Vector Mind
Cre Wallace
We have successfully integrated Hololens with Mind Vector which basically adds another dimension to our app by augmenting 3D mind maps with the real world. Hololens allows for a richer, more immersive feeling than present forms of viewing mind maps while allowing the user to be aware of their environment.
With Mind Vector, the best mind mapping software online, you can create maps and store it on the cloud. With this feature, you can collaborate with your friends and access your maps from any platform just by signing in your account.
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As discovery of cellular diversity in the brain accelerates, so does the need for tools that target cells based on multiple features. Here we developed Conditional Viral Expression by Ribozyme Guided Degradation (ConVERGD), an adeno-associated virus-based, single-construct, intersectional targeting strategy that combines a self-cleaving ribozyme with traditional FLEx switches to deliver molecular cargo to specific neuronal subtypes. ConVERGD offers benefits over existing intersectional expression platforms, such as expanded intersectional targeting with up to five recombinase-based features, accommodation of larger and more complex payloads and a vector that is easy to modify for rapid toolkit expansion. In the present report we employed ConVERGD to characterize an unexplored subpopulation of norepinephrine (NE)-producing neurons within the rodent locus coeruleus that co-express the endogenous opioid gene prodynorphin (Pdyn). These studies showcase ConVERGD as a versatile tool for targeting diverse cell types and reveal Pdyn-expressing NE+ locus coeruleus neurons as a small neuronal subpopulation capable of driving anxiogenic behavioral responses in rodents.
A.C.H. and L.A.S. conceived the project. A.C.H. designed ConVERGD, generated and tested viral constructs in vitro and in vivo and performed rabies tracing and behavioral studies. B.G.P. assisted with the cloning of viral constructs and in vitro testing. B.X. performed sequencing analysis. J.W.G. piloted manual sequencing methods and collected cells for sequencing. C.M.W. assisted with in vitro testing. H.G.N. assisted with behavioral testing. P.C. and J.B.B. provided the protocol and starter virus for generating N2c-rabies. L.A.S. generated viruses, performed in situ hybridization experiments, in vitro assessment of leak expression and in vivo testing and rabies-tracing experiments, and supervised the project. A.C.H. and L.A.S. wrote and edited the paper with feedback from the other authors.
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So, i want to sort a map by value in this kind of algorithm. There are 3 integers in the vector and i want to sort the map by the third value in the vector in the map in descending. If the third value is the same, sort by the second value descending, if the second value is the same then the first value.
You can't sort a map like that, because it sorts its keys automatically and doesn't allow you to break order. What you can do is create a wrapper class around your string and vector, define a custom comparison operator for it and use std::set instead. You won't be able to get elements by their keys, though. If you want both getting by key and sorting, you may read about Boost.MultiIndex, or combine multiple containers for your task.
If you don't use boost and you only need the alternative sorting temporarily, you can get away with an extra map std::multi_map where you put all iterators to elements, based on a new key (third value in vector). Mind you, this new map is only valid as long as the original map doesn't change. If this is not good enough, you need to put the two map in an extra class to do the bookkeeping and so you're making a Boost.MultiIndex.
Vector spaces are one of the most fundamental and important algebraic structures that are used far beyond math and physics. This algebraic structure has appeared in many real world problems and is therefore known for centuries.
In this post, we study specific vector spaces where the vectors are not tuples but functions. This raises several challenges since general function spaces are infinite dimensional and concepts like basis and linear independence might be reconsidered. We will, however, focus on mechanics of a function space without diving too deep into the realm of infinite dimensional vector spaces and its specifics.
The branch of math that studies function spaces is called functional analysis. For those who have no exposure to functional analysis, the introduction series to functional analysis provided by The Bright Side of Mathematics on YouTube or one of the book from the literature might help to get you up to speed.
Example 1.1 (Real finite-dimensional vector space )
Let , the tuples with real entries and . For as well as with and , let us define the addition and scalar multiplication as follows.
The axioms follow almost immediately by the properties of due to the definition of the addition of vectors and the scalar multiplication. The additive inverse of a vector is simply since . The null vector is , for example.
Requirements (ii) and (iii) can also be shown by using the properties of and the definition of the operation and the scalar multiplication. Let us prove (ii) , for instance. By definition the following holds true:
The last example is the raw model for the imagination of finite-dimensional vector spaces. The focus of this post is, however, on function spaces and their algebraic structure. We are particularly interested in function spaces that are (infinite dimensional) vector spaces.
Definition 1.1 (Function)
A function from a set X to a set Y is an assignment of an element of Y to each element of X. The set X is called the domain of the function and the set Y is called the codomain or range of the function.
The zero of is , and the negatives are . The addition of two functions is defined by . Since and are two vectors in , the sum also needs to be a vector in . Hence, by using the properties of the given objects it is not too hard to show that the given set is indeed a vector space. Also refer to Function space in Linear Algebra as well as to Dualraum (in German). In latter source the more general function space is introduced.
Example 2.1 (Set of all -valued functions on )
Let us check that the operations as defined in (1) are closed. If and then we can form the sum and the result is still a function on the same interval.
The role of the last example is usually considered to be small due to its generality. However, if we restrict the set and thus add more structure and corresponding properties, then the situation will drastically change.
Each of the following sets of functions together with the operations (1) form an interesting and useful vector spaces. These function spaces are used heavily, for instance, in Approximation Theory and Functional Analysis:
Note that all arguments that have been used in Example 2.1 can be re-used except the closure argument. That is, we only need to show that the sum of two elements and the scalar multiplication lies again in the corresponding function space.
The sum of two continuous real functions defined on is again a continuous real function on the same domain. This can be proved by using, for instance, the interconnection between continuous functions and the existence of limits. The closure of scalar multiplication can be shown in a similar way.
The vector space is infinite dimensional since contains polynomials of arbitrary degree. That is, you can find a set of polynomials such as that are linearly independent and generates the entire vector space (i.e. it is an infinite basis).
Inner products and norms enables us to define and apply geometrical terms such as length, distance and angle. These concepts can be very illustrative in the Euclidean space, however, what does the length of a function mean?
for any continuous function . It is ensured that a continuous and bounded function is integrable. Note, however, that not when but when almost everywhere. The failure of this axiom, however, can be overcome by defining equivalence classes . Nonetheless, we are going to use the notation while keeping in mind that for the norm this is actually an equivalence class. Refer to Remark 2.23 in [1] for further details.
The approximation of functions is a very crucial technique, that is used not only in Analysis, Numerical Math and Computer Science. Just think about how continuous functions such as the function is calculated in the computer you are using.
In functional analysis, where Banach spaces are studied, the features of metrics and norms are of utter importance. For instance, the completeness of these function spaces play a crucial role as outlined in Banach and Frchet spaces of functions.
Easy to use . I thought the easy of use was nice the reason I say that is that it was simple. Not simple child like but simple in a way that it's straight forward. I find that if I think a button to add something should be at a certain location and that it should do a certain thing and when it is there and when it does what I thought then that is almost perfect software the difference being not only do I want it predictable but I want it smart.
Was not much variety also I think it neeed problem solving templates like logical orders to things. Like you always do this and then that in certain circumstances. For example to do a presentation you will need to gather info then sort and removed then categorize then blah blah blah but that can be pulled into the mind map all at once...all those steps so once you've established that as a something your going to do , can you imagine how many different things we do that have predetermined steps and by dragging two side by side we would easily , visually see how they would related or cancel each other or show redundancy...hey shouldn't I get royalties for this one?
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