mp2: added template

mp2/Makefile

@@ -0,0 +1,14 @@
+filename=template
+
+pdf:
+	pdflatex ${filename}
+	bibtex ${filename}||true
+	pdflatex ${filename}
+	make clean
+
+read:
+	evince ${filename}.pdf &
+
+
+clean:
+	rm -f *.out *.log *.bbl *.blg *.aux ${filename}.log  ${filename}.ps ${filename}.aux ${filename}.out ${filename}.dvi ${filename}.bbl ${filename}.blg

mp2/Project.2.Maggioni.Claudio/householder/README.m

@@ -0,0 +1,43 @@
+% 
+%                      On a Matrix and Its Graph
+% 
+% At the 1993 Householder Symposium on Numerical Algebra in Lake Arrowhead,
+% Nick Trefethen posted a flip chart and invited everyone present to write
+% their name on it, and to draw lines connecting their name with the names
+% of all their coauthors.  The diagram grew denser throughout the week; at
+% the end it was a graph with 104 vertices (or people) and 211 edges. 
+% 
+% A graph is a sparse matrix, so just for fun we typed the graph into Matlab 
+% and looked at it in a few different ways.  You can say "runme" to Matlab 
+% to see the results.
+% 
+% The original flip chart is now framed on the wall of Nick's office at
+% Cornell.  He promises to bring it along to Householder 2023.
+% 
+% - John Gilbert, Cleve Moler, Nick Trefethen
+%   with thanks to Rob Schreiber, Barry Smith, and 99 others.
+% 
+% ----------------------------------------------------------------------
+% List of files in matlab/householder:
+% 
+% README.m           This file.
+% 
+% runme.m            Matlab script to show off the matrix and the graph. 
+% 
+% drawit.m           Matlab script just to draw the graph.
+% 
+% graph.ps           Black-and-white postscript picture of the graph.
+%
+% housegraph.mat     The raw data, as follows:
+% 
+%      A     is the 104x104 adjacency matrix of the graph.
+%      xy    is the array of vertex coordinates for the picture.
+%      name  is a character matrix with 104 rows, each row giving the
+%            name of the person associated with a vertex.
+%      Every person's name is also a scalar variable whose value is 
+%            that person's vertex number; for example, 
+%            Stewart = 77 and name(77,:) = 'Stewart'.
+%      prcm  is a permutation (based on reverse Cuthill-McKee) 
+%            to reorder the graph for the picture.
+
+help README

mp2/Project.2.Maggioni.Claudio/householder/drawit.m

@@ -0,0 +1,28 @@
+% DRAWIT  Script to plot the graph of coauthors from Householder 93.
+
+if ~exist('prcm') 
+    load housegraph;
+end;
+
+% A    is the adjacency matrix.
+% prcm is a permutation; any permutation could be substituted.
+% name is the vector of people's names.
+% xy   is just xy coords of points on the unit circle (and the origin).
+
+Aperm = A(prcm,prcm);
+nameperm = name(prcm,:);
+nfolks = max(size(A));
+
+clf 
+gplot(Aperm,xy);
+axis off;
+x = xy(:,1) * 1.05;
+y = xy(:,2) * 1.05;
+x(1) = .08;         % Put names(1) in the center of the circle.
+y(1) = .06;
+h = text(x,y,nameperm);
+
+for k = 2:nfolks    % Shrink the font for the other names, and rotate them.
+    set(h(k),'fontsize',10);
+    set(h(k),'rotation',180/pi*atan2(y(k),x(k)));
+end;

mp2/Project.2.Maggioni.Claudio/householder/runme.m

@@ -0,0 +1,190 @@
+% RUNME : Demonstrate the graph of coauthors from Householder 1993.
+
+load housegraph;
+
+% A    is the adjacency matrix.
+% prcm is a permutation; any permutation could be substituted.
+% name is the vector of people's names.
+% xy   is just xy coords of points on the unit circle (and the origin).
+
+  
+clc;
+more off;
+format compact;
+disp('  ');
+disp('                       On a Matrix and Its Graph');
+disp('  ');
+disp('At the 1993 Householder Symposium on Numerical Algebra in Lake Arrowhead,');
+disp('Nick Trefethen posted a flip chart and invited everyone present to write');
+disp('their name on it, and to draw lines connecting their name with the names');
+disp('of all their coauthors.  The diagram grew denser throughout the week; at');
+disp('the end it was a graph with 104 vertices (or people) and 211 edges. ');
+disp(' ');
+disp('Just for fun we typed the graph into Matlab.  Here''s the result....');
+disp('  ');
+disp('               [Hit space to continue] ');
+pause;
+
+figure(1);
+clf reset;
+spy(A);
+title('Coauthor Matrix');
+drawnow;
+
+figure(2);
+clf reset;
+drawit;
+
+disp('  ');
+disp('The adjacency matrix is symmetric with 104 rows and columns, and');
+disp('211 nonzeros above the diagonal; all the nonzeros have value 1.  ');
+
+disp('  ');
+disp('               [Hit space to continue] ');
+pause;
+
+disp('  ');
+disp('Which column has the highest nonzero count?');
+disp('  ');
+
+echo on
+[count,column] = max(sum(A))
+
+name(column,:)
+
+echo off
+
+disp('  ');
+disp('               [Hit space to continue] ');
+pause;
+
+clc;
+disp('Here''s a bandwidth-reducing order of the matrix. ');
+
+p = symrcm(A);
+figure(1);
+spy(A(p,p));
+title('Reverse Cuthill-McKee Order');
+drawnow;
+
+disp('  ');
+disp('I don''t know what to conclude from this!');
+
+disp('  ');
+disp('               [Hit space to continue] ');
+pause;
+
+clc;
+disp('Powers of the matrix give information about paths in the graph.');
+disp('Squaring the matrix gives paths of length 1 and 2.');
+
+figure(1);
+AA = A^2;
+spy(AA);
+title('A^2');
+
+disp('  ');
+disp('               [Hit space to continue] ');
+pause;
+disp('  ');
+
+disp('Have Gene Golub and Cleve Moler ever been coauthors?');
+
+disp('  ');
+disp('               [Hit space to continue] ');
+pause;
+disp('  ');
+
+echo on;
+A(Golub,Moler)
+
+echo off;
+
+disp('  ');
+disp('No.');
+disp('But how many coauthors do they have in common?');
+
+disp('  ');
+disp('               [Hit space to continue] ');
+pause;
+disp('  ');
+
+echo on;
+AA = A^2;
+AA(Golub,Moler)
+
+echo off;
+
+disp('  ');
+disp('And who are those common coauthors?  (Matlab hackers raise your hands.)');
+
+disp('  ');
+disp('               [Hit space to continue] ');
+pause;
+disp('  ');
+
+echo on;
+name( find ( A(:,Golub) .* A(:,Moler) ), :)
+
+echo off;
+
+disp('  ');
+disp('               [Hit space to continue] ');
+pause;
+
+clc;
+
+disp('If we keep taking powers of the matrix, ...');
+
+p = 2;
+while ~all(AA(1,:))
+    AA = AA*A;
+    spy(AA);
+    p = p+1;
+    title(['A^' int2str(p)]);
+    pause(1);
+end;
+
+disp('  ');
+disp('... we can find the length of the longest path ');
+disp('from Gene Golub to anybody, which is the power that');
+disp('first has row 1 full, ...');
+
+disp('  ');
+disp('               [Hit space to continue] ');
+pause;
+disp('  ');
+
+while ~all(all(AA))
+    AA = AA*A;
+    spy(AA);
+    p = p+1;
+    title(['A^' int2str(p)]);
+    pause(1);
+end;
+
+disp('... and also the diameter of the graph, which is ');
+disp('the power that first has the whole matrix full.');
+
+disp('  ');
+disp('               [Hit space to continue] ');
+pause;
+
+clc;
+
+disp('  ');
+disp('Finally, we try a minimum degree reordering of the matrix');
+disp('and discover its true nature as, of course, ....');
+disp('  ');
+
+p = symamd(A);
+spy(A(p,p));
+title('The (Lake) Arrowhead Matrix');
+pause(8);
+
+disp('  ');
+disp('Thanks to Tony Chan and Gene Golub for the meeting,');
+disp('          Rob Schreiber and Barry Smith for helping count edges,');
+disp('          and all concerned for a wonderful week.');
+disp('        - John Gilbert, Cleve Moler, and Nick Trefethen ');
+disp('  ');

mp2/Project.2.Maggioni.Claudio/karate.adj

@@ -0,0 +1,34 @@
+0 1 1 1 1 1 1 1 1 0 1 1 1 1 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 
+1 0 1 1 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 1 0 0 0 
+1 1 0 1 0 0 0 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 
+1 1 1 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
+1 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
+1 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
+1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
+1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
+1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 
+0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 
+1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
+1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
+1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
+1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 
+0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 
+0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 
+0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
+1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
+0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 
+1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 
+0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 
+1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
+0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 
+0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 1 1 
+0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 
+0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 
+0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 
+0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 
+0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 
+0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 1 1 
+0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 
+1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 1 1 
+0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 1 0 1 0 1 1 0 0 0 0 0 1 1 1 0 1 
+0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 1 0 0 1 1 1 0 1 1 0 0 1 1 1 1 1 1 1 0 

mp2/Project.2.Maggioni.Claudio/pagerank.m

@@ -0,0 +1,65 @@
+function x = pagerank(U,G,p)
+% PAGERANK  Google's PageRank
+% pagerank(U,G,p) uses the URLs and adjacency matrix produced by SURFER,
+% together with a damping factory p, (default is .85), to compute and plot
+% a bar graph of page rank, and print the dominant URLs in page rank order.
+% x = pagerank(U,G,p) returns the page ranks instead of printing.
+% See also SURFER, SPY.
+
+if nargin < 3, p = .85; end
+
+
+if(ischar(U))
+    U=cellstr(U);
+end
+
+if(isreal(U))
+   U=(num2cell(U));
+end
+
+
+% Eliminate any self-referential links
+
+G = G - diag(diag(G));
+  
+% c = out-degree, r = in-degree
+
+n = size(G,1);
+c = sum(G,1);
+r = sum(G,2);
+
+% Scale column sums to be 1 (or 0 where there are no out links).
+
+k = find(c~=0);
+D = sparse(k,k,1./c(k),n,n);
+
+% Solve (I - p*G*D)*x = e
+
+e = ones(n,1);
+I = speye(n,n);
+x = (I - p*G*D)\e;
+
+% Normalize so that sum(x) == 1.
+
+x = x/sum(x);
+
+% Bar graph of page rank.
+
+shg
+bar(x)
+title('Page Rank')
+
+% Print URLs in page rank order.
+
+if nargout < 1
+   [~,q] = sort(-x);
+   disp('     page-rank  in  out  url')
+   k = 1;
+   while (k <= n) && (x(q(k)) >= .005)
+      j = q(k);
+      temp1  = r(j);
+      temp2  = c(j);
+      fprintf(' %3.0f %8.4f %4.0f %4.0f  %s\n', j,x(j),full(temp1),full(temp2),U{j})
+      k = k+1;
+   end
+end

mp2/Project.2.Maggioni.Claudio/test.m

@@ -0,0 +1,27 @@
+clear;
+n = 1000;
+x = randperm(n);
+gs = 450;
+
+group1 = x(1:gs);
+group2 = x(gs+1:end);
+
+p_group1 = 0.5;
+p_group2 = 0.4;
+p_between = 0.1;
+
+A(group1, group1) = rand(gs, gs) < p_group1;
+A(group2, group2) = rand(n-gs, n-gs) < p_group2;
+A(group1, group2) = rand(gs, n-gs) < p_between;
+% no group2, group1 needed since we'll force the matrix to be symmetric
+
+A = triu(A,1); % upper triangular part of A without diagonal
+A = A + A'; % make it symmetric
+deg = sum(A);
+L = diag(deg) - A;
+[V, D] = eig(L);
+display(D(2,2));
+plot(sort(V(:,2)), '.-');
+
+[ignore, p] = sort(V(:,2));
+spy(A(p,p));

mp2/assignment.sty

@@ -0,0 +1,322 @@
+%%  % for readable pdf files
+%%  \usepackage{times} 
+\usepackage{ifthen}
+\usepackage{comment}
+\usepackage[utf8]{inputenc}
+%%  \usepackage{enumerate}
+%%  \usepackage{alltt}
+%%  \usepackage{xspace}
+%%  \usepackage{wrapfig}
+\usepackage{graphics}
+\usepackage{graphicx}
+\usepackage{epstopdf}
+% \usepackage{amsmath}
+%%  \usepackage{mathtools}
+\usepackage{amssymb}
+%\usepackage[xetex,bookmarks,pdfencoding=unicode,colorlinks=true,citecolor=blue,linkcolor=black,urlcolor=blue]{hyperref}
+\usepackage[bookmarks,pdfencoding=unicode,colorlinks=true,citecolor=blue,linkcolor=black,urlcolor=blue]{hyperref}
+% \usepackage{nohyperref}
+%\usepackage{url}
+%%  \usepackage{fancyvrb}
+\usepackage{verbatim}
+\usepackage{listingsutf8}
+\usepackage{color}
+%%  \usepackage{textcomp}
+%%  \usepackage{cmap}
+%%  \usepackage[colorinlistoftodos]{todonotes}
+%%  \usepackage{lineno}
+%%  \usepackage{tocloft}
+%%  \usepackage{marginnote}
+\usepackage{geometry}
+\usepackage{booktabs}
+%%  \usepackage{longtable}
+%%  \usepackage{etoolbox}
+%%  \usepackage{titlesec}
+\usepackage[font=small,labelfont=it,labelsep=period,justification=centering]{caption}
+\usepackage{array}
+%%  %\usepackage{tabularx}
+%%  \usepackage[titletoc]{appendix}%
+
+\pagestyle{plain}
+\voffset -5mm
+
+\oddsidemargin  0mm
+\evensidemargin -11mm
+\marginparwidth 2cm
+\marginparsep 0pt
+
+\topmargin 0mm
+\headheight 0pt
+\headsep 0pt
+\topskip 0pt        
+
+%\footheight 0pt
+%\footskip 0pt
+\textheight 255mm
+\textwidth 165mm
+
+% ----------------------------------------
+%
+% II. Macros
+%
+% ----------------------------------------
+
+\let\gaga=\phi \let\phi=\varphi \let\varphi=\gaga
+\let\gaga=\theta \let\theta=\vartheta \let\vartheta=\gaga
+\let\gaga=\epsilon \let\epsilon=\varepsilon \let\varepsilon=\gaga
+
+\newcommand\code[1]{ {\footnotesize \texttt{#1}} }
+
+\newcommand\isassignment {false}
+\newcommand{\setassignment}{\renewcommand\isassignment {true}}
+\newcommand{\ifassignment}[1]{\ifthenelse{\boolean{\isassignment}}{#1}{}}
+\newcommand{\ifnotassignment}[1]{\ifthenelse{\boolean{\isassignment}}{}{#1}}
+\newcommand{\ignore}[1]{}
+\newcommand{\duedate} {}
+\newcommand{\setduedate}[1]{%
+\renewcommand\duedate {Due date:~ #1}
+}
+\newcommand{\assignmentpolicy}{
+\bigskip
+\bigskip
+\begin{table}[h]
+\begin{center}
+\scalebox{0.8} {%
+\begin{tabular}{|p{0.02cm}p{16cm}|}
+\hline
+&\\
+\multicolumn{2}{|c|}{\Large\textbf{Submission instructions}}\\
+\multicolumn{2}{|c|}{\large\textbf{(Please, notice that following instructions are mandatory: }}\\
+\multicolumn{2}{|c|}{\large\textbf{submissions that don't comply with, won't be considered)}}\\
+&\\
+\textbullet & Assignments must be submitted to Moodle (i.e. in electronic format).\\
+\textbullet & Provide both executable package (single .class or .jar file) and sources (.java files). If you are using non-sdk libraries, please add them in the file. Sources must be organized in packages called:\\
+\multicolumn{2}{|c|}{\textit{ch.usi.inf.ncc12.assignment$<$assignmentNumber$>$.exercise$<$exerciseNumber$>$.$<$name$>$.$<$surname$>$}}\\
+& and  the jar file must be called:\\
+\multicolumn{2}{|c|}{\textit{assignment$<$AssignmentNumber$>$.$<$Name$>$.$<$Surname$>$.jar}}\\
+& Projects exported directly from Eclipse would be much appreciated (Please, be sure that you are including also the sources in the jar file).\\
+\textbullet & The produced files (one pdf and one jar file) must be collected into a single archive file (.zip) named:\\
+\multicolumn{2}{|c|}{\textit{assignment$<$AssignmentNumber$>$.$<$Name$>$.$<$Surname$>$.zip}}\\
+\hline
+\end{tabular}
+}
+\end{center}
+\end{table}
+}
+\newcommand{\ie}{\textit{i.e.,}\xspace}
+\newcommand{\eg}{\textit{e.g.,}\xspace}
+\newcommand{\etal}{\textit{et al.}\xspace}
+
+\newcommand\nat{{\Bbb N}}
+\def\int{{\Bbb Z}}
+\newcommand\rat{{\Bbb Q}}
+\newcommand\real{{\Bbb R}}
+\newcommand\calD{{\cal D}}
+\newcommand\calM{{\cal M}}
+\newcommand\calL{{\cal L}}
+\newcommand\Gone{\bfmath{G1}}%
+\newcommand\Gonei{\bfmath{G1i}}%
+\newcommand\Goneai{\bfmath{G1(i)}}%
+\newcommand\Gtwo{\bfmath{G2}}%
+\newcommand\Gtwoi{\bfmath{G2i}}%
+\newcommand\Gtwoai{\bfmath{G2(i)}}%
+\newcommand\Gthree{\bfmath{G3}}%
+\newcommand\Gthreei{\bfmath{G3i}}%
+\newcommand\Gthreeai{\bfmath{G3(i)}}%
+\newcommand\True{\bfmath{True}}
+\newcommand\False{\bfmath{False}}
+\newcommand\FV{\itmath{FV}}
+%
+% mathrel's
+%
+\def\maps{\mathrel{:}}
+\def\andthen{\mathrel{;}}
+\def\suchthat{\mathrel{:}}
+\def\defid{\mathrel{:\equiv}}
+\def\defeq{\mathrel{:=}}
+\def\eqdef{\mathrel{=:}}
+\def\gewenn{\leftrightarrow}
+\newcommand\tnt{\mathrel{\supset}}
+\newcommand\pr{\mathrel{\vdash}}%
+\def\prld#1#2{\mathrel{\vrule width 0.3pt height 8pt depth 2pt\mkern-2mu\textstyle{\hskip0.5ex\raise2pt\hbox{$\scriptstyle#1$}\hskip0.1ex\over\hskip0.5ex#2\hskip0.1ex}}}
+\def\defGewenn{\mathrel{{:}{\Longleftrightarrow}}}
+\def\Gewenn{\mathrel{\Longleftrightarrow}}
+\def\To{\mathrel{\Longrightarrow}}
+\def\defsimeq{\mathrel{:\simeq}}
+\def\redone{\mathrel{\vartriangleright_1}}
+\def\red{\mathrel{\vartriangleright}}
+%
+% mathbin's
+%
+\newlength{\lminus}
+\settowidth{\lminus}{\hbox{$-$}}
+\def\dotmin{\mathbin{\vbox{\lineskip0pt\baselineskip0pt\hbox to\lminus{\hfill.\hfill}\vglue-0.55ex\hbox{$-$}}}}
+
+%
+% mathop's
+%
+\def\pow{\mathop{\rm Pow}}
+\def\dom{\mathop{\rm dom}}
+\def\ran{\mathop{\rm ran}}
+\def\seq#1{\langle #1\rangle}
+\def\Seq{\mathop{\it Seq}}
+\def\lh{\mathop{\it lh}}
+
+%
+% points
+%
+\newcommand{\punkte}[1]{\hspace{1ex}\emph{\mdseries\hfill(#1~\ifcase#1{Points}\or{Points}\else{Points}\fi)}}
+
+% ----------------------------------------------------------------------
+\newcommand\secRule{\vspace{-4mm} \rule{.5\textwidth}{4pt}\vspace{-5mm}}
+\newcommand{\vf}{\vspace{7mm plus7mm minus1mm}}
+\newcommand{\compl}{{\rm c}}
+\newcommand{\blank}{\hspace{0.5em}}
+\newcommand\nyt{\rule{0pt}{0pt}}
+\newcommand{\emspace}{\hspace{1em}}
+
+\newcounter{countaufg}
+
+\newenvironment{exercise}[1]{\addtocounter{countaufg}{1}%
+      \bigskip%
+      \subsection*{Exercise \arabic{countaufg} - %\series{m}
+	   \selectfont #1%
+	 \makeatother}%
+      \bigskip%
+      }      
+
+\newenvironment{optexercise}[1]{\addtocounter{countaufg}{1}%
+      \bigskip%
+      \subsection*{Exercise \arabic{countaufg} (optional) - %\series{m}
+	   \selectfont #1%
+	 \makeatother}%
+      \bigskip%
+      }%
+
+\newcommand\hint[1]{\emph{Hint :} #1}
+\newcommand\note[1]{\emph{Note :} #1}
+
+\newcommand\serieheader[6]{
+\thispagestyle{empty}%
+\begin{flushleft}
+\includegraphics[width=0.4\textwidth]{usi_inf}
+\end{flushleft}
+  \noindent%
+  {\large\ignorespaces{\textbf{#1}}\hspace{\fill}\ignorespaces{ \textbf{#2}}}\\ \\%
+  {\large\ignorespaces #3 \hspace{\fill}\ignorespaces #4}\\
+  {\large\ignorespaces \empty{}\hspace{\fill}\ignorespaces \duedate}\\
+  \noindent%
+  \bigskip
+  \hrule\par\bigskip\noindent%
+  \bigskip {\ignorespaces {\Large{\textbf{#5}}}
+  \hspace{\fill}\ignorespaces \large \ifthenelse{\boolean{\isassignment}}{ }{\textbf{\Large }}}
+  \hrule\par\bigskip\noindent%  \linebreak
+ }
+
+\makeatletter
+\def\enumerateMod{\ifnum \@enumdepth >3 \@toodeep\else
+      \advance\@enumdepth \@ne
+      \edef\@enumctr{enum\romannumeral\the\@enumdepth}\list
+      {\csname label\@enumctr\endcsname}{\usecounter
+        {\@enumctr}%%%? the following differs from "enumerate"
+	\topsep0pt%
+	\partopsep0pt%
+	\itemsep0pt%
+	%%%? end(differs)
+	\def\makelabel##1{\hss\llap{##1}}}\fi}
+\let\endenumerateMod =\endlist
+\makeatother
+
+
+\usepackage{etex}
+\usepackage{type1ec}
+\usepackage[T2A]{fontenc}
+\usepackage{textcomp}
+%\usepackage[utf8]{inputenc}
+
+%%  \usepackage{polyglossia}
+%%  %\defaultfontfeatures{Scale=MatchLowercase, Mapping=tex-text}
+%%  \setmainfont[Scale=MatchLowercase, Mapping=tex-text]{Times New Roman}
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+%%  
+%%  \setdefaultlanguage{english}
+%%  \selectlanguage{english}
+
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+%%  \font\chapterfont="Times New Roman" at 16 pt
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+%%  \font\subsectionfont="Times New Roman" at 11 pt
+%%  \font\headerfont="Times New Roman" at 9 pt
+%%  \font\headerboldfont="Times New Roman Bold" at 9 pt
+%%  \font\footerboldfont="Times New Roman Bold" at 10 pt
+%%  \titleformat{\chapter}[display]{\chapterfont}
+%%  {\chaptertitlename\ \thechapter}{18pt}{\chaptertitlefont}
+%%  \titleformat{\section}{\sectionfont}{\thesection.}{0.5em}{}
+%%  \titleformat{\subsection}{\subsectionfont}{\thesubsection.}{0.5em}{}
+%%  \titleformat{\subsubsection}{\subsectionfont}{\thesubsubsection.}{0.5em}{}
+%%  \titleformat{\figure}{}{\thefigure\.}{0.5em}{}
+
+\usepackage{sectsty}
+
+%%  \font\smallfont="Times New Roman" at 9 pt
+%%  \font\chapterfont="Times New Roman" at 16 pt
+\chapterfont{\fontsize{16}{20}\selectfont}
+%%  \font\chaptertitlefont="Times New Roman" at 18 pt
+\chaptertitlefont{\fontsize{18}{22}\selectfont}
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+%%  \font\headerboldfont="Times New Roman Bold" at 9 pt
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+%%  \titleformat{\figure}{}{\thefigure\.}{0.5em}{}
+
+\lstset{
+    inputencoding=utf8,
+%    backgroundcolor=\color{white},
+    tabsize=4,
+    rulecolor=,
+    basicstyle=\scriptsize,
+    upquote=true,
+%    aboveskip={1.5\baselineskip},
+    columns=fixed,
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+    extendedchars=true,
+    breaklines=true,
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+}
+
+% Add dots after chapters / sections numbers in TOC.
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+\def\@seccntformat#1{\csname the#1\endcsname.\quad}
+\def\numberline#1{\hb@xt@\@tempdima{#1\if&#1&\else.\fi\hfil}}
+\makeatother
+
+%% Define a new 'leo' style for the package that will use a smaller font.
+\makeatletter
+\def\url@leostyle{%
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+%% Now actually use the newly defined style.
+\urlstyle{leo}

mp2/project.2.Maggioni.Claudio.tex

@@ -0,0 +1,50 @@
+\documentclass[unicode,11pt,a4paper,oneside,numbers=endperiod,openany]{scrartcl}
+
+\input{assignment.sty}
+
+
+\hyphenation{PageRank}
+\hyphenation{PageRanks}
+
+
+\begin{document}
+
+
+\setassignment
+\setduedate{Wednesday, 14 October 2020, 11:55 PM}
+
+\serieheader{Numerical Computing}{2020}{Student: FULL NAME}{Discussed with: FULL NAME}{Solution for Project 2}{}
+\newline
+
+\assignmentpolicy
+
+
+The purpose of this assignment\footnote{This document is originally 
+based on a blog from Cleve Moler, who wrote a fantastic blog post about the Lake Arrowhead graph, and John 
+Gilbert, who initially created the coauthor graph from the 1993 Householder Meeting. You can find more information 
+at \url{http://blogs.mathworks.com/cleve/2013/06/10/lake-arrowhead-coauthor-graph/}.  Most of this assignment is derived
+from this archived work.} is to learn the importance of sparse linear algebra algorithms to solve fundamental 
+questions in social network analyses.
+We will use the coauthor graph from the Householder Meeting and the social network of friendships from Zachary's karate club~\cite{karate}.
+These two graphs are one of the first examples where matrix methods were used in computational social network analyses.
+
+
+\section{The Reverse Cuthill McKee Ordering [10 points]}
+
+\section{Sparse Matrix Factorization [10 points]}
+
+\section{Degree Centrality [10 points]}
+
+\section{The Connectivity of the Coauthors [10 points]}
+
+\section{PageRank of the Coauthor Graph [10 points]}
+
+\section{Zachary's karate club: social network of friendships between 34 members [50 points]}
+
+\begin{thebibliography}{99}
+\bibitem{karate} The social network of a karate club at a US university, M.~E.~J. Newman and M. Girvan, Phys. Rev. E 69,026113 (2004)
+pp. 219-229.
+\end{thebibliography}
+
+
+\end{document}