text:
# What really is Color (in Physics)?

I’ll begin this with a sticky note that I’m not at all good at explaining these biological “stuff”. But as I’ve read a lot of posts on vision, repeating the same bunch of words again & again, I’ve got some grasp on the topic. Well, it’s still worth a try. Moreover, this post would be a strong base for other future posts related to vision. Because, it’s often a misconception that color is an intrinsic property of light. This may be a reason why physicists are often tackled by color questions like, “Why doesn’t sky look violet?”, etc.

## Okay, now define “color”…

First, let’s stick with the truth that light is made of the elementary particle, the quanta of electromagnetic radiation called photons. The theory of quantum electrodynamics (which I haven’t prepared for you, yet) best explains the behavior of these tiny objects that whizz around here and there, so fast that no known “thing” can overtake it. That’s enough for now.

What’s color? It can be defined in many ways. For now, (keeping aside, the technical parameters like hue, saturation, brightness, etc.) Color is the visual perception of things that emit, transmit or reflect light in the world. In other words, it’s simply the sensation produced in our eyes when electromagnetic radiation of certain frequency (i.e) specific photons impinge the retina of the eye. That’s why “color” means nothing to Physicists.

So, these  questions regarding perception, sensation, etc. should always target biologists (psychologists or physiologists, to be specific). I should remind you that there’s nothing so special in the different kinds of EM waves (as everyone think they’re). They’re not at all different. All are the same EM radiation. They’re classified as IR, UV, Gamma rays, etc. just because various range of frequencies have a wide variety of applications in different fields of study (stupid terminology). It should be noted that the “visible light” range is allotted in the spectrum only because that range (400-720 nm) supports our vision. If we were rattle snakes (IR sensors) or the bees (UV sensors) or intelligent creatures with antennae – ALIENS..!!! (at least our eyes are modified like that), then we’d have to redefine visible light. That’s why I suggest people not to believe such dodgy sayings that visible light is something very special, given a place in the EM spectrum.

## Clockwork behind eyes (shallow’ish)

Objects in the outside world, say, green leaves aren’t really green. They absorb almost all wavelengths in the visible spectrum, while reflecting green. That’s why they appear green. If you shoot a natural scene, with an IR camera, you’ll arrive at the conclusion that these leaves reflect near-infrared too…

The job of our eyes is to detect the information that worldly objects reflect. These eyes don’t have much gears and wheels (at least in a physical point of view). There are two kinds of vision – photopic (normal daylight) and scotopic (diffusely illuminated). In order to work efficiently, our eyes have two kinds of photo-receptors. They are the cone cells (photopic) and the rod cells (scotopic). The iris does the job of directing light, whether to cones or to rods…

#### Rods:

Rods are not so much important (despite their large number, around 120 million), as they don’t help us enjoy the taste of nature. They just show us black, white & gray (yuck..!!!). Because, rod cells (being tuned to scotopic vision) work only at dim light (dark room or say, at night), when the irises open up, letting more light into the retina. Hey, you should’ve experienced this as you shift from a well-lit room to a dark room, when you can easily notice the eyes adapting to the environment. As time passes by, the rods become very active (10,000 times over a period of 30 minutes) in capturing photons (unlike cones, which are active in triggering the optical nerve), but weak in detecting colors. Wonderful design…

#### Cones:

We’re always used up with the well-lit view. Thanks to the 7 million cones for letting us enjoy the beauty of things around. Destroy those and you’ll go blind. Under photopic conditions, the irises are stopped from opening outward. Cone cells, being at the center of retina are mostly struck by light photons now. As an aside business, let’s see their classification. There are three types of cone cells (no special names) – Short, Medium and Long wavelengths (abbreviated S, M & L), each sensitive to a peak wavelength (i.e) “S” to 420 nm (bluish-violet), “M” to 534 nm (bluish green) and “L” to 564 nm (yellowish-green). Plotted below, is the response curves of the three cones (responsivity vs wavelength). For the sake of difficulty, understanding or whatever, let’s just say blue, green and red cones and go along with the mechanism behind perception…

## So, what happens inside?

Different frequencies excite the cone cells (all the three) at different proportions. It’s our brain’s visual cortex that reconstructs these excitations into perceivable visualizations (the beauty). For example, if the light photons excite all the three cells equally, the color appears to be white. No excitation, it’s black. Or say, the photons smash (excite) the red and green cells equally, but unexpectedly, a lot of excitation happens at the blue cells (Duh, modulation is the fancy term for excitation). Now, there’s our blue. Note that there’s an overlapping in the response curves. What it means? No known light sources can generate something which excites only a single receptor. All the three are excited to some specific percentage. Just like you play around mixing different colors of light, the different proportions of excitations of cones correspond to different colors. Both are unambiguously analogous…

Still, there’s a necessity. While our rods (being so sensitive) can detect even a single photon, the cones are quite lazy (at least the brain and the optical nerves are), that they require a threshold of 50-100 photons (on average) arriving within a second to give a response.

#### Eyes of camera & humans

Most of the remotes use a diode for emitting near-infrared radiation to communicate with the television. The way the cones are excited modulated is very different than that of a digital camera. Don’t ever think that a camera reproduces the view of the environment exactly as seen by your eye. It just mimics the perception of eye. The colors you see in a camera and through the eye are similar, but not exact (You can notice the difference in a few photographs) Because, the natural cones in eyes and the artificial CCDs (charge-coupled device) in camera are very different. So, your eye sees apparently nothing, while the camera sees some color (purple, in this case) And, this depends on the camera you use, as different cameras make use of different filters. (Well, most of the cameras’ filters allow near-IR, which is enough for a remote) At least, this can be used to test a remote. So, are you still sticking to the definition of visible light?

## Why isn’t the sky violet then?

If you still remember the XKCD comic, and you’re so much interested in the “Why?”, I’ll try to explain, having read the Physics FAQ article. I presume that you all know about Rayleigh scattering law (although Tyndall found it, “Lord” gets the credit), that the amount of scattering varies as inverse as the fourth power of the wavelength of light. According to this abstract statement, we should see violet sky, the violet in the rainbow, etc. There are possible reasons…

• The Sun doesn’t emit radiation of constant frequency. The irradiance vs. wavelength plot shows that more photons are emitted in the 500 nm range.
• As the incoming light passes through the upper $O_2$ and $N_2$ atmosphere, much of the violet light gets absorbed by the molecules, leaving only a few to penetrate the inner levels. Still, there should be a violet tinge on the observed blue sky. But, it’s not..!!!
• So, all the remaining credits go to our eyes

Our blue and green cones are very sensitive to blue (Go, see the peak wavelength in the response curves again – bluish & bluish). Both are excited by the largely scattered blue light, in addition to the least scattered red and orange light (triggering the red cone), moderately scattered yellow & green light (green cone) and the highly scattered violet (blue cone). All these equalize each other out (I mean, the cells are almost equally excited), leaving blue cones to relatively much higher excitation.

There you go… Blue Sky…

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Tech Topics

# Managing Relations Inside Elasticsearch

Data in the real world is rarely simple - often times it is a jumble of interlocking relations.

How do you represent relational data in Elasticsearch? There are a few mechanisms that can be used to provide relation support. Each has their pros and cons, making them useful for different situations.

### Inner Objects

The simplest mechanism are named "inner objects". These are JSON objects embedded inside your parent document:

{
"name":"Zach",
"car":{
"make":"Saturn",
"model":"SL"
}
}

Simple, right? The "car" field is just another JSON object, with the inner object having two properties ("make" and "model"). This inner object mapping will work as long as you have a one-to-one relationship between the root object and the inner object. E.g. every person has at most one "car".

But what if Zach owns two cars, and we add another person (Bob) who owns just one car?

{
"name" : "Zach",
"car" : [
{
"make" : "Saturn",
"model" : "SL"
},
{
"make" : "Subaru",
"model" : "Imprezza"
}
]
}
{
"name" : "Bob",
"car" : [
{
"make" : "Saturn",
"model" : "Imprezza"
}
]
}

Ignoring the fact that Saturn never made an Imprezza car, what happens when we try to search for it? Logically, only Bob has a "Saturn Imprezza", so we should be able to do a query like:

query: car.make=Saturn AND car.model=Imprezza

Right? Well, no, that doesn't work. If you perform that query, you'll receive both documents as the result. What happens is that Elasticsearch internally flattens inner objects into a single object. So Zach's entry actually looks like this:

{
"name" : "Zach",
"car.make" : ["Saturn", "Subaru"]
"car.model" : ["SL", "Imprezza"]
}

Which explains why it was returned as a result. Elasticsearch is fundamentally flat, so internally the documents are represented as flattened fields. Hmm.

### Nested

As an alternative to inner objects, Elasticsearch provides the concept of " nested types". Nested documents look identical to inner objects at the document level, but provide the functionality we were missing above (as well as some limitations).

Example nested document:

{
"name" : "Zach",
"car" : [
{
"make" : "Saturn",
"model" : "SL"
},
{
"make" : "Subaru",
"model" : "Imprezza"
}
]
}

At the mapping level, nested types must be explicitly declared (unlike inner objects, which are automatically detected):

{
"person":{
"properties":{
"name" : {
"type" : "string"
},
"car":{
"type" : "nested"
}
}
}
}

The problem with inner objects was that each nested JSON object is not treated as an individual component of the document. Instead they were merged with other inner objects sharing the same property names.

This is not the case with nested documents. Each nested doc remains independent, and you can perform a query like car.make=Saturn AND car.model=Imprezza without a problem.

Elasticsearch is still fundamentally flat, but it manages the nested relation internally to give the appearance of nested hierarchy. When you create a nested document, Elasticsearch actually indexes two separate documents (root object and nested object), then relates the two internally. Both docs are stored in the same Lucene block on the same Shard, so read performance is still very fast.

This arrangement does come with some disadvantages. Most obvious, you can only access these nested documents using a special  nested query. Another big disadvantage comes when you need to update the document, either the root or any of the objects.

Since the docs are all stored in the same Lucene block, and Lucene never allows random write access to it's segments, updating one field in the nested doc will force a reindex of the entire document.

This includes the root and any other nested objects, even if they were not modified. Internally, ES will mark the old document as deleted, update the field and then reindex everything into a new Lucene block. If your data changes often, nested documents can have a non-negligible overhead associated with reindexing.

Lastly, it is not possible to "cross reference" between nested documents. One nested doc cannot "see" another nested doc's properties. For example, you are not able to filter on "A.name" but facet on "B.age". You can get around this by using include_in_root, which effectively copies the nested docs into the root, but this get's you back to the problems of inner objects.

### Parent/Child

The last method that Elasticsearch provides are Parent/Child types. This scheme is a looser coupling than nested, and gives you a set of slightly more powerful queries. Let's look at an example where a single person has multiple homes (in different states). Your parent has a mapping as usual, perhaps:

{
"mappings":{
"person":{
"name":{
"type":"string"
}
}
}
}

While your children have their own mapping outside the parent, with a special _parent property set:

{
"homes":{
"_parent":{
"type" : "person"
},
"state" : {
"type" : "string"
}
}
}

The _parent field tells Elasticsearch that the "Employers" type is a child of the "Person" type. Adding documents to this scheme is very easy. The parent doc is indexed as normal:

$curl -XPUT localhost:9200/test/person/zach/ -d' { "name" : "Zach" }  And indexing children documents is almost like normal, except you need to specify which parent this child belongs to in the query parameter ('zach' in this case, which is the ID that we used in the above document): $ curl -XPOST localhost:9200/homes?parent=zach -d'
{
"state" : "Ohio"
}
\$ curl -XPOST localhost:9200/test/homes?parent=zach -d'
{
"state" : "South Carolina"
}

Both of these documents are now associated with the 'zach' parent document, which allows you to use special queries such as:

You can also query the parents or children types individually, since they are first-class types and will respond to normal queries as usual (you just can't use the relationship values).

The big problem with Nested was their storage: everything is stored in the same Lucene block. Parent/Child removes this limitation by separating the two documents and only loosely coupling them. There are some pros and cons to this. The loose coupling means you are more free to update/delete children docs, since they have no effect on the parent or other children.

The downside is that Parent/Child are slightly less performant than Nested. The children docs are routed to the same shard as the parent, so they will still benefit from shard-level caches and memory filtering. But they aren't quite as fast as nested since they are not colocated in the same Lucene block. There is also a bit more memory overhead, since ElasticSearch needs to keep an in-memory "join table", which manages the relations.

Lastly, you'll run into situations where sorting or scoring are, frankly, very difficult. For example, it is impossible to tell which child documents matched your Has_Child filter, just that one of the docs of the returned parent matched the criteria. This can be frustrating depending on your use-case.

### Denormalization

Sometimes the best option is to simply denormalize your data where appropriate. The relational facilities that Elasticsearch provides are great for certain scenarios...but were never meant to provide the robust relational features that you expect from an RDBM.

At it's heart, Elasticsearch is a flat hierarchy and trying to force relational data into it can be very challenging. Sometimes the best solution is to judiciously choose which data to denormalize, and where a second query to retrieve children is acceptable. Denormalization gives you arguably the most power and flexibility.

Of course, this comes with the burden of administrative overhead. You get to manage relations, and you get to perform the required queries/filters to associate the various types. Yay!

### Conclusion and Recap

This turned into a long, wordy article, so here is a bulletted recap:

Inner Object

• Easy, fast, performant
• Only applicable when one-to-one relationships are maintained
• No need for special queries

Nested

• Nested docs are stored in the same Lucene block as each other, which helps read/query performance. Reading a nested doc is faster than the equivalent parent/child.
• Updating a single field in a nested document (parent or nested children) forces ES to reindex the entire nested document. This can be very expensive for large nested docs
• "Cross referencing" nested documents is impossible
• Best suited for data that does not change frequently

Parent/Child

• Children are stored separately from the parent, but are routed to the same shard. So parent/children are slightly less performance on read/query than nested
• Parent/child mappings have a bit extra memory overhead, since ES maintains a "join" list in memory
• Updating a child doc does not affect the parent or any other children, which can potentially save a lot of indexing on large docs
• Sorting/scoring can be difficult with Parent/Child since the Has Child/Has Parent operations can be opaque at times

Denormalization

• You get to manage all the relations yourself!


text:
# What is repulsive Coulomb’s force between two protons in a nucleus of iron? Assume a separation of 4.0×10-15 m.

F = 1/4(pi)$\varepsilon$ q1*q2/r^2


text:
# Eggtimer Quark Destruction

### Help Support The Rocketry Forum:

#### Motocrossman24

##### Well-Known Member
What about this one for $40? ttps://www.amazon.com/dp/B07RKMGPTX/ that’s the one I purchased...granted Iv only used it a few times, but it works as it should...I’m sure none of these cheap options are production worthy, but for someone putting together a few eggfinders per year, I’m sure they’ll last you a decade+...I bought a similarly cheap soldering station when I get into fpv drones7-8 years ago, and it’s been great for me, takes hakko tips and has been flawless, and used a lot. This is the solder station I use, you can likely get something better for 10-20$ more https://www.ebay.com/itm/937D-SMD-Soldering-Hot-Iron-Station-Digital-Adjustable-w-5-Tips-Japan-Heater/333525481432?epid=1955793516&_trkparms=ispr=1&hash=item4da7aaf7d8:g:uDYAAOSwB05eU5Fl

#### CalebJ

##### Well-Known Member
TRF Supporter
I've got a small variable power soldering station, but SMD is beyond anything I've done previously. This alternative looks like it would be worth every penny.

#### Greg Furtman

##### Well-Known Member
TRF Supporter
I've got a small variable power soldering station, but SMD is beyond anything I've done previously. This alternative looks like it would be worth every penny.
@CalebJ If you buy it make sure you buy a practice board. I bought one of these.

#### CalebJ

##### Well-Known Member
TRF Supporter
You think that would be necessary even with the rework station?

#### Greg Furtman

##### Well-Known Member
TRF Supporter
You think that would be necessary even with the rework station?

#### Motocrossman24

##### Well-Known Member
For those interested in why 60/40 solder should be obsolete in the marketplace. Here’s a copy and pasted explanation

60/40 solder is made of 60% tin and 40% lead. It has a melting point of around 190°C, depending on the exact composition. Iron tip temperatures of at least 300°C are recommended. It is also very soft, meaning that cracks do not form so readily if the joint moves during cooling.

63/37Edit
63/37 solder is made of 63% tin and 37% lead. It has a melting point of 183°C, slightly lower than the more common 60/40 blend. The primary advantage of this solder is not the lower melting point, but its eutectic property. Non-eutectic solders, like the 60/40 solder, have a semi-solid state between solid and liquid. If a joint is moved during this stage, it can result in what is called a cold solder joint. Eutectic solders, like the 63/37, do not have this semi-solid state and are thus considered easier to work with as it produces fewer bad joints. However, these solders typically cost more than their non-eutectic counterparts.

50/50Edit
This is made of a half and half mix of tin and lead. Never use 50/50 solder for electronics — it is meant for plumbing. (There are brands[Worthington 50/50 leaded #331887], which is used for electronics and specifically not intended for plumbing). Otherwise, you may end up with failed joints, as the 50/50 solder does not have the same properties as 60/40, having a higher melting point and lower ductility. Also, it is very unlikely to have flux included in it like rosin core solders.

#### Motocrossman24

##### Well-Known Member

Or, maybe, templates that we can print on clear media and cut out ourselves?

I'd love to try the mask method for building a TRS!
because the circuit board hasa coating between the pads, you can literally draw athin line right down the pads for a micro processor. And when heating with the air gun, the solder will naturally move from the space between the actual copper pads, and collect only on the pads. The mask method simply isn’t necessary, it only helps to make sure that the amount of solder is consistent.The only real trick is finding the correct amount so that your not over doing it, and that amount is usually much less then you would think you need. A small practice board is rlly all you need to get the technique down. And at the end of the day, if you mess up a joint, just hold the component with your tweezers, hit it with hot air and it comes right off. Rinse and repeat

#### cerving

##### Owner, Eggtimer Rocketry
TRF Supporter
I can create the paste layer files pretty easily... it's been a "get to it" for a couple of years. We posted the one for the Proton when we released it (there are a LOT of parts on the board...), so maybe I can get the rest done since I have a little "down time" while I'm waiting for a launch to happen.

** UPDATE **
I've posted the cream layers for the Quark, Quantum, Proton, TRS, WiFi Switch, and Eggfinder TX. Due to the nature of the Eggfinder Mini assembly, it really doesn't lend itself towards reflow assembly, and the other kits don't have enough SMT parts on them to make it worth reflowing them.

Last edited:

#### CalebJ

##### Well-Known Member
TRF Supporter
@CalebJ If you buy it make sure you buy a practice board. I bought one of these.
Greg - is there any trick/technique to applying the paste to the board? The practice board and hot air system came in so I gave it a quick shot at lunch. My first reaction was that the paste tends to stay on the toothpick or syringe unless I really push down, at which point I get way too much. Just curious if you'd found a better way.

#### Motocrossman24

##### Well-Known Member
Greg - is there any trick/technique to applying the paste to the board? The practice board and hot air system came in so I gave it a quick shot at lunch. My first reaction was that the paste tends to stay on the toothpick or syringe unless I really push down, at which point I get way too much. Just curious if you'd found a better way.
you really just need a small smudge of paste. If you think about what they’re doing when using a screen to apply the paste, it’s basically just wiping the paste a little thicker then the thickness of paper over the pad. Make sure the paste has warmed to room temp for 3-4 hours before working with it, or it is a lot more difficult to apply.if you weren’t aware, paste needs to be refrigerated or the flux evaporated away and makes it even harder to use.

#### CalebJ

##### Well-Known Member
TRF Supporter
I didn't know about refrigerating it - thanks for that.

The issue I'm seeing is that I basically get none at all or a tiny glob. Is there a better tool for application, perhaps the edge of a blade?

#### Motocrossman24

##### Well-Known Member
I didn't know about refrigerating it - thanks for that.

The issue I'm seeing is that I basically get none at all or a tiny glob. Is there a better tool for application, perhaps the edge of a blade?
I personally have only used the tip of the syringe, but I don’t see why a blade wouldn’t be good, just be careful not to cut through the epoxy coating on the board. If you have many small traces in a row, you can just take the blade and wipe it right down the pads, and because the paste’s flux is attracted to heats it will take the paste between the pads and pull it towards the pads(they heat up faster). Another thing I learned is that there are 3 different classifications of paste (t3/t4/t5) which is the diameter of the solder balls in the paste, with t3 being the largest and t5 being the smallest. I recently purchased some sra t5 paste, and it is much easier to work with then my t3 kester paste. The solder joints also look a lot smoother and more uniform. T5 paste is a bit more expensive, but it’s all I will buy from now on.

#### CalebJ

##### Well-Known Member
TRF Supporter
I'll definitely keep the solder ball size in mind the next time I resupply. Looks like the tube I bought based on Greg's recommendation above was T4. Thanks for all the info. Will give it another shot this evening.

#### Motocrossman24

##### Well-Known Member
I'll definitely keep the solder ball size in mind the next time I resupply. Looks like the tube I bought based on Greg's recommendation above was T4. Thanks for all the info. Will give it another shot this evening.
I would assume t4 is good stuff.

#### CalebJ

##### Well-Known Member
TRF Supporter
Probably so. It seemed to work perfectly on the one component I did attach.

#### Joe Bruce

##### Well-Known Member
TRF Supporter
Last night I used this hot air rework station and Kester EP256 solder paste to build my first EggTimer Quark. That was board #2 for the station -- I built this cheap practice board first.

I thank the many posters on this thread for the inspiration and product suggestions! Though hot air rework is its own art, my solder joints are MUCH cleaner than on my hand-soldered Quantum. The build was much faster, too, with my only issue being a little solder in the "Tx" hole for the header pin (an issue I only made worse before I fixed it). I could generally paste & place 3-6 parts at a time.

I was even able to fix a hand-soldered practice board from a few months ago where I had installed an LED backwards. It is amazing how 75% of the time, the parts just move into position. Of course, the other 25% they tombstone or flow together into a small mass of resistors, etc.

Still learning the new art, but I have much more confidence in (successfully) building the remaining Quark, Quantum, and EggFinder Tx / Rx boards! Thanks as always to Cris for designing and selling these kits!

#### CalebJ

##### Well-Known Member
TRF Supporter
I ended up attaching maybe ten components onto the practice board last night. I'm still pretty rough at handling the tiny things (even with tweezers they're frustratingly small), but the hot air system is magnificent.

Joe - since you just did the practice board and the Quark in close succession, how would you compare the two projects?

#### Greg Furtman

##### Well-Known Member
TRF Supporter
Greg - is there any trick/technique to applying the paste to the board? The practice board and hot air system came in so I gave it a quick shot at lunch. My first reaction was that the paste tends to stay on the toothpick or syringe unless I really push down, at which point I get way too much. Just curious if you'd found a better way.
@CalebJ Sorry for the late reply. I found heating up the PCB pads a little bit with the hot air gun made it easier to apply the soldering paste. And I applied it directly from the syringe with the fine tip. I also found out right away that syringes are like caulk guns, it you don't take the pressure off right away they continue to ooze.

#### CalebJ

##### Well-Known Member
TRF Supporter
Thanks! I encountered that for sure last night. Oozed a surprising amount of paste onto the table that I mostly managed to recover. And the second round of placing components went dramatically better with a warm board. Lots of learning opportunities. The suggestion to get the practice board was a good one for sure.

#### Greg Furtman

##### Well-Known Member
TRF Supporter
Thanks! I encountered that for sure last night. Oozed a surprising amount of paste onto the table that I mostly managed to recover. And the second round of placing components went dramatically better with a warm board. Lots of learning opportunities. The suggestion to get the practice board was a good one for sure.
The practice kit was fun. I might pick up another kit just to play with. And isn't it cool when the soldering paste finally melts and the component self-aligns?

#### Joe Bruce

##### Well-Known Member
TRF Supporter
Joe - since you just did the practice board and the Quark in close succession, how would you compare the two projects?
The practice board was great practice for the Quark! I did the entire practice board except I gave up on those teeny 0402 parts halfway through. Even with a lighted magnifier they are TINY, and fortunately Cris uses 0805 and 1206 parts in his designs.

On that 858D clone, I've used 380 degrees C and the air flow at about 4. Some of the parts on the Quark are a bit closer together than on the practice board, but it wasn't a huge difference. The group of 3-4 resistors to the left of the processor clumped together when the solder paste started to flow, but they were easy to coax into position (or for one, remove and re-place after things had cooled).

I had no solder bridge issues other than between IC pins -- not the pads, but the pins themselves. That was usually easy to clear with tweezers, though one time I removed the part and vacuum desoldered the excess and sort of started over.

I carefully inspected joints with a 10x loupe as I went, and reflowed or added a bit more solder paste when it wasn't up to par. Though it's a new skill, the solder joints are "professional quality" versus some obviously-not-pro joints on my hand-soldered Quantum. Overall, I agree 100% with you that the hot air is "magnificent" and I wish I hadn't delayed getting one for so long!

For the solder paste, I pressed the plunger with my right hand and "aimed" with my left hand, since I hold the board in a Panavise (elevated). When I'm done with the few parts I'd place at a time, I pulled back on the plunger to avoid the oozing. That two-handed reflex bit me ONCE during the Quark build, though -- put my left hand BRIEFLY on the hot air gun (OUCH!). Won't do that again (I hope)!

#### CalebJ

##### Well-Known Member
TRF Supporter
On the practice board I noticed some issues when I tried to do a set of nearby components at the same time. If I got too close with the hot air, it would occasionally blow them around a bit even with the air turned all the way down (I'm using an 898 from eBay, for whatever that's worth).

This whole process really is like magic. I've done plenty of hand soldering and I'm perfectly mediocre with it. This allows me to do things that are a fraction of the size with exponentially better results and in less time.

#### Joe Bruce

##### Well-Known Member
TRF Supporter
This whole process really is like magic. I've done plenty of hand soldering and I'm perfectly mediocre with it. This allows me to do things that are a fraction of the size with exponentially better results and in less time.
Agreed 100%. The practice board I hand-soldered months ago before attempting my Quantum wasn't functional and I had problems with the 0603 parts. With the same board and hot air, I no issues until I got down to the 0402 parts and I could do half a dozen resistors or capacitors at the same time. ICs are fun, too -- you can just draw a line of paste down each row of pins and watch the solder flow to the pads (and hopefully NOT bridge the pins).

EDIT: ...and the voltage regulator was a HUGE pain hand-soldering on the Quantum, but was a snap with hot air on the Quark!

#### CalebJ

##### Well-Known Member
TRF Supporter
Re drawing a line down each row - I did that but added the quick step of drawing a toothpick through the gap between each pad. Just takes a few seconds to do and definitely groups the sections of paste to the appropriate pads. Not sure it guarantees results, but it ought to at least decrease the odds of an accidental bridge.

#### Joe Bruce

##### Well-Known Member
TRF Supporter
@CalebJ I'll have to try that on the next board!

2


text:
## Proof That a Product of Connected Spaces is Connected

Theorem

A product of connected spaces is connected.

Proof

Letbe a collection of connected spaces and letbe the product space.

Letand letbe the component to whichbelongs.

Takeand letbe any open set containing

The setis homeomorphic tohence is connected.

Sincewhereis the component of

The sethence

Thenhas one component and is connected.


text:
# Does it make sense to consider non-binary logit?

Consider the nested logistic regression model’s following interpretation.

A person repeatedly chooses between two different options. These options feature different levels of the same features (e.g. car characteristics). In some cases, the person will choose option 1, in some cases the person will choose option 2.

The standard formula of the logistic regression

$$P(Y=1|X=x_{i}) = \frac{e^{\beta x_{i}}}{1-e^{\beta x_{i}}}$$

could be interpreted such that the person evaluates options according to an utility function $U(x_{i})$, assigning utility components $\beta$ to the characteristics of the options, and choosing the option which maximizes utility. In a logistic regression we would thus estimate the implicit values of the characteristics $x_{i}$.

Now suppose the setting would be such that the person does not make a discrete choice. The person could, for example, say that both options are equally attractive, that option 1 is much more attractive than option 2, or that option 2 is just slightly more attractive than option 1 etc.

We would thus compute a logit specification model with the dependant variable not being 0 or 1, but within the interval $(0,1)$.

Is it mathematically possible to do that? I believe it is.* If you take a look at the ML-process of calculating a logistic regression, it is nowhere required for y to be dichotomous, nor is it in fact required to be in the interval of $(0,1)$. You can fit regression models with the ML-method for any objective functions you desire, question is if it will make sense or not. It won’t exactly be logistic regression anymore, but it might be something different, similar.

So the question remains: Does that make any sense? Is it valid to think of a binary choice problem the way I portrayed it, and to make use of additional information on relative weighting of preferences (if available) by assuming y \e (0,1)? Would that make better use of available information, as in the case of y ~ 0.5 we know that the valuation of the options is similar?

• Err, actually you can only do ML estimation on objective functions that are also likelihoods. That's why there's an 'L'. This rules out quite a lot of functions. What you mean, I think, is that you can minimize any parameterized function you like. Indeed you can. – conjugateprior Mar 26 '12 at 14:01
• More generally than minimizing parameterized functions, you can solve any estimating equations (EEs) you like. The EEs from logistic regression are efficient, among the class of EEs which are linear in Y, so long as $Var(Y)$ is proportional to $Mean(Y)(1-Mean(Y))$. If you have more information on the mean-variance relationship, you might buy yourself a little efficiency using EEs which reflect it. – guest Mar 26 '12 at 15:43


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# Introduction to Automatic Speech Recognition

Friday, April 19, 2019

The Automatic Speech Recognition (ASR) systems are widely used nowadays. Some of the most notable uses include Siri, Alexa Google Assistant, Cortana, etc. Let’s understand the fundamentals of ASR.

## Introduction

Hidden Markov Models (HMM) can be used for ASR. The HMM based recognizer consists of two key components, feature extractor, and decoder.

• First, in feature extraction, the input audio signal is converted into a sequence of fixed size acoustic vectors $Y = y_1, \dots, y_t$.
• The decoder then finds the sequence of words $w = w_1, \dots, w_l$ corresponding to Y i.e. the decoder calculates

However, it’s difficult to model $P(w \mid Y)$, the Bayes rule is used to transform the above equation into an equivalent one as follow:

The model that determines $P(Y \mid w)$ is called acoustic model and the one that models $P(w)$ is called a language model.

## Feature extraction

The feature extraction phase deals with the representation of input signal. The Mel-frequency cepstral coefficients (MFCC) or Linear Predictive Coding (LPC) vectors can be used as acoustic vectors, Y.

## Acoustic model

A HMM is used to model $P(Y \mid w)$. The extracted feature vectors from the unknown input audio signal is scored against acoustic model, the output of the model with max score is choosen as the recognized word. The Gaussian Mixture Model (GMM) can be used as the acoustic model.

The basic unit of sound that acoustic model represents is called phoneme e.g. the word “bat” has three phonemes $/ \mathrm{b} / / \mathrm{ae} / / \mathrm{t} /$. The concatenation of these phonemes, called pronunciation, can be used to represent any word in the English language. Thus, in order to recognize a given word, the task is to extract phonemes from input signal.

Remember that HMM is a finite state machine that changes its state every time step. In HMM based speech recognition, it is assumed that the sequence of observed speech vectors corresponding to each word is generated by a Markov model. Each phoneme (basic unit) is assigned a unique HMM, with transition probability parameters $a_{ij}$ and output observation distributions $b()$.

For a isolated (single) word recognition, the whole process can be described as follows:

Each word in the vocabulary has a distinct HMM, which is trained using a number of examples of that word. To recognize an unknown word, O, it is scored against all HMM models, $M_{1,2,3}$ and the HMM model with the highest likelihood score is considered as corresponding model that identifies the word.

Now, we got the HMM model hence the corresponding sequence of phonemes that represent the unknown word. By looking at the pronunciation dictionary in a reverse way, i.e. phoneme to word, we can find the corresponding word.

## Language model

The language model, that computes the prior probability $P(w)$ for $w = w_1, \ldots, w_k$, is represented as a n-gram model that models the probability i.e.

The n-gram probabilities are estimated from the training texts by counting n-gram occurrences. For simplicity, a bi-gram model can be used, in which the probability of a certain word depends only on its previous word i.e. $P(w_n \mid w_{n-1})$.

The acoustic model, decoder, and language model works together to recognize an unknown audio word or sentence.

References:


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main-content

## Über dieses Buch

This volume constitutes the refereed proceedings of the 6th Multi-disciplinary International Workshop On Artificial Intelligence, MIWAI 2012, held in Ho Chi Minh City, Vietnam, in December 2012. The 29 revised full papers presented were carefully reviewed and selected from numerous submissions. The papers are organized in topical sections in AI-GIS for climate change, computer vision, decision theory, e-commerce and AI, multiagent planning and learning, game theory, industrial applications of AI, multiagent systems and evolving intelligence, robotics and Web services.

## Inhaltsverzeichnis

### An Approach for Tuning the Parametric Water Flow Algorithm Based on ANN

Abstract
The manuscript proposed an approach for the optimization of the parametric water flow algorithm. This algorithm introduced a water flow function as a basis for the text-line segmentation process. The function is established as the power function. It exploited two parameters: water flow angle α and exponent n. In order to tune these parameters, the artificial neural network has been used. Results are encouraging because of the improvement of the text-line segmentation for the handwritten text.
Darko Brodić, Zoran N. Milivojević, Dejan Tanikić, Dragan R. Milivojević

### Mining Frequent Common Families in Trees

Abstract
This paper is concerned with mining the frequent common families from leaf-labeled tree database, in which supports for common families are established by not only exact family subtrees but also extended family subtrees. It proposes an algorithm to determine frequent common families with control over the coverage of extended family subtrees. The suggested method has been tested to both several synthetic data sets and a real data set.
Kyung Mi Lee, Chan Hee Lee, Keon Myung Lee

### A Structure Based Approach for Mathematical Expression Retrieval

Abstract
Mathematical expression (ME) retrieval problem has currently received much attention due to wide-spread availability of MEs on the World Wide Web. As MEs are two-dimensional in nature, traditional text retrieval techniques used in natural language processing are not sufficient for their retrieval. In this paper, we have proposed a novel structure based approach to ME retrieval problem. In our approach, query given in $$\mbox{\LaTeX}$$ format is preprocessed to eliminate extraneous keywords (like \displaystyle, \begin{array} etc.) while retaining the structure information like superscript and subscript relationships. MEs in the database are also preprocessed and stored in the same manner. We have created a database of 829 MEs in $$\mbox{\LaTeX}$$ form, that covers various branches of mathematics like Algebra, Trigonometry, Calculus etc. Preprocessed query is matched against the database of preprocessed MEs using Longest Common Subsequence (LCS) algorithm. LCS algorithm is used as it preserves the order of keywords in the preprocessed MEs unlike bag of words approach in the traditional text retrieval techniques. We have incorporated structure information into LCS algorithm and proposed a measure based on the modified algorithm, for ranking MEs in the database. As proposed approach exploits structure information, it is closer to human intuition. Retrieval performance has been evaluated using standard precision measure.
P. Pavan Kumar, Arun Agarwal, Chakravarthy Bhagvati

### Toward Composite Object Classification Using a Probabilistic Inference Engine

Abstract
This paper describes a new framework for classifying objects in still images using Description Logic reasoners. Unlike classical knowledge representation, features extracted from visual images are not always certain but rather ambiguous and probabilistic. To handle such uncertainty at the reasoning level, we employ the advantage of a probabilistic inference engine besides a classical reasoner, and design an image object ontology accordingly. The ontology defines composite objects in terms of basic objects, and basic objects in terms of visual features like shapes and colors. The proposed framework aims at improving on existing works in terms of both scalability and reusability. We demonstrate the performance of our object classification framework on a collection of car side images and compare to other approaches. Not only does our method show a distinctly better accuracy, but also each object classification result is equipped with a probability range.
Suwan Tongphu, Boontawee Suntisrivaraporn

### Relocation Action Planning in Electric Vehicle Sharing Systems

Abstract
This paper presents a design of a relocation planner for electric vehicle sharing systems, which periodically redistributes vehicles over multiple stations for better serviceability. For the relocation vector, or target vehicle distribution given by a relocation strategy, the proposed planner builds two preference lists, one for vehicles in overflow stations and the other for underflow stations. Then, the matching procedure assigns each electric vehicle to a station in such a way to minimize the relocation distance and time by means of a modified stable marriage problem solver. The performance measurement is conducted by a prototype implementation on top of the previously developed analysis framework and real-life trip records in Jeju City area. The morning-focused relocation strategy can best benefit from the proposed relocation planner in terms of both the relocation distance and the number of moves, mainly due to symmetric traffic patterns in the morning and in the evening.
Junghoon Lee, Hye-Jin Kim, Gyung-Leen Park

### A Guide to Portfolio-Based Planning

Abstract
In the recent years the field of automated planing has significantly advanced and several powerful domain-independent planners have been developed. However, none of these systems clearly outperforms all the others in every known benchmark domain. This observation motivated the idea of configuring and exploiting a portfolio of planners to achieve better performances than any individual planner: some recent planning systems based on this idea achieved significantly good results in experimental analysis and International Planning Competitions. Such results let suppose that future challenges of Automated Planning community will converge on designing different approaches for combining existing planning algorithms.
This paper reviews existing techniques and provides an exhaustive guide to portfolio-based planning. In addition, the paper outlines open issues of existing approaches and highlights possible future evolution of these techniques.
Mauro Vallati

### Color and Texture Image Segmentation

Abstract
For applications, such as image recognition or scene understanding, we cannot process the whole image directly for the reason that it is inefficient and unpractical. Therefore, to reduce the complexity of the recognition of the image, segmentation is a necessary step. Image segmentation divides an image into several parts (regions) according to some local homogeneous features of the image. For this purpose, understanding of the features of the image is important. Features such as color, texture, and patterns are considered for segmentation. Therefore, the thrust of our work is on the extraction of color textural features from images. Color measurement is done in Gaussian color space and texture features are extracted with Gabor filters. The paper proposes image segmentation based on recursive splitting k-means method and experiments are focused on color natural images taken from Berkeley Segmentation Dataset (BSD).
Chitti Kokil Kumar, Arun Agarwal, Raghavendra Rao Chillarige

### Evolutionary Multi-objective Optimization Based Proportional Integral Controller Design for Induction Motor Drive

Abstract
A new proportional-integral controller optimization methodology based on a multi-objective genetic algorithm for indirect field oriented controlled induction motor drive was proposed in this paper. GA-PI offers possibility of using the mathematical precision of PI algorithm with adaptability, and flexibility of genetic algorithm. This approach is independent of the system parameters, independent of the mathematical model, and can handle the system nonlinearity, allowing eliminates and reduces the overshoot, rise-time, settling time, load disturbance, and near-zero steady state error. The validity of proposed methods is confirmed by simulation results.
Moulay Rachid Douiri, Mohamed Cherkaoui

### A Multi-agent Scheduling Model for Maximizing Agent Satisfaction

Abstract
This paper presents a multi-agent scheduling model for selecting ecology-conservation activities in a large-scale ecological system. The overall goal is to maximize the total satisfaction of the multiple agents (stakeholders). The problem is motivated by the needs for sustainable development for the Dead Sea Basin in the Middle East. A new FPTAS algorithm for solving the scheduling problem is developed.
Eugene Levner, Amir Elalouf, Huajun Tang

### Enhancing Pixel Oriented Visualization by Merging Circle View and Circle Segment Visualization Techniques

Abstract
Analyzing large datasets is a difficult task in data analysis. For this many techniques have been proposed to display data in such a way that analysis can be done easily. There are many techniques used for data visualization, like geometric, icon based, hierarchical, graph based (line graph) and pixel oriented visualization techniques. In pixel oriented technique a single pixel is represented by a single data value and pixel color depends on the scale of data value i.e. if its scale is high then pixel is represented with light color and if the scale is low then it is represented with dark color. Visualizing large amount of data onto the screen is a challenge, because large data sets cannot be displayed on single screen at a time. There are two different types of pixel oriented techniques, query dependent and query independent pixel oriented techniques. Query dependent pixel oriented visualization technique are circle segment visualization technique, spiral and generalize spiral technique. A hierarchical technique: circle view technique is like a pie chart. For better visualization new technique is proposed by combining the idea of circle segment and circle view technique. This will enhance visualization technique and will display the data in circle form. The circle will be divided into segments and sub segments. This technique will display time series data in pixel oriented visualization for better analysis.
Zainab Aftab, Huma Tuaseef

### Time Series Prediction Using Motif Information

Abstract
Recent research works pay more attention to time series prediction, which some time series data mining approaches have been exploited. In this paper, we propose a new method for time series prediction which is based on the concept of time series motifs. Time series motif is a pattern appearing frequently in a time series. In the proposed approach, we first search for time series motif by using EP-C algorithm and then exploit motif information for forecasting in combination of a neural network model. Experimental results demonstrate our proposed method performs better than artificial neural network (ANN) in terms of prediction accuracy and time efficiency. Besides, our proposed method is more robust to noise than ANN.
Cao Duy Truong, Duong Tuan Anh

### A New Approach for Measuring Semantic Similarity in Ontology and Its Application in Information Retrieval

Abstract
Word similarity assessment is one of the most important elements in Natural Language Processing (NLP) and information retrieval. Evaluating semantic similarity of concepts is a problem that has been extensively investigated in the literature in different areas, such as artificial intelligence, cognitive science, databases and software engineering. Semantic similarity relates to computing the similarity between conceptually similar but not necessarily lexically similar terms. Currently, its importance is growing in different settings, such as digital libraries, heterogeneous databases and in particular the Semantic Web. In this paper, authors present a search engine framework using Google API that expands the user query based on similarity scores of each term of user’s query. The authors calculated the semantic similarity of noun words to obtain the related concepts described by the search query using WordNet. Users query is replaced with concepts discovered from the similarity measures. Authors present a new approach to compute the semantic similarity between words. A common data set of word pairs is used to evaluate the proposed approach: first calculate the semantic similarities of 30 word pairs, then the correlation coefficient between human judgement and three computational measures are calculated, the experimental result shows new approach is better than other existing computational models.
Kishor Wagh, Satish Kolhe

### Local Stereo Matching by Joining Shiftable Window and Non-parametric Transform

Abstract
In this paper, we propose a blocking-matching approach to the problem of correspondence in stereo matching. In blocking-matching methods, the correspondence or difference between pixels of a stereo pair is measured by a local window. Despite some area-based stereo matching algorithms have been developed and work well in a number of kinds of regions such as textureless or object boundary regions, their performance can debase once working in some sorts of radiometric conditions. Our proposed algorithm, in which non-parametric transform is used in the pre-processing step and an edge-preserving filter is used in the post-processing step, is an improved method of a shiftable window method and can work robustly in various radiometric conditions. Input images first are pre-processed by the census transform that makes our method robustly when the image pair is captured in various light sources or camera uncovering conditions. The window cost in our approach is calculated from the transformed images using in the Hamming distance, and the similarity is finally selected by a Winner-Takes-All strategy. The experimental results for the Middleburry images show that our proposed algorithm outperforms test local stereo algorithms in radiometrically dissimilarity images.
Hong Phuc Nguyen, Thi Dinh Tran, Quang Vinh Dinh

### A Comprehensive Analysis and Study in Intrusion Detection System Using k-NN Algorithm

Abstract
The security of computer networks has been in the focus of research for years. Organizations have realized that network security technology has become very important in protecting its information. Any attempt, successful or unsuccessful to compromise the confidentiality, integrity and availability of any information resource or the information itself is considered as a security threat or an intrusion. Every day, new kinds of threats are being faced by industries. One of the way-out to this problem is by using Intrusion Detection System (IDS). The main function of IDS is distinguishing and predicting normal or abnormal behaviors. This paper presents new implementation strategy performing the intrusion detection system, which gives better results by improving accuracy of classification. This approach is based on by defining addition and deletion rule and updating policy for intrusion detection. The experimental results, conducted on the KDD99 dataset, prove that, this new approach outperforms several state-of-the-art methods, particularly in detecting rare attack types.
Sharmila Wagh, Gaurav Neelwarna, Satish Kolhe

### AI-Based Support for Experimentation in an Environmental Biotechnological Process

Abstract
This paper presents an AI-based system that supports experimentation and control in the domain of environmental biotechnology. The objective of the experiments is to verify hypotheses on biostimulation of an activated sludge by sustaining oscillations in its metabolism to improve degradation of a hardly removable organic waste in the wastewater treatment plants. The presented system incorporates the application of a multi agent system (MAS), which uses ontologies and rules, and also a smart image processing method. One of the main tasks of the MAS is to provide a support for analysis of the off-line microscopic measurements based on both the rules describing the trends of analytical measurements and the quantitative on-line microscopic observations. Finally, the proposed MAS may keep track of results provided by the experts with results obtained on the basis of rules. As a result, the appropriate biostimulation control may prevent or reduce the climate changes.
Dariusz Choinski, Mieczyslaw Metzger, Witold Nocon, Grzegorz Polakow, Piotr Skupin

### Stereo Matching by Fusion of Local Methods and Spatial Weighted Window

Abstract
In this paper, we proposed two window-based methods, spatial weight shiftable window and spatial weight multiple window, for correspondence problem in stereo matching. The spatial weight shiftable window is an improvement of a shiftable window method while the spatial weight multiple window is an enhancement of a multiple window method. They combine spatial weighted window for each support window, and they hence can work well in the regions of disparity discontinuity or object boundaries. The window costs in our approaches is calculated by deploying spatial weighted window for each support window, and the similarity is finally selected by a Winner-Takes-All strategy. The experimental results for the Middleburry images illustrated that the proposed algorithms outperform test local stereo algorithms.
Thi Dinh Tran, Hong Phuc Nguyen, Quang Vinh Dinh

### Efficient Handling of 2D Image Queries Using VPC + -tree

Abstract
Handling queries over images is an interesting issue emerging recently in information systems. One of the most challenging problems on that work is how to process the image rotation efficiently since the query image and the ones stored in the database were typically not taken from the same angles. In this paper, an approach that employs time series representation of images is introduced. Subsequently, Fourier Transform technique can be performed to achieve the invariant rotation between images. Moreover, the data can be compressed efficiently on that representation when working on huge amount of data.
The major contribution on this work is the proposal of VPC  + -tree, extended from VPC-tree, a well-known structure supporting indexing and retrieving compressed objects. The VPC  + -tree not only supports faster and more accurate retrieval, but it also achieves the almost ideal ratio of disc access. It is a remarkable contribution in the field of time series data processing.
Tran Cong Doi, Quan Thanh Tho, Duong Tuan Anh

### Novel Granular Framework for Attribute Reduction in Incomplete Decision Systems

Abstract
Incomplete decision systems containing missing attribute values occur frequently in real world applications. This paper proposes IQRAIG_incomplete algorithm for reduct computation in Incomplete Decision Systems using a novel granular framework. The proposed granular framework enables computation of similarity classes for a set of objects simultaneously which helps in increased effienciency of computing positive region. The merits of the proposed algorithm over IFSPA-IPR algorithm has been demonstrated empirically.
Sai Prasad P.S.V.S., Raghavendra Rao Chillarige

### Agent-Based Control System for Sustainable Wastewater Treatment Process

Abstract
Biotechnological processes are difficult to control; many different state trajectories can be obtained from the same starting conditions. A well-known process of this class encountered in the industry is the wastewater treatment process with activated sludge. In this case, the quality of process control has a strong direct impact on the natural environment. Moreover, the crucial components of the processes are living organisms, which require appropriate actions to be taken to ensure their sustainability. This paper describes the agent-based approach to the operating control tasks for the process. The implemented control system is described, which is based on a real-time agent communication protocol implementing a blackboard knowledge system. Additional functionalities of the control system include the support for a cooperation between multiple experimenters, and on-line real-time modelling of the system providing the aid in a decision making.
Grzegorz Polaków, Mieczyslaw Metzger

### Tuning the Optimization Parameter Set for Code Size

Abstract
Determining nearly optimal optimization options for modern day compilers is a combinatorial problem. Added to this, specific to a given application, platform and optimization objective, fine tuning the parameter set being used by various optimization passes, enhance the complexity further. In this paper we propose a greedy based iterative approach and investigate the impact of fine-tuning the parameter set on the code size. The effectiveness of our approach is demonstrated on some of benchmark programs from SPEC2006 benchmark suite that there is a significant impact of tuning the parameter values on the code size.
N. A. B. Sankar Chebolu, Rajeev Wankar, Raghavendra Rao Chillarige

### Mining Weighted Frequent Sub-graphs with Weight and Support Affinities

Abstract
Mining weighted frequent sub-graphs in graph databases is possible to obtain more complex and various patterns compared with finding patterns in transactional databases, and the gained sub-graphs reflect object’s charateristics in the real world due to weight conditions. However, all of the patterns do not mean really valid patterns. Though any sub-graph is frequent, supports or weights of each element composing the sub-graph can be sharply different, where the graph is more likley to be a meaningless pattern. To solve the problem, we propose novel techniques for mining only meaningful sub-graphs by applying both weight and support affinities to graph mining and a corresponding algorithm, MWSA. Through MWSA, we can effectively eliminate invalid patterns with large gaps among the pattern’s elements. MWSA not only can gain valid sub-graphs but also can improve mining efficiency such as runtime and memory-usage by pruning needless patterns. These advantages are presented through various experiments.
Gangin Lee, Unil Yun

### Simple Spatial Clustering Algorithm Based on R-tree

Abstract
In this article, we present an algorithm based on R-tree structure to solve a clustering task in spatial data mining. The algorithm can apply to cluster not only point objects but also extended spatial objects such as lines and polygons. The experimental results show that our algorithm yields the same result as any other algorithm and accommodates to clustering task in spatial database.
Nam Nguyen Vinh, Bac Le

### Minimal Generalization for Conjunctive Queries

Abstract
Relaxation is a cooperative method to provide informative answers to failing queries of user. The combination of deductive generalization operators in a certain order can avoid unnecessary generalization of duplicate queries. However, it is not expected to return all generalized queries to the user because the theoretical search space exponentially increases with the number of literals of the original query. This paper identifies the minimal generalization in relaxation of conjunctive queries and analyses its properties. The minimal generalization has improved the cooperative behavior of a query answering system to find related information to the user without relaxing all generalized queries. The generalization operators are ordered in relaxation based on its properties. Moreover, it provides a solution to deal with the problem of overgeneralization that leads to queries far from the user’s original intent. The algorithm for finding all minimal generalized queries is proposed based on keeping the fixed order when applying these generalization operators.
Thu-Le Pham, Katsumi Inoue

### Interruptibility and Its Negative Impact on Graph Exploration Missions by a Team of Robots

Abstract
Exploring an unknown graph has several fields of applications such as search and rescue operations. A team of robots is used to speed up these exploration missions; provided that they synchronize and coordinate their activities. Here, several conditions may limit the communication capabilities of robots which are crucial for coordination (e.g. high temperature). Therefore, a periodic rendezvous is needed as a work around in order to overlap their communication ranges. Attending these periodic rendezvous sessions requires that robots interrupt their current exploration progress periodically and traverse back to the rendezvous points (i.e. Interruptibility). During their trips to these points, the robots cross the explored part of the graph. Thus, they do not gain new knowledge about the graph. Furthermore, it increases the required time of exploration. Evaluating the impact of these interruptions on the exploration process through several experiments under different exploration strategies is the scope of this paper.
Hamido Hourani, Eckart Hauck, Sabina Jeschke

### Monte-Carlo Search for Snakes and Coils

Abstract
The “Snake-In-The-Box” problem is a hard combinatorial search problem, first described more than 50 years ago, which consists in finding longest induced paths in hypercube graphs. Solutions to the problem have diverse and some quite surprising practical applications, but optimal solutions are known only for problems of small dimension, as the search space grows super-exponentially in the hypercube dimension. Incomplete search algorithms based on Evolutionary Computation techniques have been considered the state-of-the-art for finding near-optimal solutions, and have until recently held most significant records. This study presents the latest results of a new technique, based on Monte-Carlo search, which finds significantly improved solutions compared to prior techniques, is considerably faster, and, unlike EC techniques, requires no tuning.
David Kinny

### Algorithms for Filtration of Unordered Sets of Regression Rules

Abstract
This paper presents six filtration algorithms for the pruning of the unordered sets of regression rules. Three of these algorithms aim at the elimination of the rules which cover similar subsets of examples, whereas the other three ones aim at the optimization of the rule sets according to the prediction accuracy. The effectiveness of the filtration algorithms was empirically tested for 5 different rule learning heuristics on 35 benchmark datasets. The results show that, depending on the filtration algorithm, the reduction of the number of rules fluctuates on average between 10% and 50% and in most cases it does not cause statistically significant degradation in the accuracy of predictions.
Łukasz Wróbel, Marek Sikora, Adam Skowron

### Evaluation of Jamendo Database as Training Set for Automatic Genre Recognition

Abstract
Research on automatic music classification has gained significance in the recent years due to a significant increase in music collections size. Music is available very easily through the mobile and internet domain, so there is a need to manage music by categorizing it for search and discovery. This paper focuses on music classification by genre which is a type of supervised learning oriented problem. That means in order to build a formal classifier model it is necessary to train it using annotated data. Researchers have to build their own training sets or rely on others that are usually limited with regards to size or due to copyright restrictions. The approach described in this paper is to use the public Jamendo database for training the chosen classifier for genre recognition task.
Mariusz Kleć

### An Integrated Model for Financial Data Mining

Abstract
Nowadays, financial data analysis is becoming increasingly important in the business market. As companies collect more and more data from daily operations, they expect to extract useful knowledge from existing collected data to help make reasonable decisions for new customer requests, e.g. user credit category, churn analysis, real estate analysis, etc. Financial institutes have applied different data mining techniques to enhance their business performance. However, simple approach of these techniques could raise a performance issue. Besides, there are very few general models for both understanding and forecasting different financial fields. We present in this paper an integrated model for analyzing financial data. We also evaluate this model with different real-world data to show its performance.
Fan Cai, N-A. LeKhac, M-Tahar Kechadi

### Correlation Based Feature Selection Using Quantum Bio Inspired Estimation of Distribution Algorithm

Abstract
Correlation based feature Selection (CFS) evaluates different subsets based on the pairwise features correlations and the features-class correlations. Machine learning techniques are applied to CFS to help in discovering the most possible differnt combinations of features especillay in large feature spaces. This paper introduces a quantum bio inspired estimation of distribution algorithm (EDA) for CFS. The proposed algorithm integrates the quantum computing concepts, vaccination process with the immune clonal selection (QVICA) and EDA. It is employed as a search technique for CFS to find the optimal feature subset from the features space. It is implemented and evaluated using benchmark dataset KDD-cup99 and compared with the GA algorithm. The obtained results showed the ability of QVICA-with EDA to obtain better feature subsets with fewer length, higher fitness values and in a reduced computation time.
Omar S. Soliman, Aliaa Rassem

### Backmatter

Weitere Informationen


text:
# Geometrical approach to Seidel's switching for strongly regular graphs - Mathematics > Combinatorics

Abstract: In this paper, we simplify the known switching theorem due to Bose andShrikhande as follows.Let $G=V,E$ be a primitive strongly regular graph with parameters$v,k,\lambda,\mu$.Let $SG,H$ be the graph from $G$ by switching with respect to a nonempty$H\subset V$.Suppose $v=2k-\theta 1$ where $\theta 1$ is the nontrivial positiveeigenvalue of the $0,1$ adjacency matrix of $G$. This strongly regular graphis associated with a regular two-graph.Then, $SG,H$ is a strongly regular graph with the same parameters if andonly if the subgraph induced by $H$ is $k-\frac{v-h}{2}$ regular. Moreover,$SG,H$ is a strognly regualr graph with the other parameters if and only ifthe subgraph induced by $H$ is $k-\mu$ regular and the size of $H$ is $v-2$. Weprove these theorems with the view point of the geometrical theory of thefinite set on the Euclidean unit sphere.

Author: Hiroshi Nozaki

Source: https://arxiv.org/


text:
# [C/C++] need a bit of help making a simple search engine.

by Piddler
Tags: c or c, engine, search, simple
 P: 1 Hi, new to the forum, it is a really spiffy place. I'm not really much of a programmer, but I have an interest in it and kind of like to piddle around with programming. I am learning C and C++ mostly by doing, browsing books, and asking dumb questions of people who know alot more about it than I do. So here is a dumb question. I have been playing with arrays and I am trying to learn how to search through arrays. I managed to pull a piece of code from a book I've been reading ( I will show it below), and it works well. I want a search that will tell me if a number is in an array, and if so all of the locations that it can be found at. Here is the code I found, it is a function and it is in C. /* compare key to every element of array until the location is found or until the end of array is reached; return subscript of element if key or -1 if key is not found */ int linearSearch( const int A[], int key, int size ) { int n; /* counter */ /* loop through array */ for ( n = 0; n < size; ++n ) { if ( A[ n ] == key ) { return n; /* return location of key */ } /* end if */ } /* end for */ return -1; /* key not found */ } /* end function linearSearch */ the problem is that only returns the first one that it finds. how do I make it so that it returns all instances of the number matching the key? Again, I am kind of a novice that just tinkers for fun, so go easy on me. Thanks, I really like your forums!
HW Helper
P: 6,931
 Quote by Piddler how do I make it so that it returns all instances of the number matching the key?
You need another array the same size as A[], perhaps name that second array B[]. Then you would fill up B[] with the indexes of A[] that matched the search value. You'd also need to return the actual number of matches, which would be the effective size of B[].
 HW Helper P: 6,189 Hi Piddler! Welcome to PF. Here's and adaptation: /* compare key to every element of array; return the number of keys found. The found locations are stored in the array foundLocations. Note that foundLocations must be an array as big as A. */ int linearSearch( const int A[], int key, int size, int foundLocations[] ) { int n; /* counter */ int nrFound = 0; /* number of keys found */ /* loop through array */ for ( n = 0; n < size; ++n ) { if ( A[ n ] == key ) { foundLocations[ nrFound ] = n; /* store location of key */ nrFound++; } /* end if */ } /* end for */ return nrFound; /* number of keys found */ } /* end function linearSearch */
Mentor
P: 11,255

## [C/C++] need a bit of help making a simple search engine.

Here's a version that uses C++ vectors instead of arrays.

/* compare key to every element of vector A; return the number of keys found.
The found locations are stored in the vector foundLocations. */
int linearSearch (const vector<int> &A, int key, vector<int> &foundLocations)
{
/* get rid of anything that's already in foundLocations and set its size to 0 */
foundLocations.clear();

/* loop through vector A */
for (int n = 0; n < A.size(); ++n)
{
if (A[n] == key)
{
foundLocations.push_back(n);
}
}

return foundLocations.size();  /* number of keys found */
}
The size of A doesn't have to be passed as a separate parameter, because vectors "know" how big they are. Also, push_back() causes foundLocations to "grow" to exactly the size needed to accommodate the number of matches. In general, with vectors you don't have to do as much fussy "bookkeeping" with index variables, as you do with arrays.

Minor point: I put the declaration of n in the loop header instead of in a separate statement because n is used only inside the loop. I usually follow the principle that variables should be declared as "locally" as possible.

 Related Discussions General Discussion 23 Computing & Technology 3


text:
Another way to go about proving Binet's Formula

As I showed in another question of mine, it is easy to prove that

$$\tag{1}\phi^{n+1} =F_{n+1} \phi+F_{n }$$

given $F_1=1$ , $F_2=1$ , $F_{n+1}=F_n+F_{n-1}\text{ ; }n\geq2$.

Now, extending $(1)$ to negative and zero indices naturally yields: \eqalign{ & {F_{ 0}} = 0 \cr & {F_{ - 1}} = 1 \cr & {F_{ - 2}} = - 1 \cr & {F_{ - 3}} = 2 \cr & {F_{ - 4}} = - 3 \cr & {F_{ - n}} = {\left( { - 1} \right)^{n+1}}{F_{n}} \cr}

From this one has

$${\phi ^{ - n}} = {\left( { - 1} \right)^{n + 1}}\left( {{F_{n }}\phi - {F_{n + 1}}} \right)$$

A few examples:

\eqalign{ & {\phi ^{ - 1}} = \phi - 1 \cr & {\phi ^{ - 2}} = 2 - \phi \cr & {\phi ^{ - 3}} = 2\phi - 3 \cr}

Then one has that

\eqalign{ & {\left( { - \frac{1}{\phi }} \right)^n} = {F_{n + 1}} - {F_n}\phi \cr & {\phi ^n} = {F_n}\phi + {F_{n - 1}} \cr}

and consequently

\eqalign{ & {\phi ^n} + {\left( { - \frac{1}{\phi }} \right)^n} = {F_n}\phi + {F_{n - 1}} + {F_{n + 1}} - {F_n}\phi \cr & {\phi ^n} + {\left( { - \frac{1}{\phi }} \right)^n} = {F_{n + 1}} + {F_{n - 1}} \cr & {\phi ^n} + {\left( { - \frac{1}{\phi }} \right)^n} = {L_n} \cr}

How can this be put into an acceptable proof? (Note that given the relation between Lucas and Fibonacci numers, this straightforwardly gives Binet's Formula:

$${F_n} = \frac{1}{{\sqrt 5 }}\left[ {{\phi ^n} - {{\left( { - \frac{1}{\phi }} \right)}^n}} \right]$$

-
@AndréNicolas Fixed! –  Pedro Tamaroff Apr 18 '12 at 23:02
Does "from this one has" follow immediately? It does if the formula you started with (from earlier post) holds for negative $n$. (It has been a while since that post.) –  André Nicolas Apr 18 '12 at 23:19
@AndréNicolas The generalization is needed for the formula to hold. –  Pedro Tamaroff Apr 18 '12 at 23:20

Below is a proof of the uniqueness theorem for second order recurrences, which is employed in Will's answer. The proof generalizes to higher-order recurrences. It is a discrete analog of the better-known result for differential equations, using variation of parameters (see this answer, and see my my 2004/4/27 sci.math post for references).

Theorem $\$ If $\rm\:f,g,h\:$ are solutions of the recurrence

$$\rm \qquad\quad\ \ y''\: =\ p\ y' + q\ y,\ \ \ where\ \ \ y'(n)\, :=\, y(n\!+\!1)$$ with  Wronskian (Casoratian) $\rm\ \ W = g\:h'-g'h \ne 0\:$

then $\rm\,\exists\,\ \color{#c00}{ constants}\ \ c,d\,$ such that $\rm\: f = c\: g + d\: h,\ \ \rm\color{#c00}{i.e.\ \ c'=c,\ d' = d}$

Proof $\$ The equations $[0],[1]$ below have unique solution $\rm\:(c,d)\:$ via det $\rm = W \ne 0.$

$\rm[0]\qquad f\ =\ c\: g \: + d\: h$

$\rm[1]\qquad f' =\ c\: g' + d\: h'$

Now $\rm\:q\:[0] + p\:[1]\:$ yields:

$\rm[2]\qquad q\:f+p\:f'\: =\ f''\: =\ c\: g'' + d\: h''\$ via $\rm\ \ q\:g+p\:g'\: =\ g'',\ \ q\:h+p\:h'\: =\ h''$

$\rm[3]\qquad 0\ =\ (c'-c)\:g' \:+ (d'-d)\:h'\:\ \$ via $\ \ [0]'-[1]$

$\rm[4]\qquad 0\ =\ (c'-c)\:g'' + (d'-d)\:h''\ \$ via $\ \ [1]'-[2]$

$[3],[4]$ have solution $\rm\:(c'\!-c,d'\!-d) = (0,0),\:$ unique by $\rm\:det = W' = g'\:h''-g''\:h' \ne 0.\:$ Therefore $\rm\:c,d\:$ are constants, since $\rm\:c' = c\:$ means $\rm\:c(n+1) = c(n).\quad$ QED

Remark $\$ Note $\rm\, W = g\:h'-g'h = 0 \iff g/h =g'/h' = (g/h)'\iff g/h = c\,$ constant.

-

The set of sequences $x_n$ that have the property that $x_{n+2} = x_{n+1} + x_n,$ with, say, real number values, makes a vector space over the reals of dimension 2. Taking the two roots of $\lambda^2 = \lambda + 1,$ the larger being $$\phi = \frac{1 + \sqrt 5}{2}$$ and the smaller being $-1 / \phi,$ any such sequence, including index shifts, whatever you like, is a linear combination of two basis sequences, $$\ldots, 1/\phi, 1, \phi, \phi^2, \ldots$$ and $$\ldots, - \phi, 1, -1 / \phi, 1/ \phi^2, \ldots$$ where I am demanding that the element with value 1 have index 0 in both sequences. If I have any favorite sequence with $x_0, x_1$ specified, the equation to be solved for coefficients $A,B$ are $$A + B = x_0, \; \; \; A \phi - B / \phi = x_1.$$

So $$\left( \begin{array}{cc} 1 & 1 \\ \phi & -1/\phi \end{array} \right) \left( \begin{array}{c} A \\ B \end{array} \right) \; \; = \; \; \left( \begin{array}{c} x_0 \\ x_1 \end{array} \right).$$ still composing...

$$\left( \begin{array}{c} A \\ B \end{array} \right) \; \; = \; \; \frac{-1}{\sqrt 5} \left( \begin{array}{cc} -1/\phi & -1 \\ -\phi & 1 \end{array} \right) \left( \begin{array}{c} x_0 \\ x_1 \end{array} \right).$$ getting there...

Evidently you are taking $x_0 = 0, x_1 = 1,$ so we get $$\left( \begin{array}{c} A \\ B \end{array} \right) \; \; = \; \; \frac{-1}{\sqrt 5} \left( \begin{array}{cc} -1/\phi & -1 \\ -\phi & 1 \end{array} \right) \left( \begin{array}{c} 0 \\ 1 \end{array} \right) \; \; = \; \; \left( \begin{array}{c} 1 / \sqrt 5 \\ -1/ \sqrt 5 \end{array} \right) .$$ My first basis sequence has elements labelled $y_n = \phi^n,$ and the second has $z_n = (-1/\phi)^n,$ so the Fibonacci sequence obeys $$x_n = \frac{1}{\sqrt 5} \; \; \phi^n \; \; \; - \; \; \; \frac{1}{\sqrt 5} \; \; \left( \frac{-1}{\phi} \right)^n.$$

-
And how does one prove that they are a linear combination of such sequences? What you're saying is that $$\left\langle {{\phi ^n},\frac{{{{\left( { - 1} \right)}^n}}}{{{\phi ^n}}}} \right\rangle$$ spans all the sequences of the form $${x_{n + 2}} = {x_{n + 1}} + {x_n}?$$ –  Pedro Tamaroff Apr 18 '12 at 23:45
@PeterT.off, yes. –  Will Jagy Apr 19 '12 at 0:10
can you provide a proof of that? I've seen this before, but as you can see, I choose other paths. –  Pedro Tamaroff Apr 19 '12 at 0:14
Such a sequence is completely determined once we know $x_0$ and $x_1$. Let $(a_n)$ and $(b_n)$ be the two sequences above. All you need to show is that we can find $u$ and $v$ such that $ua_0+vb_0=x_0$, $ua_1+vb_1=x_1$. Two linear equations in two unknowns. –  André Nicolas Apr 19 '12 at 0:16
@PeterT.off, I think I would add that the fact that such a sequence is completely determined once $x_0, x_1$ are known is an exercise in mathematical induction: if two sequences $x,y$ agree for indices from $0$ to $n,$ show that they agree at index $n+1.$ Next, if they agree for indices $1$ down to $-n,$ show that they agree at index $-n-1.$ That shows the dimension of the vector space is 2. Another basis is the Fibonacci and Lucas sequences. –  Will Jagy Apr 19 '12 at 0:25
show 3 more comments

I might as well point out how to use your way. We have the following two equations:

$$\varphi^{n+1}=F_{n+1}\varphi+F_{n} \tag{1}$$ $$(-1/\varphi)^n=F_{n+1}-F_n\varphi \tag{2}$$

For $(1)$, decrease $n$ by $1$, and for $(2)$ do the same but then divide both sides by $\varphi$. We obtain

$$\varphi^n=F_n\varphi+F_{n-1} \tag{a}$$ $$-(-1/\varphi)^n=F_n/\varphi-F_{n-1} \tag{b}$$

Now add $\rm(a)$ and $\rm(b)$ together and divide by $\varphi+1/\varphi=\sqrt{5}$ to obtain Binet's. This is analogous to what you did for Lucas numbers.

-
@PeterT.off I'm not sure I understand your question then. What's unacceptable about your current proof of Binet's, besides the fact you weren't explicit about the "straightforward" part at the end? –  anon Apr 19 '12 at 1:20


text:
# Differentiation Of Trigonometric Functions Homework

They can’t always be done, but sometimes, such as this case, they can simplify the problem.The change of variables here is to let $$\theta = 6x$$ and then notice that as $$x \to 0$$ we also have $$\theta \to 6\left( 0 \right) = 0$$.

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See the Proof of Trig Limits section of the Extras chapter to see the proof of these two limits. Students often ask why we always use radians in a Calculus class. The proof of the formula involving sine above requires the angles to be in radians.

If the angles are in degrees the limit involving sine is not 1 and so the formulas we will derive below would also change.

All we need to do is multiply the numerator and denominator of the fraction in the denominator by 7 to get things set up to use the fact. $\begin\mathop \limits_ \frac & = \frac\\ & = \frac\\ & = \frac\\ & = \frac\end$ This limit looks nothing like the limit in the fact, however it can be thought of as a combination of the previous two parts by doing a little rewriting.

First, we’ll split the fraction up as follows, $\mathop \limits_ \frac = \mathop \limits_ \frac\frac$ Now, the fact wants a $$t$$ in the denominator of the first and in the numerator of the second.

To see that we can use the fact on this limit let’s do a change of variables.

A change of variables is really just a renaming of portions of the problem to make something look more like something we know how to deal with.

$\mathop \limits_ \frac = \frac\mathop \limits_ \frac = \frac\left( 1 \right) = \frac$ Now, in this case we can’t factor the 6 out of the sine so we’re stuck with it there and we’ll need to figure out a way to deal with it.

To do this problem we need to notice that in the fact the argument of the sine is the same as the denominator ( both $$\theta$$’s).

When doing a change of variables in a limit we need to change all the $$x$$’s into $$\theta$$’s and that includes the one in the limit.

Doing the change of variables on this limit gives, $\begin\mathop \limits_ \frac & = 6\mathop \limits_ \frac\hspace\theta = 6x\ & = 6\mathop \limits_ \frac\ & = 6\left( 1 \right)\ & = 6\hspace\end$ And there we are.

## Comments Differentiation Of Trigonometric Functions Homework

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text:
# Wave function constrained to a fixed trajectory? Really?

this is probably a very stupid question. First of all, I'm a mathematician so please try to use coordinate-free notations.

It's often used in quantum mechanics a wave function depending on a fixed trajectory. For instance, in How to derive the Aharonov-Bohm effect result?, $\psi (x, \gamma)$ depends on the path $\gamma$. I can understand this in terms path integral quantization (which is essentially perturbative and I don't like). However in the philosophical scope of quantum mechanics it seems unreasonable to fix a trajectory unless the wave function is collapsed at all possible times (we know the position at every instant). Note that the holonomy $\exp (-iq_e \int A)$ is gauge invariant, but $A$ (that's actually a cocyle $A =\{A_i, {g_{ij}}\}$ representing a gauge equivalence) need not to be $d$-closed (i.e., $dA_i = F_A$ may be non-zero), therefore it really depends on the path chosen (and not just on the endpoints). Maybe this condition is simply implicitly posed on the boundary conditions?

Let me be more precise. I will treat the Aharonov-Bohm effect in order to deal with something more concrete. For simplicity, let's take the space-time $X = \mathbb{R} \times \mathbb{R}^3$ together with a charge at $(t,0)$, i.e., $$dF_A = q_m\delta_{(t, 0)}$$ and a particle of charge $q_e$ moving through fixed paths $\gamma_i$, $i = 1, 2$ with the same endpoints.

What's the meaning of $\psi (x, \gamma_i)$ in this case? Is the wave function really collapsed at every instant (i.e., do we always know the position)?

If the above questions cannot be answered without propagators or path integrals, then is the Aharonov-Bohm effect a strictly perturbative phenomenum? If no, how to derive the Aharonov-Bohm effect non-perturbatively?

By deriving the Aharonov-Bohm effect I mean obtaining a phase difference that would lead to the Dirac charge quantization condition. For instance, in the path integral formulation the phase difference is given by $\exp (-iq_e \int_{W_e} A)$ (where $W_e$ is a loop through the solenoid) and this leads to $q_m q_e \in 2\pi \mathbb{Z}$ if one wants the solenoid to be undetectable.

For sake of completeness, I will add a possible solution of the Dirac charge quantization condition that does not makes the Aharonov-Bohm effect visible in any meaningful way, so that maybe someone can include the Aharonov-Bohm effect in this context.

A possible solution (to the Dirac charge quantization and not to the Aharonov-Bohm effect) is given at page 14-16 of http://www.maths.ed.ac.uk/~jmf/Teaching/Lectures/EDC.pdf , by declaring that $\chi = \log (g)$ for some gauge transformation $g$, that is the two open charts $U_{i} = \{(x, y, z) \in \mathbb{R}^3| \ (-1)^i z > 0 \}$ covering $\mathbb{R}^3\setminus 0$ together with the potentials $A_{-}$ and $A_{+}$ defines a $U(1)$-bundle.

Thanks in advance.

## 2 Answers

Consider the following setup for electromagnetic field:

$$\phi(x,y)=U_0\theta(R^2-x^2-y^2),$$ $$\vec A(x,y)=\frac{A_0}2\begin{cases} \left(y,-x,0\right)&x^2+y^2\le R^2\\ \left(\frac{R^2y}{x^2+y^2},-\frac{R^2x}{x^2+y^2},0\right)&\mathrm{otherwise} \end{cases},$$ where $\theta(x)$ is Heaviside theta, and $U_0$ is assumed to be very large — such that the electron would never get inside (may be infinity, i.e. homogeneous Dirichlet boundary condition at $x^2+y^2=R^2$), and $R$ is the radius of a solenoid.

If you propagate an electron wave so that it would go in the direction of the solenoid, the result of the interference on the side opposite to the source would depend on $A_0$, even though $\vec B=\nabla\times\vec A$ vanishes whenever $x^2+y^2>R^2$, and the wavefunction is nonzero only there. This is the essence of the Aharonov-Bohm effect. All the talk about pairs of fixed paths in this topic is merely a simplification to aid analysis.

• Thanks for your answer. I don't get what boundary condition you're putting on the Schroedinger equation to require that the electron goes in the direction of the solenoid. – user40276 Mar 5 '16 at 9:39
• The overall boundary condition is boundedness (since the space is infinite). For electron to go in the direction of the solenoid, you use an initial condition, not a boundary condition, e.g. $\psi(x,y,t_0)=\exp(ix)\exp(\frac1{x+2})\theta(-(x+2))$ or any nicer. You just need to make sure the wave packet or what you have moves (mostly) in the needed direction and initially avoids having nonzero values in the location of the solenoid (or its value there can be neglected). – Ruslan Mar 5 '16 at 10:15
• Ops! Of course, initial value condition. Sorry but I still cannot understand how can you guarantee that the electron does not enter in a position where $B$ is non-zero. Furthermore, since I'm having some difficulties with the calculus notation (it has been like 4 years since the last time I used these notations, now I've got too used to differential forms), could you tell me what's the phase difference that you're getting from your derivation (are you really getting the holonomy? But in this case, the path must fixed?). My objective was to get the phase difference usually ... – user40276 Mar 6 '16 at 17:56
• obtained when deriving the Dirac charge quantization condition. I will edit my question to clarify myself. – user40276 Mar 6 '16 at 17:57
• The electron won't enter there because $U_0$ is taken to be large enough, up to infinity — in this limit case you can just put a homogeneous Dirichlet condition at the boundary of the solenoid, and thus the electron will automatically never appear past the border (even if it does, it won't affect the solution at all, as in infinite potential well). – Ruslan Mar 6 '16 at 17:59

Would like to add to some previous answers.

The Klein-Gordon / Schrodinger's equation masquerades as a wave equation in time and space, but it is actually a statement about frequency and wavevector.

In principle the 'wave' equation in a constant magnetic field and electron beam source can be symmetrized and solved semiclassically or by a mix of Born and partial-wave expansion techniques. Judging by your apparent math comfort level, I will describe a technique you can implement easily.

You are not measuring phase difference in path. You are measuring a curve of arrival phase by field strength, relative to the phase of arrival when no field is present. It just so happens that on one side of the solenoid the phase is wave is stretched and on the other it is compressed.

The simplest way to calculate the total phase and amplitude differenes is to pick two points opposite your solenoid, $$(x_i,y_i)$$ and $$(x_f,y_f)$$ that form a line through your solenoid, plus an arbitrary point in between, $$(x',y')$$ on the dividing plane through the solenoid whose normal is the line you just chose. You need to calculate both the transverse momentum dispersion affect on amplitude and also the phase shift which occurs on the route between your three points, which is two propagations (plane waves). Once you complete this, you can integrate over all $$(x',y')$$ points in that plane (or a section of the plane) to find your complete phasor at the final point. This weighted sum of triangle paths well-approximates the actual curved wavefront trajectories of the disturbances in the true electron phasor field.

This procedure has nothing to do with quantumness. Multiple propagation is the same procedure you use when solving Fresnel-Kirchoff optics wave problems.

Finally. Addressing your question about the regularity of the Berry curvature field. Just like the metric in GR can become singular, there are also singular points for the Berry curvature. And worse, when we generalize the problem beyond amplitudes. However, most phenomena do not require that level of inspection. Operationally the effect acts only on the 4-momentum eigenstate spectrum, which is barely connected to its dual in spacetime at all in the statistical limit.

There is actually a classical analogue known as the fast-slow adiabatic cycling drag. (See J. Hannay 1985). His mathematics is easy to understand and compare to Berry's paper on QM (1984).