This may have a proper name, if so - let's discuss. If not, let's name it. This is for a web application in C#, so whatever we call it I will start naming as such in my code.
I'm taking GPS data as a collection of n 'Points', each point has latitude (degrees), longitude (degrees), elevation (meters), and datetime(DateTime object). From this, I compute a list of n-1 'Segments.' In each Segment object, I have distance(meters), time(seconds), and velocity(meters/second), effectively taking the derivative between each consecutive point.
Now, I want to n-2 "name this object"s. Each will have acceleration (meters/second/second). A good name for a collection of segments may be 'Path' or 'Track', but this is specifically an object that is two segments only (comprised from three consecutive points), which holds the second derivative value.
I'm leaning toward 'Segue' and this will be the object's name as I flesh out the details. Is there an existing name for this concept, or does anyone have any suggestions?
Related
I want to simulate a 2D heat transfer process in the subsurface on a region which is infinite on the r-direction. So, as you know, the very basic way to model this is to draw a geometry that is very long in the r direction. I have done this, and the results that I obtain is correct as in this case, the results are matched with the analytical solution. As you know, there is a capability in Comsol called infinite element domain which serves the purpose to the problem mentioned above. In this case, we need to define a limited geometry on which we want to solve the PDE, and also need to draw a small domain acting as the Infinite Element Domain. However, in this case, the results are not correct because they are not matched with the analytical solution. Is there anything that I am missing to correctly use Infinite Element Domain in comsol?
Any help or comment would be appreciated.
Edit:
I edited the post to be more specific.
Please consider the following figure where a fluid with high temperature is being injected into a region with lower temperature:
https://i.stack.imgur.com/BQycC.png
The equation to solve is:
https://i.stack.imgur.com/qrZcK.png
With the following initial and boundary conditions (note that the upper and lower boundary condition is no-flux):
https://i.stack.imgur.com/l7pHo.png
We want to obtain the temperature profile over the length of rw<r<140 m (rw is very small and is equal to 0.005 m here) at different times. One way to model this numerically in Comsol is to draw a rectangle that is 2000 m in the r-direction, and get results only in the span of r [rw,140] m:
https://i.stack.imgur.com/BKCOi.png
The results of this case is fine, because they are well-matched with the analytical solution.
Another way to model this is to replace the above geometry with a bounded one that is [rw, 140] m in the r-direction and then augment it with an Infinite Element domain that is meshed mapped, as follows:
https://i.stack.imgur.com/m9ksm.png
Here, I have set the thickness of Infinite Element to 10 m in the r-direction. However, the results in this case are not matched with the analytical solution (or the above case where Infinite Element domain was not used). Is there anything that I am missing in Comsol? I have also changed some variables with regard to Infinite Element in Comsol such as physical width or distance, but I didn't see any changes in the results.
BTW, here are the results:
https://i.stack.imgur.com/cdaPH.png
The search algorithm is a Breadth first search. I'm not sure how to store terms from and equation into a open list. The function f(x) has the form of ax^e1 + bx^e2 + cx^e3 + k, where a, b, c, are coefficients; k is constant. All exponents, coefficients, and constants are integers between 0 and 5.
Initial state: of the problem solving process should be any term from the ax^e1, bx^e2, cX^e3, k.
The algorithm gradually expands the number of terms in each level of the list.
Not sure how to add the terms to an equation from an open Queue. That is the question.
The general problem that you are dealing belongs to the regression analysis area, and several techniques are available to find a function that fits a given data set, including the popular least squares methods for finding the line of best fit given a dataset (a brief starting point is the related page on wikipedia, but if you want to deepen this topic, you should look at the research paper out there).
If you want to stick with the breadth first search algorithm, although this kind of approach is not common for such a problem, first of all, you need to define all the elements for a search problem, namely (see for more information Chapter 3 of the book of Stuart and Russell, Artificial Intelligence: A Modern Approach):
Initial state: Some initial values for the different terms.
Actions: in your case it should be a change in the different terms. Note that you should discretize the changes in the values.
Transition function: function that determines the new states given a state and an action.
Goal test: a check to recognize whether a state is a goal state or not, and so to terminate the search. There are different ways to define this test in a regression problem. One way is to set a threshold for the sum of the square errors.
Step cost: The cost for an action. In such an abstract problem, probably you can consider the unweighted distance from the initial state on the search graph.
Note that you should carefully think about these elements, as, for example, they determine how efficient your search would be or whether you will have cycles in the search graph.
After you defined all of the elements for the search problem, you basically have to implement:
Node, that contains information about the parent, the state, and the current cost;
Function to expand a given node that returns the successor nodes (according to the transition function, the actions, and the step cost);
Goal test;
The actual search algorithm. In the queue at the beginning you will have the node containing the initial state. After, it is updated with the successor nodes.
I'm look at an example in the Mahout in Action book. It uses the StaticWordValueEncoder to encoder a text in the feature hashing manner.
When encode "text to magically vectorize" with a standard analyser and probe = 1, the vector is {12:1.0, 54:1.0, 78:1.0}. However, I can't figure out which word the hash index refers to.
Is there any method to get the [hash, original word] as a pair? e.g. hash 12 refers to the word "text"?
if you have read Mahout in Action paragraph:
"The value of a continuous
variable gets added directly to one or more locations that are allocated for the storage
of the value. The location or locations are determined by the name of the feature.
This hashed feature approach has the distinct advantage of requiring less memory
and one less pass through the training data, but it can make it much harder to reverse engineer
vectors to determine which original feature mapped to a vector location."
-----I am not sure how the reverse engineering can be done(which certainly a difficult task as Author has put) Perhaps some one might put some light on this.
I have a road map represented as a directed graph of junctions and links leading from one junction to another, each link is weighted with it's own traversal time (the time it takes to cross the link) and im asked to find an algorithm to get from junction A to junction B and back from junction B to junction A so that the total path cost (in time) takes no longer than 10% more time than the optimal path cost (that is the path cost returned by A* algorithm) while keeping the time overlaps of the path to B and the path from B to a minimum, that is if t(x,y) represents the time to cross link (x,y) i need to bring to minimum the sum of t(x,y) + t(y,x) for the links that overlap.
the algorithm should be optimal for the problem at hand and complete (it should also be efficient) and probably use some variants of A* like A*epsilon and the likes...
does anyone have a clue how to go about this problem?
i was thinking of representing the states of this problem as (junction,flag) where flag indicates whether the current node is a part of a path that already passed junction B and the goal state is (A,True) and then using A*epsilon on this... but i don't know how to take into account the time overlap issue.. i guess what im suggesting is not the way im intended to solve this.
any help would be greatly appreciated :)
Say I want to build a check-in aggregator that counts visits across platforms, so that I can know for a given place how many people have checked in there on Foursquare, Gowalla, BrightKite, etc. Is there a good library or set of tools I can use out of the box to associate the venue entries in each service with a unique place identifier of my own?
I basically want a function that can map from a pair of (placename, address, lat/long) tuples to [0,1) confidence that they refer to the same real-world location.
Someone must have done this already, but my google-fu is weak.
Yes, you can submit the two addresses using geocoder.net (assuming you're a .Net developer, you didn't say). It provides a common interface for address verification and geocoding, so you can be reasonably sure that one address equals another.
If you can't get them to standardize and match, you can compare their distances and assume they are the same place if they are below a certain threshold away from each other.
I'm pessimist that there is such a tool already accessible.
A good solution to match pairs based on the entity resolution literature would be to
get the placenames, define and use a good distance function on them (eg. edit distance),
get the address, standardize (eg. with the mentioned geocoder.net tools), and also define distance between them,
get the coordinates and get a distance (this is easy: there are lots of libraries and tools for geographic distance calculations, and that seems to be a good metric),
turn the distances to probabilities ("what is the probability of such a distance, if we suppose these are the same places")(not straightforward),
and combine the probabilities (not straightforward also).
Then maybe a closure-like algorithm (close the set according to merging pairs above a given probability treshold) also can help to find all the matchings (for example when different names accumulate for a given venue).
It wouldn't be a bad tool or service however.