets about 64 % of the light compared to a normal tree.
• Does it replace normal trees in the ecosystem? Unlikely, because it won’t be as effective in collecting light as normal trees.

2007-10-26

A musical wind instrument with electro-acoustic feedback

• How is the feedback created? By a microphone and a  small loudspeaker.
• How does one get different notes? The delay length is adjusted by the player by pressing keys.
• How is the feedback delay made? It is either an electronic/digital delay or an array of microphones is used.
• What if the speaker is of poor quality? Compensate for example by low-pass filtering. An adjustable filter would also allow coloration of the tone.