Exact controllability of multiplex networks

Date of Acceptance: 11/09/2014Peer reviewedPublisher PD

A Brauer's theorem and related results

Given a square matrix A, a Brauer's theorem [Brauer A., Limits for the characteristic roots of a matrix. IV. Applications to stochastic matrices, Duke Math. J., 1952, 19(1), 75-91] shows how to modify one single eigenvalue of A via a rank-one perturbation without changing any of the remaining eigenvalues. Older and newer results can be considered in the framework of the above theorem. In this paper, we present its application to stabilization of control systems, including the case when the system is noncontrollable. Other applications presented are related to the Jordan form of A and Wielandt's and Hotelling's deflations. An extension of the aforementioned Brauer's result, Rado's theorem, shows how to modify r eigenvalues of A at the same time via a rank-r perturbation without changing any of the remaining eigenvalues. The same results considered by blocks can be put into the block version framework of the above theorem. © 2012 Versita Warsaw and Springer-Verlag Wien.This work is supported by Fondecyt 1085125, Chile, the Spanish grant DGI MTM2010-18228 and the Programa de Apoyo a la Investigacion y Desarrollo (PAID-06-10) of the UPV.Bru García, R.; Cantó Colomina, R.; Soto, RL.; Urbano Salvador, AM. (2012). A Brauer's theorem and related results. Central European Journal of Mathematics. 10(1):312-321. https://doi.org/10.2478/s11533-011-0113-0S312321101Brauer A., Limits for the characteristic roots of a matrix. IV. Applications to stochastic matrices, Duke Math. J., 1952, 19(1), 75–91Crouch P.E., Introduction to Mathematical Systems Theory, Mathematik-Arbeitspapiere, Bremen, 1988Delchamps D.F., State-Space and Input-Output Linear Systems, Springer, New York, 1988Hautus M.L.J., Controllability and observability condition of linear autonomous systems, Nederl. Akad. Wetensch. Indag. Math., 1969, 72, 443–448Kailath T., Linear Systems, Prentice Hall Inform. System Sci. Ser., Prentice Hall, Englewood Cliffs, 1980Langville A.N., Meyer C.D., Deeper inside PageRank, Internet Math., 2004, 1(3), 335–380Perfect H., Methods of constructing certain stochastic matrices. II, Duke Math. J., 1955, 22(2), 305–311Saad Y., Numerical Methods for Large Eigenvalue Problems, Classics Appl. Math., 66, SIAM, Philadelphia, 2011Soto R.L., Rojo O., Applications of a Brauer theorem in the nonnegative inverse eigenvalue problem, Linear Algebra Appl., 2006, 416(2–3), 844–856Wilkinson J.H., The Algebraic Eigenvalue Problem, Clarendon Press, Oxford, 196

An extended multisensory temporal binding window in autism spectrum disorders

Autism spectrum disorders (ASD) form a continuum of neurodevelopmental disorders, characterized by deficits in communication and reciprocal social interaction, as well as by repetitive behaviors and restricted interests. Sensory disturbances are also frequently reported in clinical and autobiographical accounts. However, surprisingly few empirical studies have characterized the fundamental features of sensory and multisensory processing in ASD. The current study is structured to test for potential differences in multisensory temporal function in ASD by making use of a temporally dependent, low-level multisensory illusion. In this illusion, the presentation of a single flash of light accompanied by multiple sounds often results in the illusory perception of multiple flashes. By systematically varying the temporal structure of the audiovisual stimuli, a “temporal window” within which these stimuli are likely to be bound into a single perceptual entity can be defined. The results of this study revealed that children with ASD report the flash-beep illusion over an extended range of stimulus onset asynchronies relative to children with typical development, suggesting that children with ASD have altered multisensory temporal function. These findings provide valuable new insights into our understanding of sensory processing in ASD and may hold promise for the development of more sensitive diagnostic measures and improved remediation strategies

Attention wins over sensory attenuation in a sound detection task

'Sensory attenuation', i.e., reduced neural responses to self-induced compared to externally generated stimuli, is a well-established phenomenon. However, very few studies directly compared sensory attenuation with attention effect, which leads to increased neural responses. In this study, we brought sensory attenuation and attention together in a behavioural auditory detection task, where both effects were quantitatively measured and compared. The classic auditory attention effect of facilitating detection performance was replicated. When attention and sensory attenuation were both present, attentional facilitation decreased but remained significant. The results are discussed in the light of current theories of sensory attenuation

Follow the sign! Top-down contingent attentional capture of masked arrow cues

Arrow cues and other overlearned spatial symbols automatically orient attention according to their spatial meaning. This renders them similar to exogenous cues that occur at stimulus location. Exogenous cues trigger shifts of attention even when they are presented subliminally. Here, we investigate to what extent the mechanisms underlying the orienting of attention by exogenous cues and by arrow cues are comparable by analyzing the effects of visible and masked arrow cues on attention. In Experiment 1, we presented arrow cues with overall 50% validity. Visible cues, but not masked cues, lead to shifts of attention. In Experiment 2, the arrow cues had an overall validity of 80%. Now both visible and masked arrows lead to shifts of attention. This is in line with findings that subliminal exogenous cues capture attention only in a top-down contingent manner, that is, when the cues fit the observer’s intentions

Motor expertise modulates the unconscious processing of human body postures

Little is known about the cognitive background of unconscious visuomotor control of complex sports movements. Therefore, we investigated the extent to which novices and skilled high-jump athletes are able to identify visually presented body postures of the high jump unconsciously. We also asked whether or not the manner of processing differs (qualitatively or quantitatively) between these groups as a function of their motor expertise. A priming experiment with not consciously perceivable stimuli was designed to determine whether subliminal priming of movement phases (same vs. different movement phases) or temporal order (i.e. natural vs. reversed movement order) affects target processing. Participants had to decide which phase of the high jump (approach vs. flight phase) a target photograph was taken from. We found a main effect of temporal order for skilled athletes, that is, faster reaction times for prime-target pairs that reflected the natural movement order as opposed to the reversed movement order. This result indicates that temporal-order information pertaining to the domain of expertise plays a critical role in athletes’ perceptual capacities. For novices, data analyses revealed an interaction between temporal order and movement phases. That is, only the reversed movement order of flight-approach pictures increased processing time. Taken together, the results suggest that the structure of cognitive movement representation modulates unconscious processing of movement pictures and points to a functional role of motor representations in visual perception

Developmental learning impairments in a rodent model of nodular heterotopia

Developmental malformations of neocortex—including microgyria, ectopias, and periventricular nodular heterotopia (PNH)—have been associated with language learning impairments in humans. Studies also show that developmental language impairments are frequently associated with deficits in processing rapid acoustic stimuli, and rodent models have linked cortical developmental disruption (microgyria, ectopia) with rapid auditory processing deficits. We sought to extend this neurodevelopmental model to evaluate the effects of embryonic (E) day 15 exposure to the anti-mitotic teratogen methylazoxymethanol acetate (MAM) on auditory processing and maze learning in rats. Extensive cortical anomalies were confirmed in MAM-treated rats post mortem. These included evidence of laminar disruption, PNH, and hippocampal dysplasia. Juvenile auditory testing (P21–42) revealed comparable silent gap detection performance for MAM-treated and control subjects, indicating normal hearing and basic auditory temporal processing in MAM subjects. Juvenile testing on a more complex two-tone oddball task, however, revealed a significant impairment in MAM-treated as compared to control subjects. Post hoc analysis also revealed a significant effect of PNH severity for MAM subjects, with more severe disruption associated with greater processing impairments. In adulthood (P60–100), only MAM subjects with the most severe PNH condition showed deficits in oddball two-tone processing as compared to controls. However, when presented with a more complex and novel FM sweep detection task, all MAM subjects showed significant processing deficits as compared to controls. Moreover, post hoc analysis revealed a significant effect of PNH severity on FM sweep processing. Water Maze testing results also showed a significant impairment for spatial but not non-spatial learning in MAM rats as compared to controls. Results lend further support to the notions that: (1) generalized cortical developmental disruption (stemming from injury, genetic or teratogenic insults) leads to auditory processing deficits, which in turn have been suggested to play a causal role in language impairment; (2) severity of cortical disruption is related to the severity of processing impairments; (3) juvenile auditory processing deficits appear to ameliorate with maturation, but can still be elicited in adulthood using increasingly complex acoustic stimuli; and (4) malformations induced with MAM are also associated with generalized spatial learning deficits. These cumulative findings contribute to our understanding of the behavioral consequences of cortical developmental pathology, which may in turn elucidate mechanisms contributing to developmental language learning impairment in humans