text:
# How to draw a separator between the columns of a matrix.

Is there a simple way to tell TikZ that I want a vertical line to separate the columns of a matrix? I know how to draw them manually, I am looking for an automatic solution, maybe using styles or something.

-
Perhaps mention what you already know, somebody possibly might show another way you might like more before another one could come with a real automatic solution. –  Stefan Kottwitz Jan 22 '11 at 20:09

You can use "matrix of nodes" and anchors:

\begin{tikzpicture}
\matrix (mat) [matrix of nodes]
{
1 & 2 & 3 \\
1 & 2 & 3 \\
1 & 2 & 3 \\
1 & 2 & 3 \\
};
% Matrix is called 'mat' first number is row, second numer is column
\draw[thick,red] (mat-1-1.north east) -- (mat-4-1.south east);
\end{tikzpicture}

-
This fails when the entries are of different length. –  Caramdir Nov 27 '11 at 20:31

Here's an example with a matrix of math nodes, with delimiters and a separation line with some shifting for that.

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{matrix}
\begin{document}
\begin{tikzpicture}
\matrix (m) [matrix of math nodes,left delimiter=(,right delimiter=),
inner sep=2pt,outer sep=0pt]{
a & b & [1em] 0 \\
c & d & 1 \\ };
\draw ([xshift=0.5em]m-1-2.north east) -- ([xshift=0.5em]m-2-2.south east);
\end{tikzpicture}
\end{document}

If the entries would have different width, you could use |- instead of -- to get straight lines, such as

\draw ([xshift=0.5em]m-1-2.north east-|m-2-2.south east) -|
([xshift=0.5em]m-2-2.south east);

Even better: set the minimum width property for the nodes in the matrix.

-
Like @xeroc's solution this fails when the entries are of different size. –  Caramdir Nov 27 '11 at 20:32
@Caramdir I added a modification regarding this. –  Stefan Kottwitz Nov 27 '11 at 20:45
I think what @Caramdir is referring to is the cases such as the left lower entry is changed with e.g. an integral while keeping the matrix identical. Then the bar is slightly shorter but similar to your solution you can replace it by \draw([xshift=0.2em]m.north west -| m-1-2.east) to ([xshift=0.2em] m.south east -| m-2-2.east); In other words, using the matrix node itself to get the top and bottom correctly. –  percusse Nov 27 '11 at 21:04
@percusse I was only thinking of the width of the nodes, but you are right that the height also needs to be taken into account. –  Caramdir Nov 27 '11 at 23:00

Here's an answer based on answers given at Obstacles to simulating an amsmath matrix by a TiKZ matrix of math nodes and How can I set the background color of the rows and columns of a matrix node in Tikz? You don't specify in the question what type of matrix you are wanting to typeset, so I've simply gone for a similar matrix to that which Stefan and xeroc have used. Exactly what code you need depends a lot on what your matrix code looks like. The only one that you really need is the code from How can I set the background color of the rows and columns of a matrix node in Tikz? The others are there to make it look more impressive.

If the code from How can I set the background color of the rows and columns of a matrix node in Tikz? were in a package (below called tikzamsmatrix), the document would look like this:

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{matrix,decorations}
\usepackage{calligraphy}
\usepackage{matrixcells}
\usepackage{tikzamsmatrix}

\begin{document}
$\begin{tikzamatrix} a & b & 0 \\ c & a + c & {\displaystyle \int_0^1 \sin(x) d x} \end{tikzamatrix}$
\end{document}

and would produce:

Since that question isn't yet in a package, the code actually looks like this:

\documentclass{article}
%\url{http://tex.stackexchange.com/q/9492/86}
\usepackage{amsmath,tikz}
\usetikzlibrary{matrix,decorations}
\usepackage{calligraphy}
\usepackage{matrixcells}

\newlength\mtxrowsep
\setlength\mtxrowsep{1.5ex}
\newlength\mtxcolsep
\setlength\mtxcolsep{2\arraycolsep}

\makeatletter
\pgfdeclaredecoration{doubled lineto}{brace}
{
\state{brace}[width=+\pgfdecoratedremainingdistance,next state=final]
{
\pgfsyssoftpath@setcurrentpath{\pgfutil@empty}
\pgfpathmoveto{\pgfpointorigin}
\pgfpathlineto{\pgfqpoint{\pgfdecoratedremainingdistance}{0pt}}
\pgfpathmoveto{\pgfqpoint{0pt}{\pgfdecorationsegmentamplitude}}
\pgfpathlineto{\pgfqpoint{\pgfdecoratedremainingdistance}{\pgfdecorationsegmentamplitude}}
}
\state{final}{}%
}
\pgfdeclaredecoration{bracket}{brace}
{
\state{brace}[width=+\pgfdecoratedremainingdistance,next state=final]
{
\pgfsyssoftpath@setcurrentpath{\pgfutil@empty}
\pgfpathmoveto{\pgfpointorigin}
\pgfpathlineto{\pgfqpoint{0pt}{\pgfdecorationsegmentamplitude}}
\pgfpathlineto{\pgfqpoint{\pgfdecoratedremainingdistance}{\pgfdecorationsegmentamplitude}}
\pgfpathlineto{\pgfqpoint{\pgfdecoratedremainingdistance}{0pt}}
}
\state{final}{}%
}
\makeatother

\expandafter\def\csname delimiter \string\lbrace\endcsname{calligraphic brace}
\expandafter\def\csname delimiter \string(\endcsname{calligraphic curved parenthesis}
\expandafter\def\csname delimiter \string|\endcsname{lineto}
\expandafter\def\csname delimiter \string\|\endcsname{doubled lineto}
\expandafter\def\csname delimiter \string[\endcsname{bracket}
\expandafter\def\csname delimiter \string\rbrace\endcsname{calligraphic brace}
\expandafter\def\csname delimiter \string)\endcsname{calligraphic curved parenthesis}
\expandafter\def\csname delimiter \string]\endcsname{bracket}

\tikzset{
ams/.style={
baseline=-.7ex,
every delimiter/.style={yshift=-1pt},
every left delimiter/.style={xshift=2pt},
every right delimiter/.style={xshift=-2pt},
every node/.style={inner sep=0pt},
execute at end picture={
\path (current bounding box.east) ++(\pgfkeysvalueof{/tikz/ams matrix xsep},0) (current bounding box.west) ++(-\pgfkeysvalueof{/tikz/ams matrix xsep},0);
},
},
ams matrix xsep/.initial={.5ex},
ams matrix/.style={
inner sep=1pt,
column sep=\mtxcolsep,
row sep=\mtxrowsep,
%    ampersand replacement=\&,
matrix of math nodes,
},
ams delimiters/.style args={#1,#2}{
left delimiter={#1},
right delimiter={#2},
},
delimiters/.style args={#1,#2}{
\pgfkeysvalueof{/tikz/matrix delimiter type} delimiters={{#1},{#2}},
},
matrix delimiter type/.initial={tikz},
tikz delimiter style/.style={
thick,
},
tikz delimiters/.style args={#1,#2}{
left tikz delimiter={#1},
right tikz delimiter={#2},
},
left tikz delimiter/.style={
render left tikz delimiter/.expand once={\csname delimiter \string#1\endcsname}
},
render left tikz delimiter/.style={
append after command={(\tikzlastnode.north west) edge[tikz delimiter style,decorate,decoration={mirror,#1}] (\tikzlastnode.south west)}
},
right tikz delimiter/.style={
render right tikz delimiter/.expand once={\csname delimiter \string#1\endcsname}
},
render right tikz delimiter/.style={
append after command={(\tikzlastnode.north east) edge[tikz delimiter style,decorate,decoration={#1}] (\tikzlastnode.south east)}
},
bmatrix/.style={
ams,
every matrix/.style={
ams matrix,
delimiters={[,]},
}
},
Bmatrix/.style={
ams,
every matrix/.style={
ams matrix,
delimiters={\lbrace,\rbrace},
}
},
pmatrix/.style={
ams,
every matrix/.style={
ams matrix,
delimiters={(,)},
}
},
vmatrix/.style={
ams,
every matrix/.style={
ams matrix,
delimiters={|,|},
}
},
Vmatrix/.style={
ams,
every matrix/.style={
ams matrix,
delimiters={\|,\|},
}
},
}

\let\matamp=&

\catcode\&=13
\makeatletter
\def&{\iftikz@is@matrix
\pgfmatrixnextcell
\else
\matamp
\fi}
\makeatother

%\usepackage{environ}
\def\endtikzmatrix{\\\egroup;\end{tikzpicture}}
\foreach \mtype in {b,B,p,v,V} {

\expandafter\xdef\csname tikz\mtype matrix\endcsname{%
\noexpand\begin{tikzpicture}[\mtype matrix,matrix delimiter type={tikz}]
\noexpand\matrix \noexpand\bgroup}
\expandafter\xdef\csname ams\mtype matrix\endcsname{%
\noexpand\begin{tikzpicture}[\mtype matrix,matrix delimiter type={ams}]
\noexpand\matrix \noexpand\bgroup}
\expandafter\global\expandafter\let\csname endtikz\mtype matrix\endcsname=\endtikzmatrix
\expandafter\global\expandafter\let\csname endams\mtype matrix\endcsname=\endtikzmatrix
}

\def\tikzamatrix{\begin{tikzpicture}[pmatrix,matrix delimiter type={tikz}]\matrix[label cells,name=am]\bgroup}
\def\endtikzamatrix{\\\egroup;\draw (am-cell-1-\the\pgfmatrixcurrentcolumn.north west) -- (am-cell-\the\pgfmatrixcurrentrow-\the\pgfmatrixcurrentcolumn.south west);\end{tikzpicture}}

\begin{document}
\begin{tikzamatrix}
a & b & 0 \\
c & a + c & {\displaystyle \int_0^1 \sin(x) d x}
\end{tikzamatrix}
\end{document}
`

(The calligraphy and matrixcells package are available from TeX-SX launchpad page.)

-
Ah, once again, these are quite neat tools! –  percusse Nov 28 '11 at 14:21


text:
# Hypergraph Explained

In mathematics, a hypergraph is a generalization of a graph in which an edge can join any number of vertices. In contrast, in an ordinary graph, an edge connects exactly two vertices.

Formally, an undirected hypergraph

H

is a pair

H=(X,E)

where

X

is a set of elements called nodes or vertices, and

E

is (in an undirected hypergraph) a set of non-empty subsets of

X

called hyperedges or edges. Therefore,

E

is a subset of

l{P}(X)\setminus\{\emptyset\}

, where

l{P}(X)

is the power set of

X

. The size of the vertex set is called the order of the hypergraph, and the size of edges set is the size of the hypergraph.

A directed hypergraph differs in that its hyperedges are not sets, but an ordered pair of subsets of

X

, constituting the tail and head of the hyperedge.

While graph edges connect only 2 nodes, hyperedges connect an arbitrary number of nodes. However, it is often desirable to study hypergraphs where all hyperedges have the same cardinality; a k-uniform hypergraph is a hypergraph such that all its hyperedges have size k. (In other words, one such hypergraph is a collection of sets, each such set a hyperedge connecting k nodes.) So a 2-uniform hypergraph is a graph, a 3-uniform hypergraph is a collection of unordered triples, and so on. An undirected hypergraph is also called a set system or a family of sets drawn from the universal set.

Hypergraphs can be viewed as incidence structures. In particular, there is a bipartite "incidence graph" or "Levi graph" corresponding to every hypergraph, and conversely, most, but not all, bipartite graphs can be regarded as incidence graphs of hypergraphs.

Hypergraphs have many other names. In computational geometry, an undirected hypergraph may sometimes be called a range space and then the hyperedges are called ranges.[1] In cooperative game theory, hypergraphs are called simple games (voting games); this notion is applied to solve problems in social choice theory. In some literature edges are referred to as hyperlinks or connectors.[2]

The collection of hypergraphs is a category with hypergraph homomorphisms as morphisms.

## Applications

Undirected hypergraphs are useful in modelling such things as satisfiability problems,[3] databases, machine learning, and Steiner tree problems.[4] They have been extensively used in machine learning tasks as the data model and classifier regularization (mathematics). The applications include recommender system (communities as hyperedges), image retrieval (correlations as hyperedges), and bioinformatics (biochemical interactions as hyperedges). Representative hypergraph learning techniques include hypergraph spectral clustering that extends the spectral graph theory with hypergraph Laplacian, and hypergraph semi-supervised learning that introduces extra hypergraph structural cost to restrict the learning results. For large scale hypergraphs, a distributed framework built using Apache Spark is also available.

Directed hypergraphs can be used to model things including telephony applications,[5] detecting money laundering,[6] operations research,[7] and transportation planning. They can also be used to model Horn-satisfiability.

## Generalizations of concepts from graphs

Many theorems and concepts involving graphs also hold for hypergraphs, in particular:

In directed hypergraphs: transitive closure, and shortest path problems.

## Hypergraph drawing

Although hypergraphs are more difficult to draw on paper than graphs, several researchers have studied methods for the visualization of hypergraphs.

In one possible visual representation for hypergraphs, similar to the standard graph drawing style in which curves in the plane are used to depict graph edges, a hypergraph's vertices are depicted as points, disks, or boxes, and its hyperedges are depicted as trees that have the vertices as their leaves.[8] [9] If the vertices are represented as points, the hyperedges may also be shown as smooth curves that connect sets of points, or as simple closed curves that enclose sets of points.[10] [11] [12]

In another style of hypergraph visualization, the subdivision model of hypergraph drawing,[13] the plane is subdivided into regions, each of which represents a single vertex of the hypergraph. The hyperedges of the hypergraph are represented by contiguous subsets of these regions, which may be indicated by coloring, by drawing outlines around them, or both. An order-n Venn diagram, for instance, may be viewed as a subdivision drawing of a hypergraph with n hyperedges (the curves defining the diagram) and 2n − 1 vertices (represented by the regions into which these curves subdivide the plane). In contrast with the polynomial-time recognition of planar graphs, it is NP-complete to determine whether a hypergraph has a planar subdivision drawing,[14] but the existence of a drawing of this type may be tested efficiently when the adjacency pattern of the regions is constrained to be a path, cycle, or tree.[15]

An alternative representation of the hypergraph called PAOH is shown in the figure on top of this article. Edges are vertical lines connecting vertices. Vertices are aligned on the left. The legend on the right shows the names of the edges. It has been designed for dynamic hypergraphs but can be used for simple hypergraphs as well.

## Hypergraph coloring

Classic hypergraph coloring is assigning one of the colors from set

\{1,2,3,...,λ\}

to every vertex of a hypergraph in such a way that each hyperedge contains at least two vertices of distinct colors. In other words, there must be no monochromatic hyperedge with cardinality at least 2. In this sense it is a direct generalization of graph coloring. Minimum number of used distinct colors over all colorings is called the chromatic number of a hypergraph.

Hypergraphs for which there exists a coloring using up to k colors are referred to as k-colorable. The 2-colorable hypergraphs are exactly the bipartite ones.

There are many generalizations of classic hypergraph coloring. One of them is the so-called mixed hypergraph coloring, when monochromatic edges are allowed. Some mixed hypergraphs are uncolorable for any number of colors. A general criterion for uncolorability is unknown. When a mixed hypergraph is colorable, then the minimum and maximum number of used colors are called the lower and upper chromatic numbers respectively.[16]

## Properties of hypergraphs

A hypergraph can have various properties, such as:

• Empty - has no edges.
• Non-simple (or multiple) - has loops (hyperedges with a single vertex) or repeated edges, which means there can be two or more edges containing the same set of vertices.
• Simple - has no loops and no repeated edges.

d

-regular - every vertex has degree

d

, i.e., contained in exactly

d

hyperedges.
• 2-colorable - its vertices can be partitioned into two classes U and V in such a way that each hyperedge with cardinality at least 2 contains at least one vertex from both classes. An alternative term is Property B.

k

-uniform - each hyperedge contains precisely

k

vertices.

k

-partite - the vertices are partitioned into

k

parts, and each hyperedge contains precisely one vertex of each type.
• Every

k

-partite hypergraph (for

k\geq2

) is both

k

-uniform and bipartite (and 2-colorable).
• Downward-closed - every subset of an undirected hypergraph's edges is a hyperedge too. A downward-closed hypergraph is usually called an abstract simplicial complex.
• An abstract simplicial complex with the augmentation property is called a matroid.

## Related hypergraphs

Because hypergraph links can have any cardinality, there are several notions of the concept of a subgraph, called subhypergraphs, partial hypergraphs and section hypergraphs.

Let

H=(X,E)

be the hypergraph consisting of vertices

X=\lbracexi\midi\inIv\rbrace,

and having edge set

E=\lbraceei\midi\inIe,ei\subseteqX,ei\emptyset\rbrace,

where

Iv

and

Ie

are the index sets of the vertices and edges respectively.

A subhypergraph is a hypergraph with some vertices removed. Formally, the subhypergraph

HA

induced by

A\subseteqX

is defined as

HA=\left(A,\lbracee\capA\mide\inE,e\capA\emptyset\rbrace\right).

An alternative term is the restriction of H to A.

An extension of a subhypergraph is a hypergraph where each hyperedge of

H

which is partially contained in the subhypergraph

HA

is fully contained in the extension

Ex(HA)

. Formally

Ex(HA)=(A\cupA',E')

with

A'=cupee\setminusA

and

E'=\lbracee\inE\mide\subseteq(A\cupA')\rbrace

.

The partial hypergraph is a hypergraph with some edges removed. Given a subset

J\subsetIe

of the edge index set, the partial hypergraph generated by

J

is the hypergraph

\left(X,\lbraceei\midi\inJ\rbrace\right).

Given a subset

A\subseteqX

, the section hypergraph is the partial hypergraph

H x A=\left(A,\lbraceei\midi\inIe,ei\subseteqA\rbrace\right).

The dual

H*

of

H

is a hypergraph whose vertices and edges are interchanged, so that the vertices are given by

\lbraceei\rbrace

and whose edges are given by

\lbraceXm\rbrace

where

Xm=\lbraceei\midxm\inei\rbrace.

When a notion of equality is properly defined, as done below, the operation of taking the dual of a hypergraph is an involution, i.e.,

\left(H*\right)*=H.

A connected graph G with the same vertex set as a connected hypergraph H is a host graph for H if every hyperedge of H induces a connected subgraph in G. For a disconnected hypergraph H, G is a host graph if there is a bijection between the connected components of G and of H, such that each connected component G' of G is a host of the corresponding H'.

The 2-section (or clique graph, representing graph, primal graph, Gaifman graph) of a hypergraph is the graph with the same vertices of the hypergraph, and edges between all pairs of vertices contained in the same hyperedge.

## Incidence matrix

Let

V=\{v1,v2,~\ldots,~vn\}

and

E=\{e1,e2,~\ldots~em\}

. Every hypergraph has an

n x m

incidence matrix.

For an undirected hypergraph,

I=(bij)

where

bij=\left\{\begin{matrix}1&if~vi\inej\ 0&otherwise.\end{matrix}\right.

The transpose

It

of the incidence matrix defines a hypergraph

H*=(V*,E*)

called the dual of

H

, where

V*

is an m-element set and

E*

is an n-element set of subsets of

V*

. For
 * v j

\inV*

and
 * e i

\inE*,~

 * v j

\in

 * e i
if and only if

bij=1

.

For a directed hypergraph, the heads and tails of each hyperedge

ej

are denoted by

H(ej)

and

T(ej)

respectively.[17]

I=(bij)

where

bij=\left\{\begin{matrix}-1&if~vi\inT(ej)\ 1&if~vi\inH(ej)\ 0&otherwise.\end{matrix}\right.

### Incidence graph

A hypergraph H may be represented by a bipartite graph BG as follows: the sets X and E are the parts of BG, and (x1, e1) are connected with an edge if and only if vertex x1 is contained in edge e1 in H.

Conversely, any bipartite graph with fixed parts and no unconnected nodes in the second part represents some hypergraph in the manner described above. This bipartite graph is also called incidence graph.

A parallel for the adjacency matrix of a hypergraph can be drawn from the adjacency matrix of a graph. In the case of a graph, the adjacency matrix is a square matrix which indicates whether pairs of vertices are adjacent. Likewise, we can define the adjacency matrix

A=(aij)

for a hypergraph in general where the hyperedges

ek

have real weights
 w ek

\in\R

with

aij=\left\{\begin{matrix}

 w ek

&if~(vi,vj)\inE\ 0&otherwise.\end{matrix}\right.

## Cycles

In contrast with ordinary undirected graphs for which there is a single natural notion of cycles and acyclic graphs, there are multiple natural non-equivalent definitions of acyclicity for hypergraphs which collapse to ordinary graph acyclicity for the special case of ordinary graphs.

A first definition of acyclicity for hypergraphs was given by Claude Berge:[18] a hypergraph is Berge-acyclic if its incidence graph (the bipartite graph defined above) is acyclic. This definition is very restrictive: for instance, if a hypergraph has some pair

vv'

of vertices and some pair

ff'

of hyperedges such that

v,v'\inf

and

v,v'\inf'

, then it is Berge-cyclic. Berge-cyclicity can obviously be tested in linear time by an exploration of the incidence graph.

We can define a weaker notion of hypergraph acyclicity,[19] later termed α-acyclicity. This notion of acyclicity is equivalent to the hypergraph being conformal (every clique of the primal graph is covered by some hyperedge) and its primal graph being chordal; it is also equivalent to reducibility to the empty graph through the GYO algorithm[20] [21] (also known as Graham's algorithm), a confluent iterative process which removes hyperedges using a generalized definition of ears. In the domain of database theory, it is known that a database schema enjoys certain desirable properties if its underlying hypergraph is α-acyclic.[22] Besides, α-acyclicity is also related to the expressiveness of the guarded fragment of first-order logic.

We can test in linear time if a hypergraph is α-acyclic.[23]

Note that α-acyclicity has the counter-intuitive property that adding hyperedges to an α-cyclic hypergraph may make it α-acyclic (for instance, adding a hyperedge containing all vertices of the hypergraph will always make it α-acyclic). Motivated in part by this perceived shortcoming, Ronald Fagin[24] defined the stronger notions of β-acyclicity and γ-acyclicity. We can state β-acyclicity as the requirement that all subhypergraphs of the hypergraph are α-acyclic, which is equivalent to an earlier definition by Graham. The notion of γ-acyclicity is a more restrictive condition which is equivalent to several desirable properties of database schemas and is related to Bachman diagrams. Both β-acyclicity and γ-acyclicity can be tested in polynomial time.

Those four notions of acyclicity are comparable: Berge-acyclicity implies γ-acyclicity which implies β-acyclicity which implies α-acyclicity. However, none of the reverse implications hold, so those four notions are different.

## Isomorphism, symmetry, and equality

A hypergraph homomorphism is a map from the vertex set of one hypergraph to another such that each edge maps to one other edge.

A hypergraph

H=(X,E)

is isomorphic to a hypergraph

G=(Y,F)

, written as

H\simeqG

if there exists a bijection

\phi:X\toY

\pi

of

I

such that

\phi(ei)=f\pi(i)

The bijection

\phi

is then called the isomorphism of the graphs. Note that

H\simeqG

if and only if

H*\simeqG*

.

When the edges of a hypergraph are explicitly labeled, one has the additional notion of strong isomorphism. One says that

H

is strongly isomorphic to

G

if the permutation is the identity. One then writes

H\congG

. Note that all strongly isomorphic graphs are isomorphic, but not vice versa.

When the vertices of a hypergraph are explicitly labeled, one has the notions of equivalence, and also of equality. One says that

H

is equivalent to

G

, and writes

H\equivG

if the isomorphism

\phi

has

\phi(xn)=yn

and

\phi(ei)=f\pi(i)

Note that

H\equivG

if and only if

H*\congG*

\pi

is the identity, one says that

H

equals

G

, and writes

H=G

. Note that, with this definition of equality, graphs are self-dual:

\left(H*\right)*=H

A hypergraph automorphism is an isomorphism from a vertex set into itself, that is a relabeling of vertices. The set of automorphisms of a hypergraph H (= (XE)) is a group under composition, called the automorphism group of the hypergraph and written Aut(H).

### Examples

Consider the hypergraph

H

with edges

H=\lbrace e1=\lbracea,b\rbrace, e2=\lbraceb,c\rbrace, e3=\lbracec,d\rbrace, e4=\lbraced,a\rbrace, e5=\lbraceb,d\rbrace, e6=\lbracea,c\rbrace \rbrace

and

G=\lbrace f1=\lbrace\alpha,\beta\rbrace, f2=\lbrace\beta,\gamma\rbrace, f3=\lbrace\gamma,\delta\rbrace, f4=\lbrace\delta,\alpha\rbrace, f5=\lbrace\alpha,\gamma\rbrace, f6=\lbrace\beta,\delta\rbrace \rbrace

Then clearly

H

and

G

are isomorphic (with

\phi(a)=\alpha

, etc.), but they are not strongly isomorphic. So, for example, in

H

, vertex

a

meets edges 1, 4 and 6, so that,

e1\cape4\cape6=\lbracea\rbrace

In graph

G

, there does not exist any vertex that meets edges 1, 4 and 6:

f1\capf4\capf6=\varnothing

In this example,

H

and

G

are equivalent,

H\equivG

, and the duals are strongly isomorphic:

H*\congG*

.

### Symmetry

The

r(H)

of a hypergraph

H

is the maximum cardinality of any of the edges in the hypergraph. If all edges have the same cardinality k, the hypergraph is said to be uniform or k-uniform, or is called a k-hypergraph. A graph is just a 2-uniform hypergraph.

The degree d(v) of a vertex v is the number of edges that contain it. H is k-regular if every vertex has degree k.

The dual of a uniform hypergraph is regular and vice versa.

Two vertices x and y of H are called symmetric if there exists an automorphism such that

\phi(x)=y

. Two edges

ei

and

ej

are said to be symmetric if there exists an automorphism such that

\phi(ei)=ej

.

A hypergraph is said to be vertex-transitive (or vertex-symmetric) if all of its vertices are symmetric. Similarly, a hypergraph is edge-transitive if all edges are symmetric. If a hypergraph is both edge- and vertex-symmetric, then the hypergraph is simply transitive.

Because of hypergraph duality, the study of edge-transitivity is identical to the study of vertex-transitivity.

## Partitions

A partition theorem due to E. Dauber[25] states that, for an edge-transitive hypergraph

H=(X,E)

, there exists a partition

(X1,X2,,XK)

of the vertex set

X

such that the subhypergraph
 H Xk
generated by

Xk

is transitive for each

1\lek\leK

, and such that
 K \sum k=1
 r\left(H Xk

\right)=r(H)

where

r(H)

is the rank of H.

As a corollary, an edge-transitive hypergraph that is not vertex-transitive is bicolorable.

Graph partitioning (and in particular, hypergraph partitioning) has many applications to IC design and parallel computing.[26] Efficient and scalable hypergraph partitioning algorithms are also important for processing large scale hypergraphs in machine learning tasks.

## Further generalizations

One possible generalization of a hypergraph is to allow edges to point at other edges. There are two variations of this generalization. In one, the edges consist not only of a set of vertices, but may also contain subsets of vertices, subsets of subsets of vertices and so on ad infinitum. In essence, every edge is just an internal node of a tree or directed acyclic graph, and vertices are the leaf nodes. A hypergraph is then just a collection of trees with common, shared nodes (that is, a given internal node or leaf may occur in several different trees). Conversely, every collection of trees can be understood as this generalized hypergraph. Since trees are widely used throughout computer science and many other branches of mathematics, one could say that hypergraphs appear naturally as well. So, for example, this generalization arises naturally as a model of term algebra; edges correspond to terms and vertices correspond to constants or variables.

For such a hypergraph, set membership then provides an ordering, but the ordering is neither a partial order nor a preorder, since it is not transitive. The graph corresponding to the Levi graph of this generalization is a directed acyclic graph. Consider, for example, the generalized hypergraph whose vertex set is

V=\{a,b\}

and whose edges are

e1=\{a,b\}

and

e2=\{a,e1\}

. Then, although

b\ine1

and

e1\ine2

, it is not true that

b\ine2

. However, the transitive closure of set membership for such hypergraphs does induce a partial order, and "flattens" the hypergraph into a partially ordered set.

Alternately, edges can be allowed to point at other edges, irrespective of the requirement that the edges be ordered as directed, acyclic graphs. This allows graphs with edge-loops, which need not contain vertices at all. For example, consider the generalized hypergraph consisting of two edges

e1

and

e2

, and zero vertices, so that

e1=\{e2\}

and

e2=\{e1\}

. As this loop is infinitely recursive, sets that are the edges violate the axiom of foundation. In particular, there is no transitive closure of set membership for such hypergraphs. Although such structures may seem strange at first, they can be readily understood by noting that the equivalent generalization of their Levi graph is no longer bipartite, but is rather just some general directed graph.

The generalized incidence matrix for such hypergraphs is, by definition, a square matrix, of a rank equal to the total number of vertices plus edges. Thus, for the above example, the incidence matrix is simply

\left[\begin{matrix}0&1\ 1&0\end{matrix}\right].

## References

• PAOHVis: open-source PAOHVis system for visualizing dynamic hypergraphs.

## Notes and References

1. .
2. Book: Pearl, Judea . Heuristics: Intelligent Search Strategies for Computer Problem Solving . 1984 . Addison-Wesley Publishing Company . 978-0-201-05594-8 . 25.
3. Witnesses for non-satisfiability of dense random 3CNF formulas. Feige. Uriel. Kim. Jeong Han. Ofek. Eran. 2006. IEEE . 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS'06) . 497–508 . 10.1109/FOCS.2006.78.
4. Brazil . M . Zachariasen . M . 2015. Steiner Trees in Graphs and Hypergraphs. Algorithms and Combinatorics. 29. 301–317 . 10.1007/978-3-319-13915-9_5 . Springer . 978-3-319-13915-9.
5. Goldstein . A. . 1982. A Directed Hypergraph Database: A Model for the Local Loop Telephone Plant. Bell System Technical Journal. 61 . 9 . 2529–54 . 1982 . 10.1002/j.1538-7305.1982.tb03439.x . 11290643 .
6. Exchange Pattern Mining in the Bitcoin Transaction Directed Hypergraph. Financial Cryptography and Data Security. Ranshous . Stephen . Joslyn . Cliff. Kreyling . Sean . Nowak. Kathleen . Samatova. Nagiza . West . Curtis. Winters. Samuel . 2017. Springer. 10.1007/978-3-319-70278-0_16.
7. Ausiello . Giorgio . Laura . Luigi . 2017. Directed hypergraphs: Introduction and fundamental algorithms - A survey. 293–306. 10.1016/j.tcs.2016.03.016. Theoretical Computer Science. 658. free.
8. .
9. .
10. .
11. .
12. .
13. .
14. .
15. .
16. Web site: Vitaly Voloshin: Mixed Hypergraph Coloring Website . 2022-04-27 . spectrum.troy.edu.
17. G. . Gallo . G. . Longo . S. . Pallottino . S. . Nguyen . Directed hypergraphs and applications . Discrete Applied Mathematics . 42 . 2–3 . 177–201 . 1993 . 10.1016/0166-218X(93)90045-P . free .
18. Book: Berge, Claude . Graphs and Hypergraphs . Amsterdam . North-Holland . 1973 . 0-7204-2450-X .
19. C. . Beeri . Ronald Fagin . R. . Fagin . D. . Maier . Mihalis Yannakakis . M. . Yannakakis . On the Desirability of Acyclic Database Schemes . Journal of the ACM . 30 . 3 . 479–513 . 1983 . 10.1145/2402.322389 . 2418740 .
20. C. T. . Yu . M. Z. . Özsoyoğlu . An algorithm for tree-query membership of a distributed query . Proc. IEEE COMPSAC . 306–312 . 1979 . 10.1109/CMPSAC.1979.762509 .
21. M. H. . Graham . On the universal relation . Technical Report . University of Toronto . Toronto, Ontario, Canada . 1979 .
22. Book: Serge Abiteboul . S. . Abiteboul . Richard B. Hull . R. B. . Hull . Victor Vianu . V. . Vianu . Foundations of Databases . Addison-Wesley . 1995 . 0-201-53771-0 .
23. Robert Tarjan . R. E. . Tarjan . Mihalis Yannakakis . M. . Yannakakis . Simple linear-time algorithms to test chordality of graphs, test acyclicity of hypergraphs, and selectively reduce acyclic hypergraphs . SIAM Journal on Computing . 13 . 3 . 566–579 . 1984 . 10.1137/0213035 .
24. Ronald . Fagin . Degrees of Acyclicity for Hypergraphs and Relational Database Schemes . Journal of the ACM . 1983 . 30 . 3 . 514–550 . 10.1145/2402.322390 . 597990 .
25. Book: Harary, F. . Graph Theory . 2018 . CRC Press . 978-0-429-96231-8 . 1969 . 172 . We next state a theorem due to Elayne Dauber whose corollaries describe properties of line-symmetric graphs. Note the obvious but important observation that every line-symmetric graph is line-regular..
26. Catalyurek . U.V. . Aykanat . C. . A Hypergraph Model for Mapping Repeated Sparse Matrix–Vector Product Computations onto Multicomputers . Proc. International Conference on Hi Performance Computing (HiPC'95) . 1995.

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text:
## Question

### Metaculus Help: Spread the word

# When will a restaurant first serve clean-meat products containing ≥80% clean meat, at $3 per 100 grams or cheaper? ###### partnered with The Open Philanthropy Project The price of clean meat has fallen from$330,000/pound in 2013 to around $800 in 2018, and is expected to fall even further. In 2017, Mark Post, chief science officer at Mosa Meat, predicted the following in 2017: For small-scale, somewhat expensive products, most companies will have cultured meat products on the market in 3–4 years (i.e., 2020–2021). It will probably take another 3–4 years (i.e., 2023–2025) for the price to come down to the level where it’s acceptable for the broader public. In 2015, "restaurant" Bistro in Vitro offers virtual diners "food for thought" by allowing customers to create their own three-course meal from a range of dishes that could one day be created using "in vitro" meat. Unfortunately, the earliest reservation the website offers is for November 2029, but could we get one sooner? When will a restaurant first serve clean-meat containing products with ≥80% clean meat, at$3 per 100 grams or cheaper?

Resolution

This question resolves as the date when a restaurant, in any country, offers a clean meat containing product (beef, poultry, pork or fish) for consumption that contains at least 80% clean meat by weight. The product must exceed 50 grams in weight (so that it contains at least 40 grams of clean meat). The restaurant must be open to the general public in that a member of the public must be able to enter the establishment (though possibly requiring a reservation), and order the clean meat product. The restaurant must have served costumers for at least a year -- hence "pop-up" restaurants that exist for a very short amount of time (such as those at a convention like CES) do not count toward resolution. The clean meat containing product product must cost less than $3 per 100 grams. Samples given out for free don't count. If the clean meat is served as a dish with additional ingredients, an additional allowance of$5 is made for the price of the additional ingredients. For example, a quarter pound of a burger (~113,4 grams) that is 90% clean meat and 10% plant-based meat sold at any price below $8.41 would count toward positive resolution (as this is$3×1.134+$5=$8.41).

Evidence of the clean meat containing product's listing price and composition should come from the restaurant's online listing, credible media reports, or from at least three reports sourced from social media and/or submissions by Metaculus users/admin.

Prices are to be adjusted using a CPI commonly used in which the clean meat product is sold. If the clean meat product is not sold in the United States, the price is to be converted using the exchange rate listed on Google Finance at the time the question resolves.

Clean meat is here defined as meat that is grown primarily or entirely in cell culture, rather than in an animal’s body.

### Metaculus help: Predicting

Predictions are the heart of Metaculus. Predicting is how you contribute to the wisdom of the crowd, and how you earn points and build up your personal Metaculus track record.

The basics of predicting are very simple: move the slider to best match the likelihood of the outcome, and click predict. You can predict as often as you want, and you're encouraged to change your mind when new information becomes available. With tachyons you'll even be able to go back in time and backdate your prediction to maximize your points.

The displayed score is split into current points and total points. Current points show how much your prediction is worth now, whereas total points show the combined worth of all of your predictions over the lifetime of the question. The scoring details are available on the FAQ.

Note: this question resolved before its original close time. All of your predictions came after the resolution, so you did not gain (or lose) any points for it.

Note: this question resolved before its original close time. You earned points up until the question resolution, but not afterwards.

This question is not yet open for predictions.

#### Thanks for predicting!

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text:
Model a torch battery of length l to be made up of a thin cylindrical bar
Question:

Model a torch battery of length $l$ to be made up of a thin cylindrical bar of radius ‘ $a$ ‘ and a concentric thin cylindrical shell of radius ‘ $b$ ‘ filled in between with an electrolyte of resistivity $\rho$ (see figure). If the battery is connected to a resistance of value $R$, the maximum Joule heating in $R$ will take place for:

1. (1) $R=\frac{\rho}{2 \pi l}\left(\frac{b}{a}\right)$

2. (2) $R=\frac{\rho}{2 \pi l} \ln \left(\frac{b}{a}\right)$

3. (3) $R=\frac{\rho}{\pi l} \ln \left(\frac{b}{a}\right)$

4. (4) $R=\frac{2 \rho}{\pi l} \ln \left(\frac{b}{a}\right)$

Correct Option: , 2

Solution:

(2) Maximum power in external resistance is generated when it is equal to internal resistance of battery i.e., $P_{R}$ maximum when $r=R$

The maximum Joule heating in $R$ will take place for, the resistance of small element

$\Delta R=\frac{\rho d r}{2 \pi r l} \Rightarrow R=\frac{\rho}{2 \pi l} \int_{a}^{b} \frac{d r}{r}$

or, $R=\frac{\rho}{2 \pi l} \ln \frac{b}{a}$


text:
# Glossary¶

Warning

Unfortunately, our glossary is not full, but the Rally team is working on improving it. If you cannot find a definition in which you are interested, feel free to ping us via IRC (#openstack-rally channel at Freenode) or via E-Mail (openstack-dev@lists.openstack.org with tag [Rally]).

## Common¶

### Alembic¶

A lightweight database migration tool which powers Rally migrations. Read more at Official Alembic documentation

### DB Migrations¶

Rally supports database schema and data transformations, which are also known as migrations. This allows you to get your data up-to-date with latest Rally version.

### Rally¶

A testing tool that automates and unifies multi-node OpenStack deployment and cloud verification. It can be used as a basic tool for an OpenStack CI/CD system that would continuously improve its SLA, performance and stability.

### Rally Config¶

Rally behavior can be customized by editing its configuration file, rally.conf, in configparser format. While being installed, Rally generates a config with default values from its sample. When started, Rally searches for its config in “<sys.prefix>/etc/rally/rally.conf”, “~/.rally/rally.conf”, “/etc/rally/rally.conf”

### Rally DB¶

Rally uses a relational database as data storage. Several database backends are supported: SQLite (default), PostgreSQL, and MySQL. The database connection can be set via the configuration file option [database]/connection.

### Rally Plugin¶

Most parts of Rally are pluggable. Scenarios, runners, contexts and even charts for HTML report are plugins. It is easy to create your own plugin and use it. Read more at plugin reference.

## Deployment¶

### Deployment¶

A set of information about target environment (for example: URI and authentication credentials) which is saved in the database. It is used to define the target system for testing each time a task is started. It has a “type” value which changes task behavior for the selected target system; for example type “openstack” will enable OpenStack authentication and services.

## Task¶

### Cleanup¶

This is a specific context which removes all resources on target system that were created by the current task. If some Rally-related resources remain, please file a bug and attach the task file and a list of remaining resources.

### Context¶

A type of plugin that can run some actions on the target environment before the workloads start and after the last workload finishes. This allows, for example, preparing the environment for workloads (e.g., create resources and change parameters) and restoring the environment later. Each Context must implement setup() and cleanup() methods.

### Input task¶

A file that describes how to run a Rally Task. It can be in JSON or YAML format. The rally task start command needs this file to run the task. The input task is pre-processed by the Jinja2 templating engine so it is very easy to create repeated parts or calculate specific values at runtime. It is also possible to pass values via CLI arguments, using the –task-args or –task-args-file options.

### Runner¶

This is a Rally plugin which decides how to run Workloads. For example, they can be run serially in a single process, or using concurrency.

### Scenario¶

Synonym for Workload

### Service¶

Abstraction layer that represents target environment API. For example, this can be some OpenStack service. A Service provides API versioning and action timings, simplifies API calls, and reduces code duplication. It can be used in any Rally plugin.

### SLA¶

Service-Level Agreement (Success Criteria). Allows you to determine whether a subtask or workload is successful by setting success criteria rules.

### Subtask¶

A part of a Task. There can be many subtasks in a single Task.

### Task¶

An entity which includes all the necessary data for a test run, and results of this run.

### Workload¶

An important part of Task: a plugin which is run by the runner. It is usually run in separate thread. Workloads are grouped into Subtasks.

## Verify¶

Rally can run different subunit-based testing tools against a target environment, for example tempest for OpenStack.

### Verification¶

A result of running some third-party subunit-based testing tool.


text:
# Permutation Group as quotient of Free Group

I could use some help with the following question:

Let $S_{n}$ be the permutation group of $\left\{ 1,...,n\right\}$ , what is the minimal $k\in\mathbb{N}$ such that $S_{n}$ is a quotient of the free group $F_{k}$ (free group with k generators).

Thanks a lot!

-
Alternatively, what is the size of the smallest set of generators of $S_n$ – Thomas Andrews Dec 25 '12 at 20:50

Clearly, $k>1$ (except for which small values of $n$?). Can you see how $S_n=\langle(1\, 2),(1\,2\,\ldots\,n)\rangle$ and hence $k\le 2$?
I wasn't familiar with that set of generators for $S_{n}$ but it certainly clarifies it :) Obviously for n=1,2 it would be k=1 and otherwise 2. Thanks a lot :) – Serpahimz Dec 25 '12 at 21:31
Actually, when $n=1$, you can use the free group on $0$ generators... – Thomas Andrews Dec 25 '12 at 22:15


text:
# Weighted average of arbitrary k points from a line

Suppose a set of k arbitrary points, x_i, 1<=i<=k, x_i from R^2 are selected from a line. How can it be shown that a weighted barycenter x_o=(o_i*x_i)/(o_1+o_2+...+o_k) also belongs to that line (assume o_i are arbitrary weights)? Does the choice of weights restrict the solutions (ie, a particular choice to satisfy that x_o is within the 'convex hull' of other points)?

chiro
Hey onako.

If this is a straight line then from this you have n-independent coeffecients (since the o_i's are independent) and since you can specify those then you can choose the coeffecients such that these match the ones of the original line.

If all the x_i's line on a straight-line, then provided that you can pick the o_i's, then you can solve for the particular values of o_i to provide equal coeffecients.

The only thing though about this is that you are dividing by the sum of the all the o_i's which means you lose a degree of freedom and the only way you can get a solution is if you have an extra constraint on the o_i's and this constraint is exactly what is imposed.

If your line is a unique line then the solution in terms of your o_i's should be unique as well since you have a constraint on the sum of the weights which means the scalar multiples should disappear as well (I'm consider scalar multiples of a linear equation).

Let's simplify the question. Suppose that non-negative arbitrary weights o_i are associated with each x_i chosen from the straight line. Does x_o lie on that same line? The point is: points x_i are chosen as arbitrary points from the line, and are associated coefficients o_i which are non-negative.

chiro
Are you looking at the triangle simplex in R^2?

I'm concerned with a 2D case, with a straight line.

chiro
$Nx=a$


text:
• ## #FuturePub London returned to a full house!

Posted by John on April 10, 2019It had been a while, but #FuturePub London returned at the end of March! We'd like to send out a huge thank you to everyone who attended; it was great to see such a large turnout, and such a lively interaction with the speakers, with lots of questions which helped expand the discussions. It was also great to see such a large group stay after the talks, and at the pub afterwards, as $F u t u r e P u b b e c a m e$ScholarlySocial for the end of the evening. We've now hosted over a dozen #FuturePub events, since our first back in January 2014, and have somehow become known as "a staple of the London science tech/publishing scene" (thanks Eva!). This time around we hosted the event in the 'Classroom' at our WeWork offices near Kings Cross...and only just had enough seats! How it works If you've never been to #FuturePub before, this is how it works: Five or six quick-fire talks cover a range of new and exciting developments in science & publishing tech. These all fit into a one hour slot to keep the evening fast-paced and fun! People arrive early for pre-talk pizza and drinks :) The rest of the evening is then open for discussions and conversations over the remainder of the drinks and/or pizza! We get a great mixture of attendees from the research, publishing and start-up communities, and we usually head to a nearby pub to continue on into the small hours. For this $F u t u r e P u b w e o n c e a g a \in t e a m e d u p w i t h S c h o l a r l y S o c i a l f \mathmr{and} t h e t r i p \to t h e p u b a f t e r w a r \mathrm{ds} . T h e \ne x t$FuturePub will be in Sept/Oct 2019 (date TBC). Speakers & Talks Here's a recap of the talks from the event, along with a link to the projects / slides that were covered by the speakers: First, a celebration! Not only was it the first #FuturePub for a while, we were also celebrating that Overleaf now has over 4 million users worldwide! Here's the thank you note I wrote on behalf of our team, including a little look ahead at what's to come :) The story of Pint of Science Download Praveen's slides Summary: Pint of Science is an annual science festival which mainly takes place in pubs and cafes. It began as an idea between two slightly naive, bored, and soon-to-be unemployed postdocs. We wanted people to know about the cool science happening behind closed lab doors (and also find out ourselves!) as well as giving scientists a platform to share what they do. By holding all our events over three days of the year we wanted people to be spoilt for choice and choose what interested them. What started as a somewhat bonkers idea, a bit of a laugh and a one-off project to pass the time, in just a few years Pint of Science grew from events in three UK cities to a global phenomenon; during May 20-22, the festival will see 24 countries and over 300 cities taking part, bringing thousands of people together across thousands of events. I'll talk about how a community of passionate and motivated volunteers created something incredible, and where we plan to go next. Speaker: Dr Praveen Paul has a PhD in molecular neurobiology and used to be a postdoc at Imperial College London. She co-founded Pint of Science and helped it grow from a fun project between a handful of friends to a worldwide festival that has been recognised by the national media in multiple countries in just a matter of a few years. She now runs Pint of Science full time. Heron - the first accessible map of science Download Mihaly's slides Summary: Heron’s AI-first approach enables unprecedented literature-scale examination of information, promoting experimental standardisation and initiate progress on biomedical reproducibility issues particularly afflicting interdisciplinary fields such as neuroscience. Speaker: Mihaly Kollo is a Neuroscience PhD with 15 years of experimental biology research and data science. As a researcher he runs interdisciplinary projects, on the border of molecular biology, neurophysiology, engineering and machine learning. Research Square - a new model of publishing Download Damian's slides Summary: Research Square is a new pre-publication platform designed to work alongside journal workflows. As a preprint server, the platform features full HTML renderings of text and figures, commenting and annotation features, and a unique system of badges to demonstrate high standards of integrity, reproducibility and statistics. But what makes the platform really unique is the way it provides journals with a way of opening up their review process, offering more transparency and control to authors. This service, called In Review, allows authors to post their work online as a preprint at submission to a participating journal, and then see detailed updates of the paper’s journey through peer review. Authors can see reviews as soon as they are submitted, and can even suggest reviewers if their paper gets stuck. This increased control has been a big hit with authors, and has led to very high uptake in the BMC Series journals we have piloted with. As a result of this success, we are rolling out to more Springer Nature journals over the course of this year. Speaker: Damian Pattinson is VP of Publishing Innovation at Research Square - a US-based company which aims to make publishing faster, fairer and more useful. He is a journal editor by training, first at the BMJ where he worked on the clinical titles, BMJ Clinical Evidence and BMJ Best Practice, and then at PLOS where he was Editorial Director of PLOS ONE. He has a PhD in neuroscience from UCL. Scholarcy: using AI to make research more accessible for everyone Download Scholarcy's slides Summary: Scholarcy uses an ensemble of machine learning and AI techniques to turn research papers into summary flashcards which you can annotate and share, with the key learning points highlighted for you. When I was back in full-time study some years before, I'd been frustrated by the number of discovery tools that would recommend what to read, but not why or how I should read them. My problem was absorbing and understanding the information in front of me. Squinting at 100s of PDFs on screen, or printing them off and going over them with a highlighter pen was not really working. I saw a need for something that would help me master the core concepts, give me the main learning points and get me up to speed on a new subject. Around this time last year I was between jobs and was tinkering with a few project ideas in Python. Revisiting that study problem I had years before, I put together a processing pipeline that did some automated linguistic analysis on top of some machine learning libraries I was familiar with, wrapped it up into an API using Flask, and had a simple tool that would parse research PDFs, highlight what looked like important statements, and find key terms and map them to the right Wikipedia articles. Once I wrapped this in a Chrome Extension and built a simple website to promote it, interest started to grow. One year later, I'm working on it full time, I have a wonderful cofounder, and we have publishers using our API and researchers around the world using the app. Emma and I will talk about how we got there and what's coming next. Speakers: Before founding Scholarcy, Phil Gooch and Emma Warren-Jones previously worked together at RefME, a popular reference management tool. Phil has a PhD in clinical NLP and many years’ experience developing text mining solutions for the publishing, EdTech, and healthcare sectors. Emma has many years commercial experience in the Edtech, academic publishing and information industries, launching content & discovery platforms and analytics tools to the global research community. RosettaHUB, harnessing the compute clouds for collaborative science Summary: RosettaHUB aims at connecting the dots between clouds, research software and the DevOps tools and paradigm to provide a "universal" platform for collaborative science. RosettaHUB makes it easy for scientists to assemble the compute infrastructure, the tools and the data they need, access it as a service in the browser and work in collaboration with peers. The RosettaHUB virtual research environments are built on top of a new cloud-native data science and technical computing platform which itself leverages the RosettaHUB multi-cloud governance platform. The latter allows every scientist, student and educator to seamlessly gain access to a dedicated AWS account which is federated, managed and monitored in real time in terms of resources and budget. Besides mass on-boarding, it enables multi-tenant governance, hierarchical customization and compliance enforcement, easy sharing of portfolios of scientific cloud artifacts, etc . The RosettaHUB Virtual Labs leverage Infrastructure-as-Code and the scientist's "personal data center" to make seamless the creation of and control of remote collaborative Workspaces, IDEs, big data and HPC clusters and machine learning environments. The presentation will provide an overview of RosettaHUB and will share the experience gained from deploying it at scale to deliver AWS and collaborative Virtual Labs access to over 20,000 scientists, educators and students. Speaker: Karim Chine is a software architect and technology expert specializing in research e-infrastructure, cloud computing and e-science. He has over 18 years of experience in large scale distributed systems design and he has been a regular contributor to the EU research and innovation programs as evaluator and expert reviewer of European flagship projects in the areas of HPC, cloud computing, science gateways, future and emerging technologies, Open Science, etc. Karim is the co-founder of RosettaHUB. Researcher - never miss an important paper Download Ramiz's slides Summary: Researcher is an app and web platform for scientists and academics to help them keep up to date with the latest literature. We currently have over 700,000 registered users, 10 million abstracts are browsed every month on the platform and we are currently indexing over 15,000 journals. We are backed by Blenheim Chalcot, a venture builder based in Hammersmith, London. Speaker: Ramiz Nathani studied Pharmaceutical Chemistry in University of Mumbai, before moving to the UK to study MSc in Chemical Research in 2008. He went on to do a PhD in Organic Chemistry at UCL, followed by a Post-doc also at UCL. He spent a few years in industry (biotech start up in Oxford - Oxford Nanopore) before deciding to build Researcher with his co-founder Olly Cooper in 2017. They were trying to solve a well known problem - having no efficient way of tracking academic literature. Get in touch if you'd like to speak at our next event! If you'd like to put yourself forward to speak at a future #FuturePub, please let us know and we'll add you to the early shortlist! Our next event will be in Sept/Oct 2019 (date TBC).
Tags: