Paul M Van Dooren - Academia.edu (original) (raw)
Papers by Paul M Van Dooren
We consider a new idea for model reduction of second order dynamical systems. It is based on a ne... more We consider a new idea for model reduction of second order dynamical systems. It is based on a new theorem which shows under which conditions one can recover the second order form of a dynamical system. This theorem adds some constraints on the projection matrices that will be used to construct the reduced model.
In this paper we show how to compute recursively an approximation of the left and right dominant ... more In this paper we show how to compute recursively an approximation of the left and right dominant singular subspaces of a given matrix. In order to perform as few as possible operations on each column of the matrix, we use a variant of the classical Gram-Schmidt algorithm to estimate this subspace. The method is shown to be particularly suited for matrices with many more rows than columns. Bounds for the accuracy of the computed subspace are provided. Moreover, the analysis of error propagation in this algorithm provides new insights in the loss of orthogonality typically observed in the classical Gram-Schmidt method.
Physical Review E, 2009
We study the propagation of information in social networks. To do so, we focus on a cascade model... more We study the propagation of information in social networks. To do so, we focus on a cascade model where nodes are infected with probability p1 after their first contact with the information and with probability p2 at all subsequent contacts. The diffusion starts from one random node and leads to a cascade of infection. It is shown that first and subsequent trials play different roles in the propagation and that the size of the cascade depends in a non-trivial way on p1, p2 and on the network structure. Second trials are shown to amplify the propagation in dense parts of the network while first trials are dominant for the exploration of new parts of the network and launching new seeds of infection.
Numerische Mathematik, 2010
In this paper an implicit (double) shifted QR-method for computing the eigenvalues of companion a... more In this paper an implicit (double) shifted QR-method for computing the eigenvalues of companion and fellow matrices will be presented. Companion and fellow matrices are Hessenberg matrices, that can be decomposed into the sum of a unitary and a rank 1 matrix. The Hessenberg, the unitary as well as the rank 1 structures are preserved under a step of the QR-method. This makes these matrices suitable for the design of a fast QR-method.
Two distinctive features characterize the way in which sensations including pain, are evoked by h... more Two distinctive features characterize the way in which sensations including pain, are evoked by heat: (1) a thermal stimulus
is always progressive; (2) a painful stimulus activates two different types of nociceptors, connected to peripheral afferent
fibers with medium and slow conduction velocities, namely Ad- and C-fibers. In the light of a recent study in the rat, our
objective was to develop an experimental paradigm in humans, based on the joint analysis of the stimulus and the response
of the subject, to measure the thermal thresholds and latencies of pain elicited by Ad- and C-fibers. For comparison, the
same approach was applied to the sensation of warmth elicited by thermoreceptors. A CO2 laser beam raised the
temperature of the skin filmed by an infrared camera. The subject stopped the beam when he/she perceived pain. The
thermal images were analyzed to provide four variables: true thresholds and latencies of pain triggered by heat via Ad- and
C-fibers. The psychophysical threshold of pain triggered by Ad-fibers was always higher (2.5–3uC) than that triggered by Cfibers.
The initial skin temperature did not influence these thresholds. The mean conduction velocities of the corresponding
fibers were 13 and 0.8 m/s, respectively. The triggering of pain either by C- or by Ad-fibers was piloted by several factors
including the low/high rate of stimulation, the low/high base temperature of the skin, the short/long peripheral nerve path
and some pharmacological manipulations (e.g. Capsaicin). Warming a large skin area increased the pain thresholds.
Considering the warmth detection gave a different picture: the threshold was strongly influenced by the initial skin
temperature and the subjects detected an average variation of 2.7uC, whatever the initial temperature. This is the first time
that thresholds and latencies for pain elicited by both Ad- and C-fibers from a given body region have been measured in the
same experimental run. Such an approach illustrates the role of nociception as a ‘‘double level’’ and ‘‘double release’’ alarm
system based on level detectors. By contrast, warmth detection was found to be based on difference detectors. It is
hypothesized that pain results from a CNS build-up process resulting from population coding and strongly influenced by
the background temperatures surrounding at large the stimulation site. We propose an alternative solution to the
conventional methods that only measure a single ‘‘threshold of pain’’, without knowing which of the two systems is
involved.
We consider a new idea for model reduction of second order dynamical systems. It is based on a ne... more We consider a new idea for model reduction of second order dynamical systems. It is based on a new theorem which shows under which conditions one can recover the second order form of a dynamical system. This theorem adds some constraints on the projection matrices that will be used to construct the reduced model.
In this paper we show how to compute recursively an approximation of the left and right dominant ... more In this paper we show how to compute recursively an approximation of the left and right dominant singular subspaces of a given matrix. In order to perform as few as possible operations on each column of the matrix, we use a variant of the classical Gram-Schmidt algorithm to estimate this subspace. The method is shown to be particularly suited for matrices with many more rows than columns. Bounds for the accuracy of the computed subspace are provided. Moreover, the analysis of error propagation in this algorithm provides new insights in the loss of orthogonality typically observed in the classical Gram-Schmidt method.
Physical Review E, 2009
We study the propagation of information in social networks. To do so, we focus on a cascade model... more We study the propagation of information in social networks. To do so, we focus on a cascade model where nodes are infected with probability p1 after their first contact with the information and with probability p2 at all subsequent contacts. The diffusion starts from one random node and leads to a cascade of infection. It is shown that first and subsequent trials play different roles in the propagation and that the size of the cascade depends in a non-trivial way on p1, p2 and on the network structure. Second trials are shown to amplify the propagation in dense parts of the network while first trials are dominant for the exploration of new parts of the network and launching new seeds of infection.
Numerische Mathematik, 2010
In this paper an implicit (double) shifted QR-method for computing the eigenvalues of companion a... more In this paper an implicit (double) shifted QR-method for computing the eigenvalues of companion and fellow matrices will be presented. Companion and fellow matrices are Hessenberg matrices, that can be decomposed into the sum of a unitary and a rank 1 matrix. The Hessenberg, the unitary as well as the rank 1 structures are preserved under a step of the QR-method. This makes these matrices suitable for the design of a fast QR-method.
Two distinctive features characterize the way in which sensations including pain, are evoked by h... more Two distinctive features characterize the way in which sensations including pain, are evoked by heat: (1) a thermal stimulus
is always progressive; (2) a painful stimulus activates two different types of nociceptors, connected to peripheral afferent
fibers with medium and slow conduction velocities, namely Ad- and C-fibers. In the light of a recent study in the rat, our
objective was to develop an experimental paradigm in humans, based on the joint analysis of the stimulus and the response
of the subject, to measure the thermal thresholds and latencies of pain elicited by Ad- and C-fibers. For comparison, the
same approach was applied to the sensation of warmth elicited by thermoreceptors. A CO2 laser beam raised the
temperature of the skin filmed by an infrared camera. The subject stopped the beam when he/she perceived pain. The
thermal images were analyzed to provide four variables: true thresholds and latencies of pain triggered by heat via Ad- and
C-fibers. The psychophysical threshold of pain triggered by Ad-fibers was always higher (2.5–3uC) than that triggered by Cfibers.
The initial skin temperature did not influence these thresholds. The mean conduction velocities of the corresponding
fibers were 13 and 0.8 m/s, respectively. The triggering of pain either by C- or by Ad-fibers was piloted by several factors
including the low/high rate of stimulation, the low/high base temperature of the skin, the short/long peripheral nerve path
and some pharmacological manipulations (e.g. Capsaicin). Warming a large skin area increased the pain thresholds.
Considering the warmth detection gave a different picture: the threshold was strongly influenced by the initial skin
temperature and the subjects detected an average variation of 2.7uC, whatever the initial temperature. This is the first time
that thresholds and latencies for pain elicited by both Ad- and C-fibers from a given body region have been measured in the
same experimental run. Such an approach illustrates the role of nociception as a ‘‘double level’’ and ‘‘double release’’ alarm
system based on level detectors. By contrast, warmth detection was found to be based on difference detectors. It is
hypothesized that pain results from a CNS build-up process resulting from population coding and strongly influenced by
the background temperatures surrounding at large the stimulation site. We propose an alternative solution to the
conventional methods that only measure a single ‘‘threshold of pain’’, without knowing which of the two systems is
involved.