Sensory systems adapt, i.e., they adjust their sensitivity to external stimuli according to the ambient level. In this paper we show that single cell electrophysiological responses of vertebrate olfactory receptors and of photoreceptors to different input protocols exhibit several common features related to adaptation, and that these features can be used to investigate the dynamical structure of the feedback regulation responsible for the adaptation. In particular, we point out that two different forms of adaptation can be observed, in response to steps and to pairs of pulses. These two forms of adaptation appear to be in a dynamical trade-off: the more adaptation to a step is close to perfect, the slower is the recovery in adaptation to pulse pairs and viceversa. Neither of the two forms is explained by the dynamical models currently used to describe adaptation, such as the integral feedback model.

%B Nature. Scientific Reports 3, Article number: 1251, Published : 13 February 2013 %I SISSA %G en %1 6453 %2 Mathematics %4 1 %$ Submitted by Claudio Altafini (altafini@sissa.it) on 2013-02-27T14:00:21Z\nNo. of bitstreams: 0 %R 10.1038/srep01251 %0 Journal Article %J PloS one. Volume 8, Issue 7, July 2013 : e68078 %D 2013 %T Early phase of plasticity-related gene regulation and SRF dependent transcription in the hippocampus %A Giovanni Iacono %A Claudio Altafini %A Vincent Torre %X Hippocampal organotypic cultures are a highly reliable in vitro model for studying neuroplasticity: in this paper, we analyze the early phase of the transcriptional response induced by a 20 µM gabazine treatment (GabT), a GABA-Ar antagonist, by using Affymetrix oligonucleotide microarray, RT-PCR based time-course and chromatin-immuno-precipitation. The transcriptome profiling revealed that the pool of genes up-regulated by GabT, besides being strongly related to the regulation of growth and synaptic transmission, is also endowed with neuro-protective and pro-survival properties. By using RT-PCR, we quantified a time-course of the transient expression for 33 of the highest up-regulated genes, with an average sampling rate of 10 minutes and covering the time interval [10:90] minutes. The cluster analysis of the time-course disclosed the existence of three different dynamical patterns, one of which proved, in a statistical analysis based on results from previous works, to be significantly related with SRF-dependent regulation (p-value<0.05). The chromatin immunoprecipitation (chip) assay confirmed the rich presence of working CArG boxes in the genes belonging to the latter dynamical pattern and therefore validated the statistical analysis. Furthermore, an in silico analysis of the promoters revealed the presence of additional conserved CArG boxes upstream of the genes Nr4a1 and Rgs2. The chip assay confirmed a significant SRF signal in the Nr4a1 CArG box but not in the Rgs2 CArG box. %B PloS one. Volume 8, Issue 7, July 2013 : e68078 %I Public Library of Science %G en %U http://hdl.handle.net/1963/7287 %1 7332 %2 Neuroscience %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2014-03-14T11:26:18Z No. of bitstreams: 1 journal.pone.0068078.pdf: 1188661 bytes, checksum: 29e83864b33fd1a072fe4ab4da6fcc17 (MD5) %R 10.1371/journal.pone.0068078 %0 Journal Article %J IEEE Transactions on Automatic Control. Volume 58, Issue 1, 2013, Article number6228517, Pages 74-85 %D 2013 %T Stabilization of Stochastic Quantum Dynamics via Open and Closed Loop Control %A Claudio Altafini %A Francesco Ticozzi %A K. Nishio %X In this paper, we investigate parametrization-free solutions of the problem of quantum pure state preparation and subspace stabilization by means of Hamiltonian control, continuous measurement, and quantum feedback, in the presence of a Markovian environment. In particular, we show that whenever suitable dissipative effects are induced either by the unmonitored environment, or by non-Hermitian measurements, there is no need for feedback, as open-loop time-invariant control is sufficient to achieve stabilization of the target set in probability. Constructive necessary and sufficient conditions on the form of the control Hamiltonian can be provided in this case. When time-invariant control is not sufficient, state stabilization can be attained by the addition of filtering-based feedback control %B IEEE Transactions on Automatic Control. Volume 58, Issue 1, 2013, Article number6228517, Pages 74-85 %G en %U http://hdl.handle.net/1963/6503 %1 6448 %2 Mathematics %4 1 %$ Approved for entry into archive by Lucio Lubiana (lubiana@sissa.it) on 2013-02-27T15:06:12Z (GMT) No. of bitstreams: 0 %R 10.1109/TAC.2012.2206713 %0 Journal Article %J Bioinformatics (Oxford, England). 2012 Jan; 28(1):76-83 %D 2012 %T Decompositions of large-scale biological systems based on dynamical properties %A Nicola Soranzo %A Fahimeh Ramezani %A Giovanni Iacono %A Claudio Altafini %X MOTIVATION: Given a large-scale biological network represented as an influence graph, in this article we investigate possible decompositions of the network aimed at highlighting specific dynamical properties.\\r\\nRESULTS: The first decomposition we study consists in finding a maximal directed acyclic subgraph of the network, which dynamically corresponds to searching for a maximal open-loop subsystem of the given system. Another dynamical property investigated is strong monotonicity. We propose two methods to deal with this property, both aimed at decomposing the system into strongly monotone subsystems, but with different structural characteristics: one method tends to produce a single large strongly monotone component, while the other typically generates a set of smaller disjoint strongly monotone subsystems.\\r\\nAVAILABILITY: Original heuristics for the methods investigated are described in the article. %B Bioinformatics (Oxford, England). 2012 Jan; 28(1):76-83 %I Oxford University Press %G en %U http://hdl.handle.net/1963/5226 %1 5049 %2 Physics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2012-01-16T15:13:23Z\\nNo. of bitstreams: 1\\nSoIaRaAl10.pdf: 185656 bytes, checksum: df5605453eb314d79ada4355b16ad3cd (MD5) %R 10.1093/bioinformatics/btr620 %0 Journal Article %J Nucleic Acids Research, Volume 40, Issue 15, August 2012, Pages 7132-7149 %D 2012 %T Detection of transcriptional triggers in the dynamics of microbial growth: application to the respiratory-versatile bacterium Shewanella oneidensis %A Q Beg %A Mattia Zampieri %A N Klitgord %A S Collins %A M Serres %A Daniel Segrè %A Claudio Altafini %X The capacity of microorganisms to respond to variable external conditions requires a coordination of environment-sensing mechanisms and decisionmaking regulatory circuits. Here, we seek to understand the interplay between these two processes by combining high-throughput measurement of time-dependent mRNA profiles with a novel computational approach that searches for key genetic triggers of transcriptional changes. Our approach helped us understand the regulatory strategies of a respiratorily versatile bacterium with promising bioenergy and bioremediation applications, Shewanella oneidensis, in minimal and rich media. By comparing expression profiles across these two conditions, we unveiled components of the transcriptional program that depend mainly on the growth phase. Conversely, by integrating our time-dependent data with a previously available large compendium of static perturbation responses, we identified transcriptional changes that cannot be explained solely by internal network dynamics, but are rather triggered by specific genes acting as key mediators of an environment-dependent response. These transcriptional triggers include known and novel regulators that respond to carbon, nitrogen and oxygen limitation. Our analysis suggests a sequence of physiological responses, including a coupling between nitrogen depletion and glycogen storage, partially recapitulated through dynamic flux balance analysis, and experimentally confirmed by metabolite measurements. Our approach is broadly applicable to other systems %B Nucleic Acids Research, Volume 40, Issue 15, August 2012, Pages 7132-7149 %I SISSA %G en %U http://hdl.handle.net/1963/6506 %1 6452 %2 Mathematics %4 1 %$ Approved for entry into archive by Lucio Lubiana (lubiana@sissa.it) on 2013-02-27T15:39:07Z (GMT) No. of bitstreams: 0 %R 10.1093/nar/gks467 %0 Journal Article %J Biophysical Journal. Volume 102, Issue 12, 20 June 2012, Pages 2677-2686 %D 2012 %T A dynamical feedback model for adaptation in the olfactory transduction pathway %A Giovanna De Palo %A Anna Boccaccio %A Andrew Miri %A Anna Menini %A Claudio Altafini %X Olfactory transduction exhibits two distinct types of adaptation, which we denote multipulse and step adaptation. In terms of measured transduction current, multipulse adaptation appears as a decrease in the amplitude of the second of two consecutive responses when the olfactory neuron is stimulated with two brief pulses. Step adaptation occurs in response to a sustained steplike stimulation and is characterized by a return to a steady-state current amplitude close to the prestimulus value, after a transient peak. In this article, we formulate a dynamical model of the olfactory transduction pathway, which includes the kinetics of the CNG channels, the concentration of Ca ions flowing through them, and the Ca-complexes responsible for the regulation. Based on this model, a common dynamical explanation for the two types of adaptation is suggested. We show that both forms of adaptation can be well described using different time constants for the kinetics of Ca ions (faster) and the kinetics of the feedback mechanisms (slower). The model is validated on experimental data collected in voltage-clamp conditions using different techniques and animal species. %B Biophysical Journal. Volume 102, Issue 12, 20 June 2012, Pages 2677-2686 %I Biophysical Society, Elsevier %G en %U http://hdl.handle.net/1963/7019 %1 7012 %2 Neuroscience %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2013-08-12T10:21:18Z No. of bitstreams: 1 1-s2.0-S0006349512005140-main.pdf: 607871 bytes, checksum: b57c678e05477bb1551bc379bc674a88 (MD5) %R 10.1016/j.bpj.2012.04.040 %0 Journal Article %J PloS one. 2012 ; 7(6):e38135 %D 2012 %T Dynamics of opinion forming in structurally balanced social networks %A Claudio Altafini %X A structurally balanced social network is a social community that splits into two antagonistic factions (typical example being a two-party political system). The process of opinion forming on such a community is most often highly predictable, with polarized opinions reflecting the bipartition of the network. The aim of this paper is to suggest a class of dynamical systems, called monotone systems, as natural models for the dynamics of opinion forming on structurally balanced social networks. The high predictability of the outcome of a decision process is explained in terms of the order-preserving character of the solutions of this class of dynamical systems. If we represent a social network as a signed graph in which individuals are the nodes and the signs of the edges represent friendly or hostile relationships, then the property of structural balance corresponds to the social community being splittable into two antagonistic factions, each containing only friends. %B PloS one. 2012 ; 7(6):e38135 %I PLoS %G en %U http://hdl.handle.net/1963/6051 %1 5942 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2012-08-01T07:37:37Z\\nNo. of bitstreams: 1\\njournal.pone.0038135.pdf: 460419 bytes, checksum: 94138ada3b8a6340ae8f7b5d3ec08c4e (MD5) %R 10.1371/journal.pone.0038135 %0 Journal Article %J Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. Volume 86, Issue 3, 26 September 2012, Article number036116 %D 2012 %T Exploring the low-energy landscape of large-scale signed social networks %A Giuseppe Facchetti %A Giovanni Iacono %A Claudio Altafini %X Analogously to a spin glass, a large-scale signed social network is characterized by the presence of disorder, expressed in this context (and in the social network literature) by the concept of structural balance. If, as we have recently shown, the signed social networks currently available have a limited amount of true disorder (or frustration), it is also interesting to investigate how this frustration is organized, by exploring the landscape of near-optimal structural balance. What we obtain in this paper is that while one of the networks analyzed shows a unique valley of minima, and a funneled landscape that gradually and smoothly worsens as we move away from the optimum, another network shows instead several distinct valleys of optimal or near-optimal structural balance, separated by energy barriers determined by internally balanced subcommunities of users, a phenomenon similar to the replica-symmetry breaking of spin glasses. Multiple, essentially isoenergetic, arrangements of these communities are possible. Passing from one valley to another requires one to destroy the internal arrangement of these balanced subcommunities and then to reform it again. It is essentially this process of breaking the internal balance of the subcommunities which gives rise to the energy barriers. %B Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. Volume 86, Issue 3, 26 September 2012, Article number036116 %I SISSA %G en %U http://hdl.handle.net/1963/6504 %1 6451 %2 Mathematics %4 1 %$ Approved for entry into archive by Lucio Lubiana (lubiana@sissa.it) on 2013-02-27T15:27:42Z (GMT) No. of bitstreams: 0 %R 10.1103/PhysRevE.86.036116 %0 Journal Article %J IEEE Transactions on Automatic Control. Volume 57, Issue 8, 2012, Article number6189035, Pages 1898-1917 %D 2012 %T Modeling and control of quantum systems: An introduction %A Claudio Altafini %A Francesco Ticozzi %X The scope of this work is to provide a self-contained introduction to a selection of basic theoretical aspects in the modeling and control of quantum mechanical systems, as well as a brief survey on the main approaches to control synthesis. While part of the existing theory, especially in the open-loop setting, stems directly from classical control theory (most notably geometric control and optimal control), a number of tools specifically tailored for quantum systems have been developed since the 1980s, in order to take into account their distinctive features: the probabilistic nature of atomic-scale physical systems, the effect of dissipation and the irreversible character of the measurements have all proved to be critical in feedback-design problems. The relevant dynamical models for both closed and open quantum systems are presented, along with the main results on their controllability and stability. A brief review of several currently available control design methods is meant to provide the interested reader with a roadmap for further studies %B IEEE Transactions on Automatic Control. Volume 57, Issue 8, 2012, Article number6189035, Pages 1898-1917 %I Institute of Electrical and Electronics Engineers %G en %U http://hdl.handle.net/1963/6505 %1 6449 %2 Mathematics %4 1 %$ Approved for entry into archive by Lucio Lubiana (lubiana@sissa.it) on 2013-02-27T15:32:35Z (GMT) No. of bitstreams: 0 %R 10.1109/TAC.2012.2195830 %0 Journal Article %J BMC Systems Biology. 29 August 2012, Page 115 %D 2012 %T Predicting and characterizing selective multiple drug treatments for metabolic diseases and cancer. %A Giuseppe Facchetti %A Claudio Altafini %A Mattia Zampieri %X Background: In the field of drug discovery, assessing the potential of multidrug therapies is a difficult task because of the combinatorial complexity (both theoretical and experimental) and because of the requirements on the selectivity of the therapy. To cope with this problem, we have developed a novel method for the systematic in silico investigation of synergistic effects of currently available drugs on genome-scale metabolic networks. The algorithm finds the optimal combination of drugs which guarantees the inhibition of an objective function, while minimizing the side effect on the overall network. Results: Two different applications are considered: finding drug synergisms for human metabolic diseases (like diabetes, obesity and hypertension) and finding antitumoral drug combinations with minimal side effect on the normal human metabolism.The results we obtain are consistent with some of the available therapeutic indications and predict some new multiple drug treatments.A cluster analysis on all possible interactions among the currently available drugs indicates a limited variety on the metabolic targets for the approved drugs. Conclusion: The in silico prediction of drug synergism can represent an important tool for the repurposing of drug in a realistic perspective which considers also the selectivty of the therapy. Moreover, for a more profitable exploitation of drug-drug interactions, also drugs which show a too low efficacy but which have a non-common mechanism of action, can be reconsider as potential ingredients of new multicompound therapeutic indications.Needless to say the clues provided by a computational study like ours need in any case to be thoroughly evaluated experimentally. %B BMC Systems Biology. 29 August 2012, Page 115 %I BioMed Central %G en %U http://hdl.handle.net/1963/6515 %1 6450 %2 Mathematics %4 1 %$ Submitted by Claudio Altafini (altafini@sissa.it) on 2013-02-27T13:12:49Z\nNo. of bitstreams: 0 %R doi:10.1186/1752-0509-6-115 %0 Journal Article %J IET systems biology. 2011 Jul; 5(4):269-79 %D 2011 %T Adaptation as a genome-wide autoregulatory principle in the stress response of yeast. %A F Eduati %A B Di Camillo %A G Toffolo %A Claudio Altafini %A Giovanna De Palo %A Mattia Zampieri %X The gene expression response of yeast to various types of stresses/perturbations shows a common functional and dynamical pattern for the vast majority of genes, characterised by a quick transient peak (affecting primarily short genes) followed by a return to the pre-stimulus level. Kinetically, this process of adaptation following the transient excursion can be modelled using a genome-wide autoregulatory mechanism by means of which yeast aims at maintaining a preferential concentration in its mRNA levels. The resulting feedback system explains well the different time constants observable in the transient response, while being in agreement with all the known experimental dynamical features. For example, it suggests that a very rapid transient can be induced also by a slowly varying concentration of the gene products. %B IET systems biology. 2011 Jul; 5(4):269-79 %I The Institution of Engineering and Technology %G en %U http://hdl.handle.net/1963/5106 %1 4922 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2011-11-25T13:05:49Z\\r\\nNo. of bitstreams: 1\\r\\nDePaEdal10.pdf: 2390366 bytes, checksum: f6550b1052efeb53942e47cae9632899 (MD5) %R 10.1049/iet-syb.2009.0050 %0 Journal Article %J Proceedings of the National Academy of Sciences of the United States of America. Volume 108, Issue 52, 27 December 2011, Pages 20953-20958 %D 2011 %T Computing global structural balance in large-scale signed social networks. %A Giuseppe Facchetti %A Giovanni Iacono %A Claudio Altafini %K Combinatorial optimization %X Structural balance theory affirms that signed social networks (i.e., graphs whose signed edges represent friendly/hostile interactions among individuals) tend to be organized so as to avoid conflictual situations, corresponding to cycles of negative parity. Using an algorithm for ground-state calculation in large-scale Ising spin glasses, in this paper we compute the global level of balance of very large online social networks and verify that currently available networks are indeed extremely balanced. This property is explainable in terms of the high degree of skewness of the sign distributions on the nodes of the graph. In particular, individuals linked by a large majority of negative edges create mostly \\\"apparent disorder,\\\" rather than true \\\"frustration.\\\" %B Proceedings of the National Academy of Sciences of the United States of America. Volume 108, Issue 52, 27 December 2011, Pages 20953-20958 %I National Academy of Sciences %G en %U http://hdl.handle.net/1963/6426 %1 6362 %2 Physics %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2013-01-25T12:27:12Z\\r\\nNo. of bitstreams: 1\\r\\npnas.1109521108-1.pdf: 1293098 bytes, checksum: 288a1ce2e9407b58249c5ea58a06f31b (MD5) %R 10.1073/pnas.1109521108 %0 Journal Article %J Bioinformatics (Oxford, England). 2011 Dec; 27(24):3407-14 %D 2011 %T A system-level approach for deciphering the transcriptional response to prion infection %A Mattia Zampieri %A Giuseppe Legname %A Daniel Segrè %A Claudio Altafini %X MOTIVATION: Deciphering the response of a complex biological system to an insulting event, at the gene expression level, requires adopting theoretical models that are more sophisticated than a one-to-one comparison (i.e. t-test). Here, we investigate the ability of a novel reverse engineering approach (System Response Inference) to unveil non-obvious transcriptional signatures of the system response induced by prion infection.\\r\\nRESULTS: To this end, we analyze previously published gene expression data, from which we extrapolate a putative full-scale model of transcriptional gene-gene dependencies in the mouse central nervous system. Then, we use this nominal model to interpret the gene expression changes caused by prion replication, aiming at selecting the genes primarily influenced by this perturbation. Our method sheds light on the mode of action of prions by identifying key transcripts that are the most likely to be responsible for the overall transcriptional rearrangement from a nominal regulatory network. As a first result of our inference, we have been able to predict known targets of prions (i.e. PrP(C)) and to unveil the potential role of previously unsuspected genes.\\r\\nCONTACT: altafini@sissa.it\\r\\nSUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online. %B Bioinformatics (Oxford, England). 2011 Dec; 27(24):3407-14 %I Oxford University Press %G en %U http://hdl.handle.net/1963/5745 %1 5600 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2012-04-23T08:12:17Z\\nNo. of bitstreams: 1\\nZaLeSeAl11.pdf: 1229345 bytes, checksum: eb5500741d42ed30ef38112ebd4eae91 (MD5) %R 10.1093/bioinformatics/btr580 %0 Journal Article %J Systems and Control Letters, 59 (12):782-786, 2010 %D 2010 %T Feedback schemes for radiation damping suppression in NMR: a control-theoretical perspective %A Claudio Altafini %A Paola Cappellaro %A David Cory %X In NMR spectroscopy, the collective measurement is weakly invasive and its back-action is called radiation damping. The aim of this paper is to provide a control-theoretical analysis of the problem of suppressing this radiation damping. It is shown that the two feedback schemes commonly used in the NMR practice correspond one to a high gain oputput feedback for the simple case of maintaining the spin 1/2 in its inverted state, and the second to a 2-degree of freedom control design with a prefeedback that exactly cancels the radiation damping field. A general high gain feedback stabilization design not requiring the knowledge of the radiation damping time constant is also investigated. %B Systems and Control Letters, 59 (12):782-786, 2010 %I Elsevier %G en %U http://hdl.handle.net/1963/4384 %1 4132 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2011-09-30T10:33:33Z\\nNo. of bitstreams: 1\\nAlCaCo09.pdf: 172729 bytes, checksum: b8f2ae1517b057b5f24fd2d8b3666002 (MD5) %R 10.1016/j.sysconle.2010.09.004 %0 Journal Article %J Mathematical Biosciences and Engineering 7(2):301-312, 2010 %D 2010 %T A kinetic mechanism inducing oscillations in simple chemical reactions networks %A Julien Coatleven %A Claudio Altafini %X It is known that a kinetic reaction network in which one or more secondary substrates are acting as cofactors may exhibit an oscillatory behavior. The aim of this work is to provide a description of the functional form of such a cofactor action guaranteeing the\\r\\nonset of oscillations in sufficiently simple reaction networks. %B Mathematical Biosciences and Engineering 7(2):301-312, 2010 %I American Institute of Mathematical Sciences %G en_US %U http://hdl.handle.net/1963/2393 %1 2304 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-11-12T13:08:42Z\\r\\nNo. of bitstreams: 1\\r\\nCoAl07.pdf: 254781 bytes, checksum: 0906fef8209903070cd78781f52b13b1 (MD5) %R 10.3934/mbe.2010.7.301 %0 Journal Article %J BMC Systems Biology 2010, 4:83 %D 2010 %T Monotonicity, frustration, and ordered response: an analysis of the energy landscape of perturbed large-scale biological networks %A Giovanni Iacono %A Claudio Altafini %X Background. \\nFor large-scale biological networks represented as signed graphs, the index of frustration measures how far a network is from a monotone system, i.e., how incoherently the system responds to perturbations.\\nResults. \\nIn this paper we find that the frustration is systematically lower in transcriptional networks (modeled at functional level) than in signaling and metabolic networks (modeled at stoichiometric level). A possible interpretation of this result is in terms of energetic cost of an interaction: an erroneous or contradictory transcriptional action costs much more than a signaling/metabolic error, and therefore must be avoided as much as possible. Averaging over all possible perturbations, however, we also find that unlike for transcriptional networks, in the signaling/metabolic networks the probability of finding the system in its least frustrated configuration tends to be high also in correspondence of a moderate energetic regime, meaning that, in spite of the higher frustration, these networks can achieve a globally ordered response to perturbations even for moderate values of the strength of the interactions. Furthermore, an analysis of the energy landscape shows that signaling and metabolic networks lack energetic barriers around their global optima, a property also favouring global order.\\nConclusion. \\nIn conclusion, transcriptional and signaling/metabolic networks appear to have systematic differences in both the index of frustration and the transition to global order. These differences are interpretable in terms of the different functions of the various classes of networks. %B BMC Systems Biology 2010, 4:83 %I BioMed Central %G en_US %U http://hdl.handle.net/1963/4055 %1 347 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-09-13T10:31:59Z\\nNo. of bitstreams: 1\\n1752-0509-4-83.pdf: 1153140 bytes, checksum: 11a6235e8d975094d5fefbdb911af66b (MD5) %R 10.1186/1752-0509-4-83 %0 Journal Article %J BMC Research Notes (2009) 2:13 %D 2009 %T Characterization of the time course of changes of the evoked electrical activity in a model of a chemically-induced neuronal plasticity %A Frederic D. Broccard %A Silvia Pegoraro %A Maria Elisabetta Ruaro %A Claudio Altafini %A Vincent Torre %X BACKGROUND: Neuronal plasticity is initiated by transient elevations of neuronal networks activity leading to changes of synaptic properties and providing the basis for memory and learning 1. An increase of electrical activity can be caused by electrical stimulation 2 or by pharmacological manipulations: elevation of extracellular K+ 3, blockage of inhibitory pathways 4 or by an increase of second messengers intracellular concentrations 5. Neuronal plasticity is mediated by several biochemical pathways leading to the modulation of synaptic strength, density of ionic channels and morphological changes of neuronal arborisation 6. On a time scale of a few minutes, neuronal plasticity is mediated by local protein trafficking 7 while, in order to sustain modifications beyond 2-3 h, changes of gene expression are required 8. FINDINGS: In the present manuscript we analysed the time course of changes of the evoked electrical activity during neuronal plasticity and we correlated it with a transcriptional analysis of the underlying changes of gene expression. Our investigation shows that treatment for 30 min. with the GABAA receptor antagonist gabazine (GabT) causes a potentiation of the evoked electrical activity occurring 2-4 hours after GabT and the concomitant up-regulation of 342 genes. Inhibition of the ERK1/2 pathway reduced but did not abolish the potentiation of the evoked response caused by GabT. In fact not all the genes analysed were blocked by ERK1/2 inhibitors. CONCLUSION: These results are in agreement with the notion that neuronal plasticity is mediated by several distinct pathways working in unison. %B BMC Research Notes (2009) 2:13 %I BioMed Central %G en_US %U http://hdl.handle.net/1963/3706 %1 599 %2 Neuroscience %3 Neurobiology %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-08-12T11:40:38Z\\nNo. of bitstreams: 1\\n1756-0500-2-13.pdf: 518127 bytes, checksum: 0cd264c3567a0d1776a5141b6dc5ef4e (MD5) %R 10.1186/1756-0500-2-13 %0 Journal Article %J Systems Control Lett. 58 (2009) 213-216 %D 2009 %T Controllability and simultaneous controllability of isospectral bilinear control systems on complex flag manifolds %A Claudio Altafini %X For isospectral bilinear control systems evolving on the so-called complex flag manifolds (i.e., on the orbits of the Hermitian matrices under unitary conjugation action) it is shown that controllability is almost always verified. Easy and generic sufficient conditions are provided. The result applies to the problem of density operator controllability of finite dimensional quantum mechanical systems. In addition, we show that systems having different drifts (corresponding for example to different Larmor frequencies) are simultaneously controllable by the same control field. %B Systems Control Lett. 58 (2009) 213-216 %I Elsevier %G en_US %U http://hdl.handle.net/1963/3523 %1 741 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-02-19T09:39:57Z\\nNo. of bitstreams: 1\\nquens-controll.pdf: 158724 bytes, checksum: 19e7a4ce17acbe97895e145a95916c7a (MD5) %R 10.1016/j.sysconle.2008.10.008 %0 Journal Article %J Bioinformatics 25 (2009) 2853-2854 %D 2009 %T ERNEST: a toolbox for chemical reaction network theory %A Nicola Soranzo %A Claudio Altafini %X Summary: ERNEST Reaction Network Equilibria Study Toolbox is a MATLAB package which, by checking various different criteria on the structure of a chemical reaction network, can exclude the multistationarity of the corresponding reaction system. The results obtained are independent of the rate constants of the reactions, and can be used for model discrimination.\\nAvailability and Implementation: The software, implemented in MATLAB, is available under the GNU GPL free software license from http://people.sissa.it/~altafini/papers/SoAl09/. It requires the MATLAB Optimization Toolbox. %B Bioinformatics 25 (2009) 2853-2854 %I Oxford University Press %G en_US %U http://hdl.handle.net/1963/3826 %1 501 %2 Physics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-01-22T11:56:56Z\\nNo. of bitstreams: 1\\nSoAl09.pdf: 30345 bytes, checksum: a3c73c1a74eb623da69be9a9eba3ca72 (MD5) %R 10.1093/bioinformatics/btp513 %0 Journal Article %J PLoS Comput Biol 2009;5(7): e1000420 %D 2009 %T Investigating the Conformational Stability of Prion Strains through a Kinetic Replication Model %A Mattia Zampieri %A Giuseppe Legname %A Claudio Altafini %X Prion proteins are known to misfold into a range of different aggregated forms, showing different phenotypic and pathological states. Understanding strain specificities is an important problem in the field of prion disease. Little is known about which PrPSc structural properties and molecular mechanisms determine prion replication, disease progression and strain phenotype. The aim of this work is to investigate, through a mathematical model, how the structural stability of different aggregated forms can influence the kinetics of prion replication. The model-based results suggest that prion strains with different conformational stability undergoing in vivo replication are characterizable in primis by means of different rates of breakage. A further role seems to be played by the aggregation rate (i.e. the rate at which a prion fibril grows). The kinetic variability introduced in the model by these two parameters allows us to reproduce the different characteristic features of the various strains (e.g., fibrils\\\' mean length) and is coherent with all experimental observations concerning strain-specific behavior. %B PLoS Comput Biol 2009;5(7): e1000420 %I PLoS %G en_US %U http://hdl.handle.net/1963/3989 %1 413 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-08-11T10:35:47Z\\nNo. of bitstreams: 1\\njournal.pcbi.1000420.pdf: 468491 bytes, checksum: fda67b47ac16d98d11bc4ac879c17ec0 (MD5) %R 10.1371/journal.pcbi.1000420 %0 Journal Article %J BMC Systems Biology (2009) 3:18 %D 2009 %T mRNA stability and the unfolding of gene expression in the long-period yeast metabolic cycle %A Nicola Soranzo %A Mattia Zampieri %A Lorenzo Farina %A Claudio Altafini %X Background: In yeast, genome-wide periodic patterns associated with energy-metabolic oscillations have been shown recently for both short (approx. 40 min) and long (approx. 300 min) periods.\\nResults: The dynamical regulation due to mRNA stability is found to be an important aspect of the genome-wide coordination of the long-period yeast metabolic cycle. It is shown that for periodic genes, arranged in classes according either to expression profile or to function, the pulses of mRNA abundance have phase and width which are directly proportional to the corresponding turnover rates.\\nConclusion: The cascade of events occurring during the yeast metabolic cycle (and their correlation with mRNA turnover) reflects to a large extent the gene expression program observable in other dynamical contexts such as the response to stresses/stimuli. %B BMC Systems Biology (2009) 3:18 %I BioMed Central %G en_US %U http://hdl.handle.net/1963/3630 %1 674 %2 Physics %3 Statistical and Biological Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-05-07T10:19:22Z\\nNo. of bitstreams: 1\\n1752-0509-3-18.pdf: 1143957 bytes, checksum: 3f6f6d33e3da5ee922c0a2c47af61560 (MD5) %R 10.1186/1752-0509-3-18 %0 Journal Article %J Bioinformatics 24 (2008) 1510-1515 %D 2008 %T Discerning static and causal interactions in genome-wide reverse engineering problems %A Mattia Zampieri %A Nicola Soranzo %A Claudio Altafini %X Background. In the past years devicing methods for discovering gene regulatory mechanisms at a genome-wide level has become a fundamental topic in the field of system biology. The aim is to infer gene-gene interactions in a more sophisticated and reliable way through the continuously improvement of reverse engineering algorithms exploiting microarray technologies. Motivation. This work is inspired by the several studies suggesting that co-expression is mostly related to \\\"static\\\" stable binding relationships, like belonging to the same protein complex, rather than other types of interactions more of a \\\"causal\\\" and transient nature (metabolic pathway or transcription factor-binding site interaction). Discerning static relationships from causal ones on the basis of their characteristic regulatory structures and in particular identifing \\\"dense modules\\\" with protein complex, and \\\"sparse modules\\\" with causal interactions such as those between transcription factor and corresponding binding site, the performances of different network inference algorithms in artificial and real networks (derived from E.coli and S.cerevisiae) can be tested and compared. Results. Our study shows that methods that try to prune indirect interactions from the inferred gene networks may fail to retrieve genes co-participating in a protein complex. On the other hand they are more robust in the identification of transcription factor-binding sites dependences when multiple transcription factors regulate the expression of the same gene. In the end we confirm the stronger co-expression regarding genes belonging to a protein complex than transcription factor-binding site, according, also, to the effect of multiple transcription factors and a low expression variance. %B Bioinformatics 24 (2008) 1510-1515 %G en_US %U http://hdl.handle.net/1963/2757 %1 1943 %2 Physics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-08-29T08:29:34Z\\nNo. of bitstreams: 1\\nZaSoAl08.pdf: 5513978 bytes, checksum: a0f45096ba7e82edddd03194f8623b1f (MD5) %R 10.1093/bioinformatics/btn220 %0 Journal Article %J PLoS ONE 3 (2008) e2981 %D 2008 %T Origin of Co-Expression Patterns in E.coli and S.cerevisiae Emerging from Reverse Engineering Algorithms %A Mattia Zampieri %A Nicola Soranzo %A Daniele Bianchini %A Claudio Altafini %X Background: The concept of reverse engineering a gene network, i.e., of inferring a genome-wide graph of putative genegene interactions from compendia of high throughput microarray data has been extensively used in the last few years to deduce/integrate/validate various types of \\\"physical\\\" networks of interactions among genes or gene products. Results: This paper gives a comprehensive overview of which of these networks emerge significantly when reverse engineering large collections of gene expression data for two model organisms, E.coli and S.cerevisiae, without any prior information. For the first organism the pattern of co-expression is shown to reflect in fine detail both the operonal structure of the DNA and the regulatory effects exerted by the gene products when co-participating in a protein complex. For the second organism we find that direct transcriptional control (e.g., transcription factor-binding site interactions) has little statistical significance in comparison to the other regulatory mechanisms (such as co-sharing a protein complex, colocalization on a metabolic pathway or compartment), which are however resolved at a lower level of detail than in E.coli. Conclusion: The gene co-expression patterns deduced from compendia of profiling experiments tend to unveil functional categories that are mainly associated to stable bindings rather than transient interactions. The inference power of this systematic analysis is substantially reduced when passing from E.coli to S.cerevisiae. This extensive analysis provides a way to describe the different complexity between the two organisms and discusses the critical limitations affecting this type of methodologies. %B PLoS ONE 3 (2008) e2981 %G en_US %U http://hdl.handle.net/1963/2722 %1 1379 %2 Physics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-08-25T15:50:20Z\\nNo. of bitstreams: 1\\nPLOSe2981.pdf: 853455 bytes, checksum: 91361e24e96e09bbaa6f3083a73e3db4 (MD5) %R 10.1371/journal.pone.0002981 %0 Journal Article %J Bioinformatics 23 (2007) 1640-1647 %D 2007 %T Comparing association network algorithms for reverse engineering of large scale gene regulatory networks: synthetic vs real data %A Nicola Soranzo %A Ginestra Bianconi %A Claudio Altafini %X Motivation: Inferring a gene regulatory network exclusively from microarray expression profiles is a difficult but important task. The aim of this work is to compare the predictive power of some of the most popular algorithms in different conditions (like data taken at equilibrium or time courses) and on both synthetic and real microarray data. We are in particular interested in comparing similarity measures both of linear type (like correlations and partial correlations) and of nonlinear type (mutual information and conditional mutual information), and in investigating the underdetermined case (less samples than genes). Results: In our simulations we see that all network inference algorithms obtain better performances from data produced with \\\"structural\\\" perturbations, like gene knockouts at steady state, than with any dynamical perturbation. The predictive power of all algorithms is confirmed on a reverse engineering problem from E. coli gene profiling data: the edges of the \\\"physical\\\" network of transcription factor-binding sites are significantly overrepresented among the highest weighting edges of the graph that we infer directly from the data without any structure supervision. Comparing synthetic and in vivo data on the same network graph allows us to give an indication of how much more complex a real transcriptional regulation program is with respect to an artificial model. Availability: Software and supplementary material are freely available at the URL http://people.sissa.it/~altafini/papers/SoBiAl07/ %B Bioinformatics 23 (2007) 1640-1647 %G en_US %U http://hdl.handle.net/1963/2028 %1 2168 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-09-03T12:44:53Z\\nNo. of bitstreams: 1\\nSoBiAl07.pdf: 261510 bytes, checksum: dde8f62bdbd57a761204f8533569885a (MD5) %R 10.1093/bioinformatics/btm163 %0 Report %D 2007 %T Feedback control of spin systems %A Claudio Altafini %X The feedback stabilization problem for ensembles of coupled spin 1/2 systems is discussed from a control theoretic perspective. The noninvasive nature of the bulk measurement allows for a fully unitary and deterministic closed loop. The Lyapunov-based feedback design presented does not require spins that are selectively addressable. With this method, it is possible to obtain control inputs also for difficult tasks, like suppressing undesired couplings in identical spin systems. %B Quantum Inf. Process. 6 (2007) 9-36 %G en_US %U http://hdl.handle.net/1963/1808 %1 2406 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-04-12T07:08:54Z\\nNo. of bitstreams: 1\\nquant-ph0601016.pdf: 557249 bytes, checksum: 7285125f31ec5e7e75c04033506d986b (MD5) %R 10.1007/s11128-006-0038-x %0 Journal Article %J 45th IEEE Conference on Decision and Control (2007) 2471-2476 %D 2007 %T Feedback stabilization of quantum ensembles: a global convergence analysis on complex flag manifolds %A Claudio Altafini %X In an N-level quantum mechanical system, the problem of unitary feedback stabilization of mixed density operators to periodic orbits admits a natural Lyapunov-based time-varying feedback design. A global description of the domain of attraction of the closed-loop system can be provided based on a \\\"root-space\\\"-like structure of the space of density operators. This convex set foliates as a complex flag manifold where each leaf is identified with the coadjoint orbit of the eigenvalues of the density operator. The converging conditions are time-independent but depend from the topology of the flag manifold: it is shown that the closed loop must have a number of equilibria at least equal to the Euler characteristic of the manifold, thus imposing obstructions of topological nature to global stabilizability. %B 45th IEEE Conference on Decision and Control (2007) 2471-2476 %G en_US %U http://hdl.handle.net/1963/1729 %1 2422 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-01-30T13:15:57Z\\nNo. of bitstreams: 1\\nquant-ph0506268.pdf: 339036 bytes, checksum: 0deeffc30853814638abac71df2a136d (MD5) %R 10.1109/CDC.2006.377774 %0 Report %D 2006 %T Almost Global Stochastic Feedback Stabilization of Conditional Quantum Dynamics %A Claudio Altafini %A Francesco Ticozzi %X We propose several parametrization-free solutions to the problem of quantum state reduction control by means of continuous measurement and smooth quantum feedback. In particular, we design a feedback law for which almost global stochastic feedback stabilization can be proved analytically by means of Lyapunov techinques. This synthesis arises very naturally from the physics of the problem, as it relies on the variance associated with the quantum filtering process. %G en_US %U http://hdl.handle.net/1963/1727 %1 2424 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-01-30T12:56:41Z\\nNo. of bitstreams: 1\\nquant-ph0510222.pdf: 574764 bytes, checksum: d53ebd4e4afe123a6476bed544c4b9df (MD5) %0 Journal Article %J IEEE Trans. Automat. Control 51 (2006) 1566-1571 %D 2006 %T Homogeneous polynomial forms for simultaneous stabilizability of families of linear control systems: a tensor product approach %A Claudio Altafini %X The paper uses the formalism of tensor products in order to deal with the problem of simultaneous\\nstabilizability of a family of linear control systems by means of Lyapunov functions which are homogeneous polynomial forms. While the feedback synthesis seems to be nonconvex, the simultaneous stability by means of homogeneous polynomial forms of the uncontrollable modes yields (convex) necessary but not sufficient conditions for simultaneous stabilizability. %B IEEE Trans. Automat. Control 51 (2006) 1566-1571 %G en_US %U http://hdl.handle.net/1963/2226 %1 2018 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-15T14:17:52Z\\nNo. of bitstreams: 1\\nhompol.pdf: 129083 bytes, checksum: b5ec376b1dc4ee7dde55d731b63ac25c (MD5) %R 10.1109/TAC.2006.880811 %0 Journal Article %J J. Math. Phys. 47 (2006) 032104 %D 2006 %T Reflection symmetries for multiqubit density operators %A Claudio Altafini %A Timothy F. Havel %X For multiqubit density operators in a suitable tensorial basis, we show that a number of nonunitary operations used in the detection and synthesis of entanglement are classifiable as reflection symmetries, i.e., orientation changing rotations. While one-qubit reflections correspond to antiunitary symmetries, as is known for example from the partial transposition criterion, reflections on the joint density of two or more qubits are not accounted for by the Wigner Theorem and are well-posed only for sufficiently mixed states. One example of such nonlocal reflections is the unconditional NOT operation on a multiparty density, i.e., an operation yelding another density and such that the sum of the two is the identity operator. This nonphysical operation is admissible only for sufficiently mixed states. %B J. Math. Phys. 47 (2006) 032104 %G en_US %U http://hdl.handle.net/1963/2121 %1 2122 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-09-18T06:51:45Z\\nNo. of bitstreams: 1\\n0405123v2.pdf: 247264 bytes, checksum: c504f911bff46e503941a0298617759a (MD5) %R 10.1063/1.2181827 %0 Journal Article %J Phys. Rev. A 72 (2005) 012112 %D 2005 %T Commuting multiparty quantum observables and local compatibility %A Claudio Altafini %X A formula for the commutator of tensor product matrices is used to shows that, for qubits, compatibility of quantum multiparty observables almost never implies local compatibility at each site and to predict when this happens/does not happen in a concise manner. In particular, it is shown that two ``fully nontrivial\\\'\\\' $n$-qubit observables are compatible locally and globally if and only if they are equal up to sign. In addition, the formula gives insight into the construction of new paradoxes of the type of the Kochen-Specker Theorem, which can then be easily rephrased into proposals for new no hidden variable experiments of the type of the ``Bell Theorem without inequalities\\\'\\\'. %B Phys. Rev. A 72 (2005) 012112 %G en_US %U http://hdl.handle.net/1963/2228 %1 2016 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-15T14:36:34Z\\nNo. of bitstreams: 1\\nqu-ent-comm.pdf: 168766 bytes, checksum: 05858df702df633ee1fa71d76f76d1b4 (MD5) %R 10.1103/PhysRevA.72.012112 %0 Journal Article %J Systems and Control Letters, 54 (11):1121-1130, 2005 %D 2005 %T Explicit Wei–Norman formulae for matrix Lie groups via Putzer\\\'s method %A Claudio Altafini %X The Wei–Norman formula locally relates the Magnus solution of a system of linear time-varying ODEs with the solution expressed in terms of products of exponentials by means of a set of nonlinear differential equations in the parameters of the two types of solutions. A closed form expression of such formula is proposed based on the use of Putzer\\\'s method. %B Systems and Control Letters, 54 (11):1121-1130, 2005 %I Elsevier %G en %U http://hdl.handle.net/1963/4538 %1 4299 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2011-10-06T12:04:23Z\\nNo. of bitstreams: 1\\nwei-norman.pdf: 201660 bytes, checksum: 6081c4fd935c318f831c791518f8b9c9 (MD5) %R 10.1016/j.sysconle.2005.03.006 %0 Journal Article %J Phys. Rev. A 70 (2004) 062321 %D 2004 %T Coherent control of open quantum dynamical systems %A Claudio Altafini %X A systematic analysis of the behavior of the quantum Markovian master equation driven by coherent control fields is proposed. Its irreversible character is formalized using control-theoretic notions and the sets of states that can be reached via cohere nt controls are described. The analysis suggests to which extent (and how) it is possible to counteract the effect of dissipation. %B Phys. Rev. A 70 (2004) 062321 %G en_US %U http://hdl.handle.net/1963/2227 %1 2017 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-15T14:29:53Z\\nNo. of bitstreams: 1\\nqopen-coher2.pdf: 226720 bytes, checksum: c93d394691258c3d18b40d7992b70274 (MD5) %R 10.1103/PhysRevA.70.062321 %0 Journal Article %J ESAIM: COCV 10 (2004) 526-548 %D 2004 %T Reduction by group symmetry of second order variational problems on a semidirect product of Lie groups with positive definite Riemannian metric %A Claudio Altafini %X For a Riemannian structure on a semidirect product of Lie groups, the variational problems can be reduced using the group symmetry. Choosing the Levi-Civita connection of a positive definite metric tensor, instead of any of the canonical connections for the Lie group, simplifies the reduction of the variations but complicates the expression for the Lie algebra valued covariant derivatives. The origin of the discrepancy is in the semidirect product structure, which implies that the Riemannian exponential map and the Lie group exponential map do not coincide. The consequence is that the reduced equations look more complicated than the original ones. The main scope of this paper is to treat the reduction of second order variational problems (corresponding to geometric splines) on such semidirect products of Lie groups. Due to the semidirect structure, a number of extra terms appears in the reduction, terms that are calculated explicitely. The result is used to compute the necessary conditions of an optimal control problem for a simple mechanical control system having invariant Lagrangian equal to the kinetic energy corresponding to the metric tensor. As an example, the case of a rigid body on the Special Euclidean group is considered in detail. %B ESAIM: COCV 10 (2004) 526-548 %I EDP Sciences %G en_US %U http://hdl.handle.net/1963/3521 %1 743 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-02-18T11:36:09Z\\nNo. of bitstreams: 1\\ncocv0318.pdf: 296243 bytes, checksum: d9c2fc54e6a7b051fd350dfc5556c06e (MD5) %R 10.1051/cocv:2004018 %0 Journal Article %J Phys. Rev. A 70 (2004) 032331 %D 2004 %T Representing multiqubit unitary evolutions via Stokes tensors %A Claudio Altafini %X For the Stokes tensor parametrization of a multiqubit density operator, we provide an explicit formulation of the corresponding unitary dynamics at the infinitesimal level. The main advantage of this formalism (clearly reminiscent of the ideas of ``coherences\\\'\\\' and ``coupling Hamiltonians\\\'\\\' of spin systems) is that the pattern of correlation between qubits and the pattern of infinitesimal correlation are highlighted simultaneously and can be used constructively for qubit manipulation. For example, it allows to compute explicitly a Rodrigues\\\' formula for the one-parameter orbits of nonlocal Hamiltonians. The result is easily generalizable to orbits of Cartan subalgebras and allows to express the Cartan decomposition of unitary propagators as a linear action directly in terms of the infinitesimal generators. %B Phys. Rev. A 70 (2004) 032331 %G en_US %U http://hdl.handle.net/1963/2307 %1 1709 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-29T12:24:28Z\\nNo. of bitstreams: 1\\n0404006v2.pdf: 225292 bytes, checksum: 7e44f5dc452e09ecabe9744c757b4b03 (MD5) %R 10.1103/PhysRevA.70.032331 %0 Journal Article %J Phys. Rev. A 69 (2004) 012311 %D 2004 %T Tensor of coherences parametrization of multiqubit density operators for entanglement characterization %A Claudio Altafini %X For multiqubit densities, the tensor of coherences (or Stokes tensor) is a real parameterization obtained by the juxtaposition of the affine Bloch vectors of each qubit. While it maintains the tensorial structure of the underlying space, it highlights the pattern of correlations, both classical and quantum, between the subsystems and, due to the affine parameterization, it contains in its components all reduced densities of all orders. The main purpose of our use of this formalism is to deal with entanglement. For example, the detection of bipartite entanglement is straightforward, as it is the synthesis of densities having positive partial transposes between desired qubits. In addition, finding explicit mixtures for families of separable states becomes a feasible issue for few qubit symmetric densities (we compute it for Werner states) and, more important, it provides some insight on the possible origin of entanglement for such densities. %B Phys. Rev. A 69 (2004) 012311 %I American Physical Society %G en_US %U http://hdl.handle.net/1963/2845 %1 1855 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-09-05T11:46:53Z\\nNo. of bitstreams: 1\\n0308019v1.pdf: 274876 bytes, checksum: 4f994250adf7a774cb709fad174c528e (MD5) %R 10.1103/PhysRevA.69.012311 %0 Journal Article %J J. Math. Phys. 44 (2003) 2357-2372 %D 2003 %T Controllability properties for finite dimensional quantum Markovian master equations %A Claudio Altafini %X Various notions from geometric control theory are used to characterize the behavior of the Markovian master equation for N-level quantum mechanical systems driven by unitary control and to describe the structure of the sets of reachable states. It is shown that the system can be accessible but neither small-time controllable nor controllable in finite time. In particular, if the generators of quantum dynamical semigroups are unital, then the reachable sets admit easy characterizations as they monotonically grow in time. The two level case is treated in detail. %B J. Math. Phys. 44 (2003) 2357-2372 %I American Institute of Physics %G en_US %U http://hdl.handle.net/1963/2909 %1 1791 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-09-11T12:05:33Z\\nNo. of bitstreams: 1\\nquant-ph0211194.pdf: 250415 bytes, checksum: e28216a9c4ccbc9174b725f864ec205a (MD5) %R 10.1063/1.1571221 %0 Journal Article %J J. Robotic Syst. 20 (2003) 211-227 %D 2003 %T Geometric motion control for a kinematically redundant robotic chain: application to a holonomic mobile manipulator %A Claudio Altafini %X For kinematically redundant robotic manipulators, the extra degrees of freedom available allows freedom in the generation of the trajectories of the end-effector. In this paper, for this scope, we use techniques for motion control of rigid bodies on Riemannian manifolds (and Lie groups in particular) to design workspace control algorithms for the end-effector of the robotic chain and then to pull them back to joint space, all respecting the different geometric structures of the two underlying model spaces. The trajectory planner makes use of geometric splines. Examples of the different kinds of curves that are obtained via the De Casteljau algorithm in correspondence of different metric structures in SE(3) are reported. The feedback module, instead, consists of a Lyapunov based PD controller defined from a suitable notion of error distance on the Lie group. The motivating application of our work is a holonomic mobile manipulator for which simulation results are described in detail. %B J. Robotic Syst. 20 (2003) 211-227 %I Wiley %G en_US %U http://hdl.handle.net/1963/3019 %1 1314 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-02T14:53:17Z\\nNo. of bitstreams: 1\\ngeometric.pdf: 355957 bytes, checksum: 4ef01346a7567eb489c48c1bc40cb9c5 (MD5) %R 10.1002/rob.10084 %0 Journal Article %J Syst. Control Lett. 50 (2003) 241-250 %D 2003 %T Motion on submanifolds of noninvariant holonomic constraints for a kinematic control system evolving on a matrix Lie group %A Claudio Altafini %A Ruggero Frezza %X For a control system on a matrix Lie group with one or more configuration constraints that are not left/right invariant, finding the combinations of (kinematic) control inputs satisfying the motion constraints is not a trivial problem. Two methods, one coordinate-dependent and the other coordinate-free are suggested. The first is based on the Wei-Norman formula; the second on the calculation of the annihilator of the coadjoint action of the constraint one-form at each point of the group manifold. The results are applied to a control system on SE(3) with a holonomic inertial constraint involving the noncommutative part in a nontrivial way. The difference in terms of compactness of the result between the two methods is considerable. %B Syst. Control Lett. 50 (2003) 241-250 %I Elsevier %G en_US %U http://hdl.handle.net/1963/3018 %1 1315 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-02T14:31:06Z\\nNo. of bitstreams: 1\\nclaruSCL.pdf: 174518 bytes, checksum: 3ccf0767619fa61ad2d126abba2999e5 (MD5) %R 10.1016/S0167-6911(03)00168-3 %0 Journal Article %J Rep. Math. Phys. 52 (2003) 381-400 %D 2003 %T Parameter differentiation and quantum state decomposition for time varying Schrödinger equations %A Claudio Altafini %X For the unitary operator, solution of the Schroedinger equation corresponding to a time-varying Hamiltonian, the relation between the Magnus and the product of exponentials expansions can be expressed in terms of a system of first order differential equations in the parameters of the two expansions. A method is proposed to compute such differential equations explicitly and in a closed form. %B Rep. Math. Phys. 52 (2003) 381-400 %I Elsevier %G en_US %U http://hdl.handle.net/1963/3017 %1 1316 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-02T14:22:29Z\\nNo. of bitstreams: 1\\n0201034v2.pdf: 190050 bytes, checksum: 10fb8e5406eaa55002c2d9486a099ee8 (MD5) %R 10.1016/S0034-4877(03)80037-X %0 Journal Article %J J.Math.Phys. 43(2002), no.5, 2051 %D 2002 %T Controllability of quantum mechanical systems by root space decomposition of su(N) %A Claudio Altafini %B J.Math.Phys. 43(2002), no.5, 2051 %I SISSA Library %G en %U http://hdl.handle.net/1963/1613 %1 2505 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:05:18Z (GMT). No. of bitstreams: 1\\nquant-ph0110147.pdf: 211574 bytes, checksum: a43e52a6eec3e4a8127b810133d57645 (MD5)\\n Previous issue date: 2002 %R 10.1063/1.1467611 %0 Journal Article %J IEEE Trans. Automatic Control 47 (2002) 1551-1556 %D 2002 %T Following a path of varying curvature as an output regulation problem %A Claudio Altafini %X Given a path of nonconstant curvature, local asymptotic stability can be proven for the general n trailer whenever the curvature can be considered as the output of an exogenous dynamical system. The controllers that provide convergence to zero of the tracking error chosen for the path-following problem are composed of a prefeedback that input-output linearizes the system, plus a linear controller. %B IEEE Trans. Automatic Control 47 (2002) 1551-1556 %I IEEE %G en_US %U http://hdl.handle.net/1963/3143 %1 1190 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-20T11:01:46Z\\nNo. of bitstreams: 1\\nfollowing.pdf: 236416 bytes, checksum: c98dbcaee3416675cc45749d7af72bb6 (MD5) %R 10.1109/TAC.2002.802750 %0 Journal Article %J Quantum Inf.Process. 1 (2002),no.3,207 %D 2002 %T On the generation of sequential unitary gates from continuous time Schrodinger equations driven by external fields %A Claudio Altafini %B Quantum Inf.Process. 1 (2002),no.3,207 %I SISSA Library %G en %U http://hdl.handle.net/1963/1614 %1 2504 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:05:20Z (GMT). No. of bitstreams: 1\\nquant-ph0203005.pdf: 180528 bytes, checksum: e67198980430d8f35b340c0aa590096c (MD5)\\n Previous issue date: 2002 %R 10.1023/A:1019825109040 %0 Journal Article %J Systems Control Lett. 47 (2002) 343-353 %D 2002 %T The reachable set of a linear endogenous switching system %A Claudio Altafini %X In this work, switching systems are named endogenous when their switching pattern is controllable. Linear endogenous switching systems can be considered as a particular class of bilinear control systems. The key idea is that both types of systems are equivalent to polysystems, i.e. to systems whose flow is piecewise smooth. The reachable set of a linear endogenous switching system can be studied consequently. The main result is that, in general, it has the structure of a semigroup, even when the Lie algebra rank condition is satisfied since the logic inputs cannot reverse the direction of the flow. The adaptation of existing controllability criteria for bilinear systems is straightforward. %B Systems Control Lett. 47 (2002) 343-353 %I Elsevier %G en_US %U http://hdl.handle.net/1963/3142 %1 1191 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-20T10:54:15Z\\nNo. of bitstreams: 1\\nreachswitch.pdf: 196896 bytes, checksum: 2682b7b9d90c38e08cffe3e8e9228d73 (MD5) %R 10.1016/S0167-6911(02)00228-1