## Literature request: Generating all vertex subsets of a graph

I made the same post here in Mathematics Exchange but maybe here is a better place.

I am working in an algorithm which finds a unique maximal independent set of vertices which generates all other vertex subsets. This is done using two measures of ‘importance’ for vertices. I assume this might have some applications outside mathematics, especially in computer science, but I am not sure where I can read about such applications. Does anyone have any good literature suggestions?

## Literature about In-Memory Database Systems

I am currently writing my bachelor thesis on IMDBS and would like to ask if any of you have any recommendations for literature which summarizes the technical conception/architecture of IMDBS as apparently I am not able to find articles, papers, books etc which are covering the physical architecture or to In-Memory Database Systems but just on logical data storage, indexing etc.

Any recommendations would be highly appreciated.

## Literature Attachments on Pivotal 5.9

Literature Attachments on Pivotal 5.9

We need to extract all Literature Attachments from the database . We cannot find any tool to assist with this effort . Please describe how we can extract the attachments .

Version – SQL 2008 R2 as database .

Literature attachements could be found either under RM_attachment or attachment_table .

The attachment are stored in the DB as blobs datatype and we need help bulk extracting from database .

Our request is for assistance with extracting those documents without having to open each one and doing as Save as manually recording .

## Is it common in the literature to define regular languages and serialization languages as programming languages?

Often when I create programs I use operating-programming language such as Bash for automating OS operations, structure (“markup”) language such as HTML to define structures, styling language such as CSS to style structures, and programming (behavior defining) language such as JavaScript, to define the “nature of interaction” with programming by user interface.
I might use some of these languages “expanded” as with using a template engine for a programming (behavior defining) language, such as the Twig template engine for PHP.

But there are two other types of languages I sometimes use when creating programs:

Regular languages such as POSIX basic regular extensions/ PERL compatible regular extensions, and Serialization languages such as YAML/JSON;
from my experience, it is reasonable to assume that the former can be combined with generally all operating-programming languages and behavior defining languages, while the latter I usually combined with JavaScript (I almost never worked with YAML, but I did work a bit with JSON).

I ask the following as a humble scripter usually writing small imperative programs with Bash and JavaScript and almost never used any other programming language.

Is it common in the (Computer Science) literature to define regular languages and serialization languages as programming languages (as sharpening the behavior of a program)?

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## Where is the original literature for the specification of an Associative Array ADT?

I’m looking for the formal specification for the Abstract Data Type Algebra for the Associative Array, Associative List (AKA multimap), and other similar ADT to cite for use in a data specification similar to Binary JSON. The Wikipedia Associative Array entry uses non-standard math terminology and their sources are all secondary sources with no original sources. There is an algebra for the Dictionary and it starts with Let x be a set and it defines operations on that set. Who invented the dictionary and when? It should be pretty old, possible from the Journal of the Association of Computer Machinery or similar publication.

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## Is it just me not understanding some implicit rules or most of definitions of functions appearing in literature are ambiguous (in part. in physics)? I’m especially interested in the ambiguity of the sign of equality (see the explanations below) i.e. is it really ambiguous or I don’t understand something?

The following definition of a function seem ambiguous, at least to me: y = 5; it is because the definition neither explicitly says nor implies that it is dependent on some variable. I admit that normally such a definition is given in a context e.g. x and y axes, etc. However, even then one still can argue that y = 5 is not dependent on x and merely represents one point at mark 5 on the y axis. The given example is maybe to trivial to explain the ambiguity. Let’s concern a function in R^2 which is given as follows f = < 2t, sin(t) >. The assumption is that it is a vector function in 2D which depends only on t (i.e. f(t) = = < 2t, sin(t) >) and therefore represents a curve (a set of points in 2D). However, as dependencies are not indicated, it also can be that it depends on further variables e.g. on x, y and t, which means that the function f(x,y,t), for instance, represents a time dependent, 2D vector field (an infinite set of vectors for each given t). Equally, t may be not a parameter but one of two space coordinates i.e. f(t,u) which means that it represents a constant, 2D vector field (an infinite set of vectors). Furthermore, the very sign of equality when “defining” functions may be ambiguous. Consider a generalised position vector in R^3 e.g. r = < x,y,z >. When I say g = r do I define a vector field g or do I simply define another position vector g? To my taste g(r) = r would rather indicate definition of the vector field, whereas g = r would rather define another position vector. Or maybe, for some obscure reason, it is assumed that only one “generalised” position vector (“the” infinite set of vectors pointing from the origin to all possible locations in R^3) may exist so if you define r as a generalised position vector, each time you say e.g. u = r you automatically define a vector filed?

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## Is there literature on a de Rham analogue of the Mumford-Tate group or ell-adic monodromy group?

Let $$X$$ be a smooth projective variety over $$\mathbb{Q}$$. The theory of motives predicts that for each cohomology theory, there should be a distinguished Zariski closed subgroup of $$GL(H^k_{\bullet}(X))$$, the motivic Galois group. This group has conjectural descriptions for Betti and $$\ell$$-adic cohomology, and I am wondering if there is any literature on this group for de Rham cohomology.

The Betti cohomology $$H^k_B(X)$$ is a rational Hodge structure, hence there is a representation $$\mathrm{Res}_{\mathbb{C}/\mathbb{R}}\mathbb{G}_m\to GL(H^k_B(X)\otimes\mathbb{R})$$. The Mumford-Tate group $$MT^k(X)\leq GL(H^k_B(X))$$ is defined to be the smallest Zariski-closed subgroup containing the image of the representation. The Hodge conjecture would imply that $$MT^k(X)$$ has finite index in the Betti motivic Galois group.

The $$\ell$$-adic cohomology $$H^k(X;\mathbb{Q}_\ell)$$ is a representation of the absolute Galois group, and the $$\ell$$-adic monodromy group $$G_\ell^k(X)\leq GL(H^k(X;\mathbb{Q}_\ell))$$ is defined to be the smallest Zariski-closed subgroup containing the image of the representation. The Tate conjecture would imply that $$G_\ell^k(X)$$ is the full $$\ell$$-adic motivic Galois group.

Is there any literature on an analogue of the Mumford-Tate group or the $$\ell$$-adic monodromy group inside $$GL(H^k_{dR}(X))$$?

I believe that a conjecture of Ogus would imply that the de Rham motivic Galois group is smallest Zariski closed subgroup whose $$\mathbb{Q}_p$$ points contain $$F_p$$ for all sufficiently large $$p$$ (where $$F_p\in GL(H^k_{dR}(X))(\mathbb{Q}_p)$$ is the crystalline Frobenius). However I have some doubt about this, because André’s book on motives states the relationship between the Hodge conjecture and the Mumford-Tate group (Proposition 7.2.2.1), and the relationship between the Tate conjecture and the $$\ell$$-adic monodromy group (Proposition 7.3.2.1), but does not give an analogous statement for the Ogus conjecture.

I also believe that the period conjecture of Grothendieck would imply that the de Rham motivic Galois group is the smallest Zariski closed subgroup containing all elements $$\varphi\in GL(H^k_{dR}(X))(\mathbb{Q})$$ whose image in $$GL(H^k_{B}(X))(\mathbb{C})$$ under the Betti-de Rham comparison isomorphism is contained in $$GL(H^k_{B}(X))(\mathbb{Q})$$. However, I also cannot find a statement like this in André’s book.