Characterization Notes Pdf: Fill & Download for Free

I've used both Evernote and Asana for collaboration.I'd characterize Asana as a 'get stuff done tool'. It emphasizes speed both on note creation (keyboard shortcuts) and checking off tasks. It is easier to assign tasks or onboard somebody onto the Asana. The search tool only looks through the note headings (not attachments or note section).Evernote is great for personal use. The downloadable software and online access is convenient (sometimes ASana is slow or down completely). It also integrates with other Evernote products such as Clearly and Web Clipper. The universal search feature is great.Feature comparison:Evernote:Free versionAttachment support (up to 60MB/mo, 25MB/file)Collaborators have read only accessPremium versionAttachment support (1GB/mo, 100MB/file)PDF searchCollaborator have read/write access$45/yearOffline note accessNote history versionAsana:Free for up to 30 colloboratorsPlain text notes (with hyperlinking as exception)Attachment support (unlimited per month / 100MB per file)Note tagging/search capability

Let us start with some differences between matrices and tensors. Tensors in general can be thought as multi-dimensional arrays. A 2-dimensional tensor is called a matrix. Thus, when I talk about tensors in this note, I am only referring to the tensors with more than or equal to 3 dimensions (modes). This convention helps to distinguish between tensors (more than 2-D) and matrices (exactly 2-D tensors).Tensor problems are usually much harder than matrix problems and many concepts and algorithms that are well-established and developed for matrices can not be easily extended and analyzed for tensors. To elaborate on the difference between matrix and tensor analyses and properties, I provide the following examples.* The rank of a tensor can be larger than its dimension (here dimension refers to the dimension of each mode). For instance, a 2-by-2-by-2 tensor (dimension along each mode is 2) can have rank equal to 3. Note that this is not the case for matrices where a 2-by-2 matrix can only have rank at most 2.* Subtracting the best rank-1 approximation of a tensor might increase its rank (surprising resutl!). Note that for matrices, subtracting the best rank-1 approximation always reduces the rank by 1.* The rank-1 components of a matrix (computing through SVD) are orthogonal to each other, while this is not true for tensors in general.* The problem of uniqueness of eigen-decomposition is also different in matrices and tensors. For matrices, we know that if the eigenvalues are different, the eigen-decomposition is unique which is not true for tensors.* Many more …Given the above differences between matrices and tensors, it is expected that the analysis of matrix and tensor methods are also different. One way to formally characterize the difficulties of analyzing tensor methods is their computational complexity. There is a nice paper by Christopher Hillar and Lek-Heng Lim titled "Most tensor problems are NP-Hard" (Page on uchicago.edu) which shows these differences in the sense of computational complexity!Note that the NP-hardness is talking about the computational complexity of the problem (recall that NP-hard problems are the problems which are as hard as the hardest problems in the NP class). Among many of these tensor problems which are discussed in the paper and shown to be NP-hard, I mention the following ones:* Determining the rank or best rank-1 approximation of a 3rd order tensor.* Deciding whether a 3rd order tensor possesses a given eigenvalue, singular value, or spectral norm.* Approximating an eigenvalue, eigenvector, singular vector, or the spectral norm of the tensor.They also show that restricting these problems to symmetric tensors does not resolve the NP-hardness.On the other side, note that all these hardness results are in the worst case. There also exists efficient algorithms for some tensor problems such as tensor decomposition, but they need some additional assumptions to make the problem tractable.As an excellent survey article for tensor decomposition, I suggest the paper by Tamara Kolda and Brett Bader: PDF (Society for Industrial and Applied Mathematics).P.S. Quoted from Hillar and Lim's paper: "Bernd Sturmfels once made the remark to us that “All interesting problems are NP-hard.” In light of this, we would like to view our article as evidence that most tensor problems are interesting."! :)

No, I can’t, and no one can.First of all, they aren’t Jung’s. He didn’t invent them, he discovered them. They arise in the collective unconscious, and are common to all of us. Second, Jung didn’t catalogue them. In The Archetypes And The Collective Unconscious, in just under 500 pages he only discusses a few in detail.Third, many confuse the archetype with its manifestation, the archetypal symbol or image. Jacobi’s Complex, Archetype, Symbol In The Psychology of C. G. Jung is a relatively short (just over 200 pages) but dense work that focuses on simply defining those three terms in a meaningful way. I’ll quote from Jung’s “A Psychological Approach To The Dogma Of The Trinity”:“Archetypes are, by definition, factors and motifs that arrange the psychic elements into certain images, characterized as archetypal, but in such a way that they can be recognized only for the effectives they produce. They exist preconsciously, and presumably they form the structural dominants of the psyche in general a priori conditioning factors they represent a special psychological instance of the biological ‘pattern of behavior,’ which gives all things their specific qualities. Just as the manifestations of this biological ground plan may change in the course of development, so also can those of the archetype. Empirically considered, however, the archetype did not ever come into existence as a phenomenon of organic life, but entered into the picture with life itself.”An archetype can be seen as a kind of potential in the collective unconscious, which, arising into the conscious mind, expresses itself in metaphors of that potential. You could, for example, call anima, the female principle, a very basic archetype. Its manifestations are uncountable. As a concrete example, one aspect of anima is motherhood, which in turn can be manifested as the archetypal image or metaphor of the Great Mother, in both positive and negative forms. Erich Neumann, one of the most perceptive writers on depth psychology, takes 377 pages of text, notes, and index, and 185 pages of illustrations, to explore the manifestations of the Great Mother in The Great Mother: An Analysis Of The Archetype. It’s possible, reductively, to list the major underlying archetypes or psychic potentials, but it’s not particularly useful. It’s literally like motherhood and apple pie. At the level where things become meaningful—the level where archetypal images appear in dreams, for instance—there are thousands of possibilities, and again merely listing them does really do very little, since they must be understood in the context of a dream, along with all of its other images.If you want to read something analyzing an archetype, and, as I noted, it’s difficult to draw a firm boundary between archetype and manifestation, I would suggest Jung’s own relatively short essay “The Spirit Mercurius”. Here is a link to a pdf: https://essexmyth.files.wordpress.com/2015/02/roderick_main_20150217_091937.pdf