⌘ ⊕ ⊙ ∈ ⋂ ⋃ ⋀ ⋁ ⊂ ⊆∖ ∑ ∏ ∃ ∀ ⇒ → ∞ ✕ ≤ ≥ ℝ ℕ ℤ ∙ ✶ ∅ ★ ⌻ ⊚ ⊛ √ ← ● ✿ Δ
Let the binary matrix A=[aep] describe a two-mode network on the set of events E and the set of of participants P:
aep = 1 if p participated in the event e ; and 0 otherwise.
The function d: E → T assigns to each event e the date d(e) when it happened. T = [first, last]. Using these data we can construct two temporal affiliation matrices:
Using the multiplication of temporal matrices over the combinatorial semiring we get the corresponding instantaneous and cumulative co-occurrence matrices Ci = AiT ∙ Ai and Cc = AcT ∙ Ac .
A typical example of such a matrix is the papers authorship matrix where E is the set of papers, P is the set of authors and d is the publication year \citep{bibnet}.
Temporal collaboration.
ci['IDI/B','HCL/B'] cc['IDI/B','HCL/B']
1 : (2003, 2004, 1) 1 : (2003, 2004, 1)
2 : (2004, 2005, 2) 2 : (2004, 2005, 3)
3 : (2005, 2006, 3) 3 : (2005, 2006, 6)
4 : (2006, 2007, 2) 4 : (2006, 2007, 8)
5 : (2007, 2008, 1) 5 : (2007, 2008, 9)
6 : (2008, 2009, 7) 6 : (2008, 2009, 16)
7 : (2009, 2010, 6) 7 : (2009, 2010, 22)
8 : (2010, 2011, 7) 8 : (2010, 2011, 29)
9 : (2011, 2013, 18) 9 : (2011, 2012, 47)
10 : (2012, 2013, 65)
ci['HCL/B','HCL/B'] cc['HCL/B','HCL/B']
1 : (1997, 1998, 2) 1 : (1997, 1998, 2)
2 : (1998, 1999, 5) 2 : (1998, 1999, 7)
3 : (1999, 2000, 8) 3 : (1999, 2000, 15)
4 : (2000, 2001, 7) 4 : (2000, 2001, 22)
5 : (2001, 2002, 5) 5 : (2001, 2002, 27)
6 : (2002, 2003, 6) 6 : (2002, 2003, 33)
7 : (2003, 2004, 14) 7 : (2003, 2004, 47)
8 : (2004, 2005, 20) 8 : (2004, 2005, 67)
9 : (2005, 2006, 10) 9 : (2005, 2006, 77)
10 : (2006, 2007, 14) 10 : (2006, 2007, 91)
11 : (2007, 2008, 20) 11 : (2007, 2008, 111)
12 : (2008, 2009, 28) 12 : (2008, 2009, 139)
13 : (2009, 2010, 56) 13 : (2009, 2010, 195)
14 : (2010, 2011, 78) 14 : (2010, 2011, 273)
15 : (2011, 2012, 84) 15 : (2011, 2012, 357)
16 : (2012, 2013, 112) 16 : (2012, 2013, 469)
The triple (s,f,v) in a temporal quantity cipq tells that in the time interval [s,f) there were v events in which both p and q took part.
The triple (s,f,v) in a temporal quantity ccpq tells that in the time interval [s,f) there were in total v accumulated events in which both p and q took part.
The diagonal matrix entries cipp and ccpp contain the temporal quantities counting the number of events in the time intervals in which the participant p took part.
For example, in a data set on the stem cell research during 1997–2012 in Spain collected by Gisela Cantos-Mateos \citep{stem} we get from the basic two-mode network, where E is the set of papers and P is the set of institutions, for selected two institutions (HCL/B = University Hospital Clínic de Barcelona, Barcelona and IDI/B = Institut d'Investigacions Biomèdiques August Pi i Sunyer, Barcelona) the collaboration temporal quantities presented in Table~\ref{tec}.
The first column in the table contains the yearly collaboration (co-authorship) data and the second column contains the cumulative collaboration data. Let's read the table:
ci[IDI/B, HCL/B](2005, 2006) = 3 - in the year 2005 researchers from both institutions published 3 joint papers;
ci[IDI/B, HCL/B](2011, 2013) = 18 - in the years 2011 and 2012 researchers from both institutions published 18 joint papers each year;
ci[HCL/B, HCL/B](2010, 2011) = 78 - in the year 2010 researchers from the institution HCL/B published 78 papers;
cc[IDI/B, HCL/B](2008, 2009) = 16 - till the year 2008 (included) researchers from both institutions published 16 joint papers.
Note that the violence network from Section~\ref{activ} is essentially a co-occurrence network that could be obtained from the more primitive instantaneous two-mode network about violent actions reported in journal articles and the involved political actors.
>>> print('start WIT:',datetime.datetime.now().ctime()) start WIT: Tue Jun 23 10:05:52 2015 >>> print('Network WIT') Network WIT >>> WIT = TQ.Ianus2Mat("./gisela/WIT.ten") >>> print('input done:',datetime.datetime.now().ctime()) input done: Tue Jun 23 10:06:55 2015 >>> print('sum =',TQ.MatSummary(WIT['mat'])) sum = (1997, 2013, 1, 1) >>> print(WIT.keys()) dict_keys(['met', 'tit', 'til', 'typ', 'tin', 'mat', 'dim', 'nam']) >>> print('dim =',WIT['dim']) dim = (5839, 577, 1997, 2013) >>> print('met =',WIT['met']) met = re au Gisela Cantos Mateos ti Spanish "Stem cell" research (1997-2012) de Gisela collected from WoS data about Spanish “Stem cell” research (1997-2012). She manually unified the names of institutions in Excel and produced the CSV files with tables: (Documents,Institutions), (Documents,KeyWordsPlus) and (Documents,PublicationYear). dt October, 2014 er re au Vladimir Batagelj ti transformation to Ianus format dt October 28, 2014 de The data in CSV format were transformed into Ianus format. er >>> print('nam =',WIT['nam'][0:10]) nam = ['5', '8', '9', '15', '30', '43', '44', '45', '46', '47'] >>> print('tit =',WIT['tit']) tit = papersXinstitutions >>> print('tin =',WIT['tin'][0:10]) tin = [[(2007, 2013, 1)], [(2007, 2013, 1)], [(2007, 2013, 1)], [(2007, 2013, 1)], [(2007, 2013, 1)], [(2007, 2013, 1)], [(2007, 2013, 1)], [(2007, 2013, 1)], [(2007, 2013, 1)], [(2007, 2013, 1)]] >>> print('til =',WIT['til'][0:10]) til = [] >>> print('transpose:',datetime.datetime.now().ctime()) transpose: Tue Jun 23 10:09:50 2015 >>> IWTmat = TQ.MatTrans(WIT['mat']) >>> print('done:',datetime.datetime.now().ctime()) done: Tue Jun 23 10:10:26 2015 >>> print('multiply:',datetime.datetime.now().ctime()) multiply: Tue Jun 23 10:11:48 2015