Applied Mathematics

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The Applied Mathematics group gathers 10 professors and about twenty researchers who are working on several subfields.

Principal Investigators :

Pierre-Antoine AbsilVincent Blondel, Jean-Charles Delvenne, François Glineur, Raphaël Jungers, Roland Keunings, Yurii Nesterov, Paul Van Dooren, Jean-Pierre Tignol, Vincent Wertz

Research Lab :

INMA (Mathematical Engineering research division)

Research Areas :

Research in the algebra team focuses on various structures whose automorphism groups are linear algebraic groups, notably quadratic forms and algebras over arbitrary fields. These structures are studied using methods from number theory and algebraic geometry, such as valuation theory and Galois cohomology. The current projects aim at developing new cohomological invariants and a noncommutative valuation theory for central simple algebras with involution. This activity is run in cooperation with the group theory team of the IRMP.

Balance laws are hyperbolic partial differential equations that are commonly used to express the fundamental dynamics of open conservative systems. Many physical systems having an engineering interest are described by systems of one-dimensional hyperbolic balance laws. Typical examples are for instance the telegrapher equations for electrical lines, the shallow water (Saint-Venant) equations for open channels, the Euler equations for gas flow in pipelines or the Aw-Rascle equations for road traffic. In this research, our concern is to analyse the exponential stability (in the sense of Lyapunov) of the steady-states of such systems.

This research relies on the use of non-negative convex algebra for solving underdetermined linear systems of equations under positive constraints. Such problems arise in various domains of Systems Biology. We are particularly concerned with the decomposition of complex metabolic networks into elementary pathways and with the metabolic flux analysis which aims at computing the entire intracellular flux distribution from a limited number of flux measurements.

The group works on numerical methods for rational approximation, linear algebra and optimization with applications in systems and control, economy, biology and medicine. In approximation theory we look at approximation problems in the complex plane (orthogonal polynomials, quadrature formulas) and at the solution of functional equations, with applications in science, technology and economy. In linear algebra we study the model reduction problem via interpolation and projection of state-space models. We also look at optimal Hankel-norm approximations and their formulation via convex optimization techniques.  In optimization, we are looking for general schemes with provable global complexity estimates. This extends onto the methods for solving systems of nonlinear equations and optimization on nonlinear manifolds. These techniques are applied to problems in signals and systems.

We study several types of matrix factorization techniques, in particular variants where nonnegative factors are required. We focus on both algorithmic (mehods and computational complexity) and applicative (machine learning, graph problems, polyhedral combinatorics) points of view.

The complex rheological behaviour of non-Newtonian liquids is dictated by the flow induced evolution of their internal microstructure. For example, in homogeneous polymeric fluids, the relevant microstructure is the conformation of the macromolecules. Each macroscopic fluid element contains a large number of polymers with a statistical distribution of conformations. During flow, the polymer conformations evolve along the fluid trajectories. Also, the macroscopic stress carried by each fluid element is itself governed by the distribution of conformations within that element. One thus faces a highly non-linear coupling between rheological behaviour, flow-induced evolution of the microstructure, and flow conditions. The fundamental scientific challenges in rheology and non-Newtonian fluid mechanics are indeed to fully comprehend the nature of this non-linear coupling and to predict its consequences in flow problems of interest. We currently focus on the development of molecular models of kinetic theory and methods of computational rheology.

Most recent publications

Below are listed the 10 most recent journal articles and conference papers produced in this research area. You also can access all publications by following this link : see all applied mathematics publications.

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<type 'exceptions.IOError'>
Python 2.7.9: /usr/bin/python
Mon May 20 13:27:08 2019

A problem occurred in a Python script. Here is the sequence of function calls leading up to the error, in the order they occurred.

 /var/www/sites/tools/export/export.py in ()
    104         t.encode("utf-8"))
    105 
=>  106     tmp = urllib.urlopen(q)
    107     
    108     resp = eval( urllib.urlopen(q).read() )
tmp undefined, urllib = <module 'urllib' from '/usr/lib/python2.7/urllib.pyc'>, urllib.urlopen = <function urlopen>, q = 'https://dial.uclouvain.be/solr6/repository/selec...de%20p%C3%A9riodique%20%28Journal%20article%29%22'
 /usr/lib/python2.7/urllib.py in urlopen(url='https://dial.uclouvain.be/solr6/repository/selec...de%20p%C3%A9riodique%20%28Journal%20article%29%22', data=None, proxies=None, context=None)
     85         opener = _urlopener
     86     if data is None:
=>   87         return opener.open(url)
     88     else:
     89         return opener.open(url, data)
opener = <urllib.FancyURLopener instance>, opener.open = <bound method FancyURLopener.open of <urllib.FancyURLopener instance>>, url = 'https://dial.uclouvain.be/solr6/repository/selec...de%20p%C3%A9riodique%20%28Journal%20article%29%22'
 /usr/lib/python2.7/urllib.py in open(self=<urllib.FancyURLopener instance>, fullurl='https://dial.uclouvain.be/solr6/repository/selec...de%20p%C3%A9riodique%20%28Journal%20article%29%22', data=None)
    211         try:
    212             if data is None:
=>  213                 return getattr(self, name)(url)
    214             else:
    215                 return getattr(self, name)(url, data)
builtin getattr = <built-in function getattr>, self = <urllib.FancyURLopener instance>, name = 'open_https', url = '//dial.uclouvain.be/solr6/repository/select?&sta...de%20p%C3%A9riodique%20%28Journal%20article%29%22'
 /usr/lib/python2.7/urllib.py in open_https(self=<urllib.FancyURLopener instance>, url='//dial.uclouvain.be/solr6/repository/select?&sta...de%20p%C3%A9riodique%20%28Journal%20article%29%22', data=None)
    441             if realhost: h.putheader('Host', realhost)
    442             for args in self.addheaders: h.putheader(*args)
=>  443             h.endheaders(data)
    444             errcode, errmsg, headers = h.getreply()
    445             fp = h.getfile()
h = <httplib.HTTPS instance>, h.endheaders = <bound method HTTPSConnection.endheaders of <httplib.HTTPSConnection instance>>, data = None
 /usr/lib/python2.7/httplib.py in endheaders(self=<httplib.HTTPSConnection instance>, message_body=None)
   1033         else:
   1034             raise CannotSendHeader()
=> 1035         self._send_output(message_body)
   1036 
   1037     def request(self, method, url, body=None, headers={}):
self = <httplib.HTTPSConnection instance>, self._send_output = <bound method HTTPSConnection._send_output of <httplib.HTTPSConnection instance>>, message_body = None
 /usr/lib/python2.7/httplib.py in _send_output(self=<httplib.HTTPSConnection instance>, message_body=None)
    877             msg += message_body
    878             message_body = None
=>  879         self.send(msg)
    880         if message_body is not None:
    881             #message_body was not a string (i.e. it is a file) and
self = <httplib.HTTPSConnection instance>, self.send = <bound method HTTPSConnection.send of <httplib.HTTPSConnection instance>>, msg = 'GET /solr6/repository/select?&start=0&rows=99999....uclouvain.be\r\nUser-Agent: Python-urllib/1.17\r\n\r\n'
 /usr/lib/python2.7/httplib.py in send(self=<httplib.HTTPSConnection instance>, data='GET /solr6/repository/select?&start=0&rows=99999....uclouvain.be\r\nUser-Agent: Python-urllib/1.17\r\n\r\n')
    839         if self.sock is None:
    840             if self.auto_open:
=>  841                 self.connect()
    842             else:
    843                 raise NotConnected()
self = <httplib.HTTPSConnection instance>, self.connect = <bound method HTTPSConnection.connect of <httplib.HTTPSConnection instance>>
 /usr/lib/python2.7/httplib.py in connect(self=<httplib.HTTPSConnection instance>)
   1248 
   1249             self.sock = self._context.wrap_socket(self.sock,
=> 1250                                                   server_hostname=server_hostname)
   1251 
   1252     __all__.append("HTTPSConnection")
server_hostname = 'dial.uclouvain.be'
 /usr/lib/python2.7/ssl.py in wrap_socket(self=<ssl.SSLContext object>, sock=<socket._socketobject object>, server_side=False, do_handshake_on_connect=True, suppress_ragged_eofs=True, server_hostname='dial.uclouvain.be')
    348                          suppress_ragged_eofs=suppress_ragged_eofs,
    349                          server_hostname=server_hostname,
=>  350                          _context=self)
    351 
    352     def set_npn_protocols(self, npn_protocols):
_context undefined, self = <ssl.SSLContext object>
 /usr/lib/python2.7/ssl.py in __init__(self=<ssl.SSLSocket object>, sock=<socket._socketobject object>, keyfile=None, certfile=None, server_side=False, cert_reqs=0, ssl_version=2, ca_certs=None, do_handshake_on_connect=True, family=2, type=1, proto=0, fileno=None, suppress_ragged_eofs=True, npn_protocols=None, ciphers=None, server_hostname='dial.uclouvain.be', _context=<ssl.SSLContext object>)
    564                         # non-blocking
    565                         raise ValueError("do_handshake_on_connect should not be specified for non-blocking sockets")
=>  566                     self.do_handshake()
    567 
    568             except (OSError, ValueError):
self = <ssl.SSLSocket object>, self.do_handshake = <bound method SSLSocket.do_handshake of <ssl.SSLSocket object>>
 /usr/lib/python2.7/ssl.py in do_handshake(self=<ssl.SSLSocket object>, block=False)
    786             if timeout == 0.0 and block:
    787                 self.settimeout(None)
=>  788             self._sslobj.do_handshake()
    789         finally:
    790             self.settimeout(timeout)
self = <ssl.SSLSocket object>, self._sslobj = <_ssl._SSLSocket object>, self._sslobj.do_handshake = <built-in method do_handshake of _ssl._SSLSocket object>

<type 'exceptions.IOError'>: [Errno socket error] [SSL: CERTIFICATE_VERIFY_FAILED] certificate verify failed (_ssl.c:581)
      args = ('socket error', SSLError(1, u'[SSL: CERTIFICATE_VERIFY_FAILED] certificate verify failed (_ssl.c:581)'))
      errno = 'socket error'
      filename = None
      message = ''
      strerror = SSLError(1, u'[SSL: CERTIFICATE_VERIFY_FAILED] certificate verify failed (_ssl.c:581)')

--> -->
 
 
<type 'exceptions.IOError'>
Python 2.7.9: /usr/bin/python
Mon May 20 13:27:08 2019

A problem occurred in a Python script. Here is the sequence of function calls leading up to the error, in the order they occurred.

 /var/www/sites/tools/export/export.py in ()
    106     tmp = urllib.urlopen(q)
    107     
=>  108     resp = eval( urllib.urlopen(q).read() )
    109     if ( resp['response']['numFound'] > 0 ):
    110         #print '<h/>%s (%d)</h2>' % (pubType[t].encode("utf-8"), \
resp undefined, builtin eval = <built-in function eval>, urllib = <module 'urllib' from '/usr/lib/python2.7/urllib.pyc'>, urllib.urlopen = <function urlopen>, q = 'https://dial.uclouvain.be/solr6/repository/selec...de%20p%C3%A9riodique%20%28Journal%20article%29%22', ).read undefined
 /usr/lib/python2.7/urllib.py in urlopen(url='https://dial.uclouvain.be/solr6/repository/selec...de%20p%C3%A9riodique%20%28Journal%20article%29%22', data=None, proxies=None, context=None)
     85         opener = _urlopener
     86     if data is None:
=>   87         return opener.open(url)
     88     else:
     89         return opener.open(url, data)
opener = <urllib.FancyURLopener instance>, opener.open = <bound method FancyURLopener.open of <urllib.FancyURLopener instance>>, url = 'https://dial.uclouvain.be/solr6/repository/selec...de%20p%C3%A9riodique%20%28Journal%20article%29%22'
 /usr/lib/python2.7/urllib.py in open(self=<urllib.FancyURLopener instance>, fullurl='https://dial.uclouvain.be/solr6/repository/selec...de%20p%C3%A9riodique%20%28Journal%20article%29%22', data=None)
    211         try:
    212             if data is None:
=>  213                 return getattr(self, name)(url)
    214             else:
    215                 return getattr(self, name)(url, data)
builtin getattr = <built-in function getattr>, self = <urllib.FancyURLopener instance>, name = 'open_https', url = '//dial.uclouvain.be/solr6/repository/select?&sta...de%20p%C3%A9riodique%20%28Journal%20article%29%22'
 /usr/lib/python2.7/urllib.py in open_https(self=<urllib.FancyURLopener instance>, url='//dial.uclouvain.be/solr6/repository/select?&sta...de%20p%C3%A9riodique%20%28Journal%20article%29%22', data=None)
    441             if realhost: h.putheader('Host', realhost)
    442             for args in self.addheaders: h.putheader(*args)
=>  443             h.endheaders(data)
    444             errcode, errmsg, headers = h.getreply()
    445             fp = h.getfile()
h = <httplib.HTTPS instance>, h.endheaders = <bound method HTTPSConnection.endheaders of <httplib.HTTPSConnection instance>>, data = None
 /usr/lib/python2.7/httplib.py in endheaders(self=<httplib.HTTPSConnection instance>, message_body=None)
   1033         else:
   1034             raise CannotSendHeader()
=> 1035         self._send_output(message_body)
   1036 
   1037     def request(self, method, url, body=None, headers={}):
self = <httplib.HTTPSConnection instance>, self._send_output = <bound method HTTPSConnection._send_output of <httplib.HTTPSConnection instance>>, message_body = None
 /usr/lib/python2.7/httplib.py in _send_output(self=<httplib.HTTPSConnection instance>, message_body=None)
    877             msg += message_body
    878             message_body = None
=>  879         self.send(msg)
    880         if message_body is not None:
    881             #message_body was not a string (i.e. it is a file) and
self = <httplib.HTTPSConnection instance>, self.send = <bound method HTTPSConnection.send of <httplib.HTTPSConnection instance>>, msg = 'GET /solr6/repository/select?&start=0&rows=99999....uclouvain.be\r\nUser-Agent: Python-urllib/1.17\r\n\r\n'
 /usr/lib/python2.7/httplib.py in send(self=<httplib.HTTPSConnection instance>, data='GET /solr6/repository/select?&start=0&rows=99999....uclouvain.be\r\nUser-Agent: Python-urllib/1.17\r\n\r\n')
    839         if self.sock is None:
    840             if self.auto_open:
=>  841                 self.connect()
    842             else:
    843                 raise NotConnected()
self = <httplib.HTTPSConnection instance>, self.connect = <bound method HTTPSConnection.connect of <httplib.HTTPSConnection instance>>
 /usr/lib/python2.7/httplib.py in connect(self=<httplib.HTTPSConnection instance>)
   1248 
   1249             self.sock = self._context.wrap_socket(self.sock,
=> 1250                                                   server_hostname=server_hostname)
   1251 
   1252     __all__.append("HTTPSConnection")
server_hostname = 'dial.uclouvain.be'
 /usr/lib/python2.7/ssl.py in wrap_socket(self=<ssl.SSLContext object>, sock=<socket._socketobject object>, server_side=False, do_handshake_on_connect=True, suppress_ragged_eofs=True, server_hostname='dial.uclouvain.be')
    348                          suppress_ragged_eofs=suppress_ragged_eofs,
    349                          server_hostname=server_hostname,
=>  350                          _context=self)
    351 
    352     def set_npn_protocols(self, npn_protocols):
_context undefined, self = <ssl.SSLContext object>
 /usr/lib/python2.7/ssl.py in __init__(self=<ssl.SSLSocket object>, sock=<socket._socketobject object>, keyfile=None, certfile=None, server_side=False, cert_reqs=0, ssl_version=2, ca_certs=None, do_handshake_on_connect=True, family=2, type=1, proto=0, fileno=None, suppress_ragged_eofs=True, npn_protocols=None, ciphers=None, server_hostname='dial.uclouvain.be', _context=<ssl.SSLContext object>)
    564                         # non-blocking
    565                         raise ValueError("do_handshake_on_connect should not be specified for non-blocking sockets")
=>  566                     self.do_handshake()
    567 
    568             except (OSError, ValueError):
self = <ssl.SSLSocket object>, self.do_handshake = <bound method SSLSocket.do_handshake of <ssl.SSLSocket object>>
 /usr/lib/python2.7/ssl.py in do_handshake(self=<ssl.SSLSocket object>, block=False)
    786             if timeout == 0.0 and block:
    787                 self.settimeout(None)
=>  788             self._sslobj.do_handshake()
    789         finally:
    790             self.settimeout(timeout)
self = <ssl.SSLSocket object>, self._sslobj = <_ssl._SSLSocket object>, self._sslobj.do_handshake = <built-in method do_handshake of _ssl._SSLSocket object>

<type 'exceptions.IOError'>: [Errno socket error] [SSL: CERTIFICATE_VERIFY_FAILED] certificate verify failed (_ssl.c:581)
      args = ('socket error', SSLError(1, u'[SSL: CERTIFICATE_VERIFY_FAILED] certificate verify failed (_ssl.c:581)'))
      errno = 'socket error'
      filename = None
      message = ''
      strerror = SSLError(1, u'[SSL: CERTIFICATE_VERIFY_FAILED] certificate verify failed (_ssl.c:581)')