Stimuli of varying spatial scale induce gamma activity with distinct temporal characteristics in human visual cortex

Gamma activity to stationary grating stimuli was studied non-invasively using MEG recordings in humans. Using a spatial filtering technique, we localized gamma activity to primary visual cortex. We tested the hypothesis that spatial frequency properties of visual stimuli may be related to the temporal frequency characteristics of the associated cortical responses. We devised a method to assess temporal frequency differences between stimulus-related responses that typically exhibit complex spectral shapes. We applied this methodology to either single-trial (induced) or time-averaged (evoked) responses in four frequency ranges (0-40, 20-60, 40-80 and 60-100 Hz) and two time windows (either the entire duration of stimulus presentation or the first second following stimulus onset). Our results suggest that stimuli of varying spatial frequency induce responses that exhibit significantly different temporal frequency characteristics. These effects were particularly accentuated for induced responses in the classical gamma frequency band (20-60 Hz) analyzed over the entire duration of stimulus presentation. Strikingly, examining the first second of the responses following stimulus onset resulted in significant loss in stimulus specificity, suggesting that late signal components contain functionally relevant information. These findings advocate a functional role of gamma activity in sensory representation. We suggest that stimulus specific frequency characteristics of MEG signals can be mapped to processes of neuronal synchronization within the framework of coupled dynamical systems.

A new entropy measure based on the Renyi entropy rate using Gaussian kernels

The concept of entropy rate is well defined in dynamical systems theory but is impossible to apply it directly to finite real world data sets. With this in mind, Pincus developed Approximate Entropy (ApEn), which uses ideas from Eckmann and Ruelle to create a regularity measure based on entropy rate that can be used to determine the influence of chaotic behaviour in a real world signal. However, this measure was found not to be robust and so an improved formulation known as the Sample Entropy (SampEn) was created by Richman and Moorman to address these issues. We have developed a new, related, regularity measure which is not based on the theory provided by Eckmann and Ruelle and proves a more well-behaved measure of complexity than the previous measures whilst still retaining a low computational cost.

Bayesian online algorithms for learning in discrete Hidden Markov Models

We propose and analyze two different Bayesian online algorithms for learning in discrete Hidden Markov Models and compare their performance with the already known Baldi-Chauvin Algorithm. Using the Kullback-Leibler divergence as a measure of generalization we draw learning curves in simplified situations for these algorithms and compare their performances.

On-off and multistate intermittencies in cascaded random distributed feedback fibre laser

A range of physical and engineering systems exhibit an irregular complex dynamics featuring alternation of quiet and burst time intervals called the intermittency. The intermittent dynamics most popular in laser science is the on-off intermittency [1]. The on-off intermittency can be understood as a conversion of the noise in a system close to an instability threshold into effective time-dependent fluctuations which result in the alternation of stable and unstable periods. The on-off intermittency has been recently demonstrated in semiconductor, Erbium doped and Raman lasers [2-5]. Recently demonstrated random distributed feedback (random DFB) fiber laser has an irregular dynamics near the generation threshold [6,7]. Here we show the intermittency in the cascaded random DFB fiber laser. We study intensity fluctuations in a random DFB fiber laser based on nitrogen doped fiber. The laser generates first and second Stokes components 1120 nm and 1180 nm respectively under an appropriate pumping. We study the intermittency in the radiation of the second Stokes wave. The typical time trace near the generation threshold of the second Stokes wave (Pth) is shown at Fig. 1a. From the number of long enough time-traces we calculate statistical distribution between major spikes in time dynamics, Fig. 1b. To eliminate contribution of high frequency components of spikes we use a low pass filter along with the reference value of the output power. Experimental data is fitted by power law, ~(P-Pth)y, where is a mean time between pikes. There are two different intermittency regimes. Just above Pth, the mean time is approximated by the -3/2 power law. The -3/2 power law is typical to the on-off intermittency with hopping between two states (first and second Stokes waves in our case) [7]. At higher power, the mean time is approximated by -4 power law, that indicates a change in intermittency type to multistate. Multistable dynamics is observed in erbium-doped fiber lasers [8]. The origin of multiples states in our system could be probably connected with polarization hopping or other reasons and should be further investigated. We have presented a first experimental statistical characterisation of the on-off and multistate intermittencies that occur in the generation of the second Stokes wave in nitrogen doped random DFB fiber laser. References [1] H. Fujisaka and T. Yamada, “A New Intermittency in Coupled Dynamical Systems,” Prog. Theor. Phys. 74, 918 (1985). [2] S. Osborne, A. Amann, D. Bitauld, and S. O’Brien, “On-off intermittency in an optically injected semiconductor laser,” Phys. Rev. E 85, 056204 (2012). [3] S. Sergeyev, K. O'Mahoney, S. Popov, and A. T. Friberg, “Coherence and anticoherence resonance in high-concentration erbium-doped fiber laser,” Opt. Lett. 35, 3736 (2010). [4] A.E. El-Taher, S.V. Sergeyev, E.G. Turitsyna, P. Harper, and S. K. Turitsyn, “Intermittent Self-Pulsing in a Fiber Raman Laser”, In proc. Conf. Nonlin. Photon., paper ID 1367139, Colorado Springs, USA, 2012 [5] S.K. Turitsyn, S.A. Babin, A.E. El-Taher, P. Harper, D.V. Churkin, S.I. Kablukov, J.D. Ania-Castañón, V. Karalekas, and E.V. Podivilov, “Random distributed feedback fibre laser”, Nat. Photon..4, 231 (2010). [6] I. D. Vatnik, D. V. Churkin, S. A. Babin, and S. K. Turitsyn, "Cascaded random distributed feedback Raman fiber laser operating at 1.2 μm," Opt. Express 19, 18486 (2011). [7] W. Feller, An introduction to probability theory and its applications, Vol. 1, 3rd ed. (Wiley, New-York, 1968). [8] G. Huerta-Cuellar, A.N. Pisarchik, and Y.O. Barmenkov, “Experimental characterization of hopping dynamics in a multistable fiber laser,” Phys. Rev. E 78, 035202(R) (2008).

Computer-Assisted Proofs and Symbolic Computations

We discuss some main points of computer-assisted proofs based on reliable numerical computations. Such so-called self-validating numerical methods in combination with exact symbolic manipulations result in very powerful mathematical software tools. These tools allow proving mathematical statements (existence of a fixed point, of a solution of an ODE, of a zero of a continuous function, of a global minimum within a given range, etc.) using a digital computer. To validate the assertions of the underlying theorems fast finite precision arithmetic is used. The results are absolutely rigorous. To demonstrate the power of reliable symbolic-numeric computations we investigate in some details the verification of very long periodic orbits of chaotic dynamical systems. The verification is done directly in Maple, e.g. using the Maple Power Tool intpakX or, more efficiently, using the C++ class library C-XSC.

High-Order Control Variations and Small-Time Local Controllability

The importance of “control variations” for obtaining local approximations of the reachable set of nonlinear control systems is well known. Heuristically, if one can construct control variations in all possible directions, then the considered control system is small-time locally controllable (STLC). Two concepts of control variations of higher order are introduced for the case of smooth control systems. The relation between these variations and the small-time local controllability is studied and a new sufficient STLC condition is proved.

The Asymptotic Behaviour of the First Eigenvalue of Linear Second-Order Elliptic Equations in Divergente Form

2000 Mathematics Subject Classification: 35J70, 35P15.

Towards probabilistic synchronization of local controllers

The traditional use of global and centralised control methods, fails for large, complex, noisy and highly connected systems, which typify many real world industrial and commercial systems. This paper provides an efficient bottom up design of distributed control in which many simple components communicate and cooperate to achieve a joint system goal. Each component acts individually so as to maximise personal utility whilst obtaining probabilistic information on the global system merely through local message-passing. This leads to an implied scalable and collective control strategy for complex dynamical systems, without the problems of global centralised control. Robustness is addressed by employing a fully probabilistic design, which can cope with inherent uncertainties, can be implemented adaptively and opens a systematic rich way to information sharing. This paper opens the foreseen direction and inspects the proposed design on a linearised version of coupled map lattice with spatiotemporal chaos. A version close to linear quadratic design gives an initial insight into possible behaviours of such networks.

Control of the in-cavity dynamics in mode-locked fibre lasers

At the level of fundamental research, fibre lasers provide convenient and reproducible experimental settings for the study of a variety of nonlinear dynamical processes, while at the applied research level, pulses with different and optimised features – e.g., in terms of pulse duration, temporal and/or spectral intensity profile, energy, repetition rate and emission bandwidth – are sought with the general constraint of developing efficient cavity architectures. In this talk, we review our recent progress on the realisation of different regimes of pulse generation in passively mode-locked fibre lasers through control of the in-cavity propagation dynamics. We report on the possibility to achieve both parabolic self-similar and triangular pulse shaping in a mode-locked fibre laser via adjustment of the net normal dispersion and integrated gain of the cavity [1]. We also show that careful control of the gain/loss parameters of a net-normal dispersion laser cavity provides the means of achieving switching among Gaussian pulse, dissipative soliton and similariton pulse solutions in the cavity [2,3]. Furthermore, we report on our recent theoretical and experimental studies of pulse shaping by inclusion of an amplitude and phase spectral filter into the cavity of a laser. We numerically demonstrate that a mode-locked fibre laser can operate in dif- ferent pulse-generation regimes, including parabolic, flattop and triangular waveform generations, depending on the amplitude profile of the in-cavity spectral filter [4]. An application of technique using a flat-top spectral filter is demonstrated to achieve the direct generation of sinc-shaped optical Nyquist pulses of high quality and of a widely tuneable bandwidth from the laser [5]. We also report on a recently-developed versa- tile erbium-doped fibre laser, in which conventional soliton, dispersion-managed soli- ton (stretched-pulse) and dissipative soliton mode-locking regimes can be selectively and reliably targeted by programming different group-velocity dispersion profiles and bandwidths on an in-cavity programmable filter [6]. References: 1. S. Boscolo and S. K. Turitsyn, Phys. Rev. A 85, 043811 (2012). 2. J. Peng et al., Phys. Rev. A 86, 033808 (2012). 3. J. Peng, Opt. Express 24, 3046-3054 (2016). 4. S. Boscolo, C. Finot, H. Karakuzu, and P. Petropoulos, Opt. Lett. 39, 438-441 (2014). 5. S. Boscolo, C. Finot, and S. K. Turitsyn, IEEE Photon. J. 7, 7802008 (2015). 6. J. Peng and S. Boscolo, Sci. Rep. 6, 25995 (2016).

In-cavity pulse shaping and dissipative parametric instability mode-locking in fibre lasers

At the level of fundamental research, fibre lasers provide convenient and reproducible experimental settings for the study of a variety of nonlinear dynamical processes, while at the applied research level, pulses with different and optimised features – e.g., in terms of pulse duration, temporal and/or spectral shape, energy, repetition rate and emission bandwidth – are sought with the general constraint of developing efficient cavity architectures. In this work, we review our recent progress on the realisation of pulse shaping in passively- mode-locked fibre lasers by inclusion of an amplitude and phase spectral filter into the laser cavity. We present a fibre laser design in which pulse shaping occurs through filtering of a spectrally nonlinearly broadened pulse in the cavity. This strategy of pulse shaping is illustrated through the numerical demonstration of the laser operation in different pulse-generation regimes, including parabolic, flattop and triangular waveform generations, depending on the amplitude profile of the in-cavity spectral filter [1]. As an application of this general approach, we show that the use of an in-cavity flat-top spectral filter makes it possible to directly generate sinc-shaped Nyquist pulses of high quality and of a widely tunable bandwidth from the laser [2]. We also report on a recently-developed versatile erbium-doped fibre laser, in which conventional soliton, dispersion-managed soliton (stretched-pulse) and dissipative soliton mode-locking regimes can be selectively and reliably targeted by programming different group-velocity dispersion profiles and bandwidths on an in-cavity programmable filter [3]. Further, we report on our recent results on the passive mode locking of a Raman fibre laser by a recently predicted new type of parametric instability – the dissipative Faraday instability [4], where spatially periodic zig-zag modulation of spectrally dependent losses can lead to pattern formation in the temporal domain. High-order harmonic mode locking is achieved in a very simple experimental configuration, with the laser cavity including an optical fibre and two chirped fibre Bragg gratings, and no additional mode-locking elements. The results not only open up new possibilities for the design of mode-locked lasers, but extend beyond fibre optics to other fields of physics and engineering. References [1] S. Boscolo, C. Finot, H. Karakuzu, P. Petropoulos, “Pulse shaping in mode-locked fiber laser by in-cavity spectral filter,” Opt. Lett., vol. 39, pp. 438–441, 2014. [2] S. Boscolo, C. Finot, S. K. Turitsyn, “Bandwidth programmable optical Nyquist pulse generation in passively mode-locked fiber laser,” IEEE Photon. J., vol. 7, 7802008(8), 2015. [3] J. Peng, S. Boscolo, “Filter-based dispersion-managed versatile ultrafast fibre laser,” Sci. Rep., 2016, In press. [4] A. M. Perego, N. Tarasov, D. V. Churkin, S. K. Turitsyn, K. Staliunas, “Pattern generation by dissipative parametric instability,” Phys. Rev. Lett., vol. 116, 028701, 2016.

A Harrod modell strukturális stabilitása (Structural stability of the Harrod model)

In this study it is shown that the nontrivial hyperbolic fixed point of a nonlinear dynamical system, which is formulated by means of the adaptive expectations, corresponds to the unstable equilibrium of Harrod. We prove that this nonlinear dynamical (in the sense of Harrod) model is structurally stable under suitable economic conditions. In the case of structural stability, small changes of the functions (C1-perturbations of the vector field) describing the expected and the true time variation of the capital coefficients do not influence the qualitative properties of the endogenous variables, that is, although the trajectories may slightly change, their structure is the same as that of the unperturbed one, and therefore these models are suitable for long-time predictions. In this situation the critique of Lucas or Engel is not valid. There is no topological conjugacy between the perturbed and unperturbed models; the change of the growth rate between two levels may require different times for the perturbed and unperturbed models.

A C80 DSP-based active vision system for real-time tracking

[EN]Active Vision Systems can be considered as dynamical systems which close the loop around artificial visual perception, controlling camera parameters, motion and also controlling processing to simplify, accelerate and do more robust visual perception. Research and Development in Active Vision Systems [Aloi87], [Bajc88] is a main area of interest in Computer Vision, mainly by its potential application in different scenarios where real-time performance is needed such as robot navigation, surveillance, visual inspection, among many others. Several systems have been developed during last years using robotic-heads for this purpose...

Passivity Framework for Modeling, Composing and Mitigating Cyber Attacks

Thesis (Ph.D.)--University of Washington, 2016-08

Quantification of the human postural control system to perturbations

Human standing posture is inherently unstable. The postural control system (PCS), which maintains standing posture, is composed of the sensory, musculoskeletal, and central nervous systems. Together these systems integrate sensory afferents and generate appropriate motor efferents to adjust posture. The PCS maintains the body center of mass (COM) with respect to the base of support while constantly resisting destabilizing forces from internal and external perturbations. To assess the human PCS, postural sway during quiet standing or in response to external perturbation have frequently been examined descriptively. Minimal work has been done to understand and quantify the robustness of the PCS to perturbations. Further, there have been some previous attempts to assess the dynamical systems aspects of the PCS or time evolutionary properties of postural sway. However those techniques can only provide summary information about the PCS characteristics; they cannot provide specific information about or recreate the actual sway behavior. This dissertation consists of two parts: part I, the development of two novel methods to assess the human PCS and, part II, the application of these methods. In study 1, a systematic method for analyzing the human PCS during perturbed stance was developed. A mild impulsive perturbation that subjects can easily experience in their daily lives was used. A measure of robustness of the PCS, 1/MaxSens that was based on the inverse of the sensitivity of the system, was introduced. 1/MaxSens successfully quantified the reduced robustness to external perturbations due to age-related degradation of the PCS. In study 2, a stochastic model was used to better understand the human PCS in terms of dynamical systems aspect. This methodology also has the advantage over previous methods in that the sway behavior is captured in a model that can be used to recreate the random oscillatory properties of the PCS. The invariant density which describes the long-term stationary behavior of the center of pressure (COP) was computed from a Markov chain model that was applied to postural sway data during quiet stance. In order to validate the Invariant Density Analysis (IDA), we applied the technique to COP data from different age groups. We found that older adults swayed farther from the centroid and in more stochastic and random manner than young adults. In part II, the tools developed in part I were applied to both occupational and clinical situations. In study 3, 1/MaxSens and IDA were applied to a population of firefighters to investigate the effects of air bottle configuration (weight and size) and vision on the postural stability of firefighters. We found that both air bottle weight and loss of vision, but not size of air bottle, significantly decreased balance performance and increased fall risk. In study 4, IDA was applied to data collected on 444 community-dwelling elderly adults from the MOBILIZE Boston Study. Four out of five IDA parameters were able to successfully differentiate recurrent fallers from non-fallers, while only five out of 30 more common descriptive and stochastic COP measures could distinguish the two groups. Fall history and the IDA parameter of entropy were found to be significant risk factors for falls. This research proposed a new measure for the PCS robustness (1/MaxSens) and a new technique for quantifying the dynamical systems aspect of the PCS (IDA). These new PCS analysis techniques provide easy and effective ways to assess the PCS in occupational and clinical environments.

Absolutely Continuous Spectrum for Parabolic Flows/Maps

This work is devoted to creating an abstract framework for the study of certain spectral properties of parabolic systems. Specifically, we determine under which general conditions to expect the presence of absolutely continuous spectral measures. We use these general conditions to derive results for spectral properties of time-changes of unipotent flows on homogeneous spaces of semisimple groups regarding absolutely continuous spectrum as well as maximal spectral type; the time-changes of the horocycle flow are special cases of this general category of flows. In addition we use the general conditions to derive spectral results for twisted horocycle flows and to rederive spectral results for skew products over translations and Furstenberg transformations.