Question: I have two dropdowns DD1 & DD2 , I want that if user selects option HELLO (value="100") in DD1 and presses a key , then the same value option in DD2 is removed, DD1 will have that option,
it would only be removed from DD2

```
var selectedItems = $('#DD1').val();

 for ( var i = 0 ; i < selectedItems.length; i++) 
        {
           $("#DD2 option[value='"+selectedItems[i]+']"').remove();
        }                                                                       

```

Answer: 
From what I understand of HTM's, the structure of layers and columns mimics the structure of the neocortex. See appendix B here: <http://www.numenta.com/htm-overview/education/HTM_CorticalLearningAlgorithms.pdf>

So the short answer would be that since the brain can understand non-linear phenomenon with this structure, so can an HTM.

Initial, instantaneous sensory input is indeed mapped to 2D regions within an HTM. This does not limit HTM's to dealing with 2D representations any more than a one dimensional string of bits is limited to representing only one dimensional things. It's just a way of encoding stuff so that sparse distributed representations can be formed and their efficiencies can be taken advantage of.

To answer your question about Project Gutenberg, I don't think an HTM will really understand language without first understanding the physical world on which language is based and creates symbols for. That said, this is a very interesting sequence for an HTM, since predictions are only made in one direction, and in a way the understanding of what's happening to the fruit goes backwards. i.e. I see the pattern 'flies like a' and assume the phrase applies to the fruit the same way it did to time. HTM's do group subsequent input (words in this case) together at higher levels, so if you used Fuzzy Grouping (perhaps) as Davide Maltoni has shown to be effective, the two halves of the sentence could be grouped together into the same high level representation and feedback could be sent down linking the two specific sentences. Numenta, to my knowledge has not done too much with feedback messages yet, but it's definitely part of the theory.
The software which runs the HTM is called NuPIC (Numenta Platform for Intelligent Computing). A NuPIC region (representing a region of neocortex) can be configured to either use topology or not, depending on the type of data it's receiving. 

If you use topology, the usual setup maps each column to a set of inputs which is centred on the corresponding position in the input space (the connections will be selected randomly according to a probability distribution which favours the centre). The spatial pattern recognising component of NuPIC, known as the Spatial Pooler (SP), will then learn to recognise and represent localised topological features in the data. 

There is absolutely no restriction on the "linearity" of the input data which NuPIC can learn. NuPIC can learn sequences of spatial patterns in extremely high-dimensional spaces, and is limited only by the presence (or lack of) spatial and temporal structure in the data.

To answer the specific part of your question, yes, NuPIC can learn non-Euclidean and non-linear relationships, because NuPIC is not, and cannot be modelled by, a linear system. On the other hand, it seems logically impossible to infer relationships of a dimensionality which exceeds that of the data.

The best place to find out about HTM and NuPIC, its Open Source implementation, is at NuPIC's [community website](http://numenta.org) (and mailing list).