Fast Synchronization of Perpetual Grouping in Laminar Visual Cortical Circuits

Perceptual grouping is well-known to be a fundamental process during visual perception, notably grouping across scenic regions that do not receive contrastive visual inputs. Illusory contours are a classical example of such groupings. Recent psychophysical and neurophysiological evidence have shown that the grouping process can facilitate rapid synchronization of the cells that are bound together by a grouping, even when the grouping must be completed across regions that receive no contrastive inputs. Synchronous grouping can hereby bind together different object parts that may have become desynchronized due to a variety of factors, and can enhance the efficiency of cortical transmission. Neural models of perceptual grouping have clarified how such fast synchronization may occur by using bipole grouping cells, whose predicted properties have been supported by psychophysical, anatomical, and neurophysiological experiments. These models have not, however, incorporated some of the realistic constraints on which groupings in the brain are conditioned, notably the measured spatial extent of long-range interactions in layer 2/3 of a grouping network, and realistic synaptic and axonal signaling delays within and across cells in different cortical layers. This work addresses the question: Can long-range interactions that obey the bipole constraint achieve fast synchronization under realistic anatomical and neurophysiological constraints that initially desynchronize grouping signals? Can the cells that synchronize retain their analog sensitivity to changing input amplitudes? Can the grouping process complete and synchronize illusory contours across gaps in bottom-up inputs? Our simulations show that the answer to these questions is Yes.Office of Naval Research (N00014-01-1-0624); Air Force Office of Scientific Research (F49620-01-1-03097

Periodic Sequences of Arbitrage: A Tale of Four Currencies

This paper investigates arbitrage chains involving four currencies and four foreign exchange trader-arbitrageurs. In contrast with the three-currency case, we find that arbitrage operations when four currencies are present may appear periodic in nature, and not involve smooth convergence to a "balanced" ensemble of exchange rates in which the law of one price holds. The goal of this article is to understand some interesting features of sequences of arbitrage operations, features which might well be relevant in other contexts in finance and economics.Comment: 35 pages, 48 bibliography references, submitted to Metroeconomic

Periodic Sequences of Arbitrage: A Tale of Four Currencies

This paper investigates arbitrage chains involving four currencies and four foreign exchange trader-arbitrageurs. In contrast with the three-currency case, we find that arbitrage operations when four currencies are present may appear periodic in nature, and not involve smooth convergence to a "balanced" ensemble of exchange rates in which the law of one price holds. The goal of this article is to understand some interesting features of sequences of arbitrage operations, features which might well be relevant in other contexts in finance and economics.Comment: 35 pages, 48 bibliography references, submitted to Metroeconomic

Recovery time after localized perturbations in complex dynamical networks

Maintaining the synchronous motion of dynamical systems interacting on complex networks is often critical to their functionality. However, real-world networked dynamical systems operating synchronously are prone to random perturbations driving the system to arbitrary states within the corresponding basin of attraction, thereby leading to epochs of desynchronized dynamics with a priori unknown durations. Thus, it is highly relevant to have an estimate of the duration of such transient phases before the system returns to synchrony, following a random perturbation to the dynamical state of any particular node of the network. We address this issue here by proposing the framework of single-node recovery time (SNRT) which provides an estimate of the relative time scales underlying the transient dynamics of the nodes of a network during its restoration to synchrony. We utilize this in differentiating the particularly slow nodes of the network from the relatively fast nodes, thus identifying the critical nodes which when perturbed lead to significantly enlarged recovery time of the system before resuming synchronized operation. Further, we reveal explicit relationships between the SNRT values of a network, and its global relaxation time when starting all the nodes from random initial conditions. Earlier work on relaxation time generally focused on investigating its dependence on macroscopic topological properties of the respective network. However, we employ the proposed concept for deducing microscopic relationships between topological features of nodes and their respective SNRT values. The framework of SNRT is further extended to a measure of resilience of the different nodes of a networked dynamical system. We demonstrate the potential of SNRT in networks of Rössler oscillators on paradigmatic topologies and a model of the power grid of the United Kingdom with second-order Kuramoto-type nodal dynamics illustrating the conceivable practical applicability of the proposed concept.Bundesministerium für Bildung und Forschunghttps://doi.org/10.13039/501100002347Deutsche Forschungsgemeinschafthttps://doi.org/10.13039/501100001659Peer Reviewe

Periodic Sequences of Arbitrage: A Tale of Four Currencies

This paper investigates arbitrage chains involving four currencies and four foreign ex-change trader-arbitrageurs. In contrast with the three-currency case, we find that arbitrage operations when four currencies are present may appear periodic in nature, and not involve smooth convergence to a "balanced" ensemble of exchange rates in which the law of one price holds. The goal of this article is to understand some interesting features of sequences of arbitrage operations, features which might well be relevant in other contexts in finance and economics.Limits to arbitrage, Four currencies, Recurrent sequences, Asynchronous systems

Passive heaving of elliptical cylinders with active pitching – From cylinders towards flapping foils

This paper presents a study of the flow past elastically mounted cylinders with prescribed rotational oscillation about the cylinder centre, which are free to heave, or oscillate transverse to the flow. The configuration serves as an idealized model of a flapping-foil energy harvester. A range of geometries are tested, from the circular cylinder with an aspect ratio of 1.0 to elliptical cylinders up to aspect ratio of 6.0 approaching a flat plate. The driving frequency of the rotational oscillation is varied, while the amplitude of rotation is fixed at π/2, meaning both axes of the geometries present fully to the oncoming flow each cycle. The Reynolds number is 200. The natural frequency of the elastic-mounting is set to the Strouhal frequency for a circular cylinder. The ratio of the mass of the cylinder to the mass of the equivalent volume of displaced fluid is set to 5.0. Configurations with zero-damping reveal a rich parameter space, with increasing cross-stream oscillation with increasing geometry aspect ratio. Driving frequencies for peak oscillation amplitude are grouped around a driving frequency of 0.9 times the natural frequency of the elastic structure. The variation of the power input to actuate the rotational oscillation of the cylinder is also analysed. The fluid structure interaction is analysed for energy harvesting potential; power output is modelled by linear damping on the heave. Increasing the damping on the structure leads to optimal values of driving frequency and damping for each aspect ratio tested. For each aspect ratio, comparisons are drawn and similarities found between these optimal cases for power output and the undamped cases for maximum oscillation amplitude and velocity. The study of the parameter space serves as a useful starting point for further study of the many parameters affecting the performance of flapping-foil energy harvesting

Position estimation from direction or range measurements

International audienceThis paper revisits the problems of estimating the position of an object moving in n (≥ 2)-dimensional Euclidean space using velocity measurements and either direction or range measurements of one or multiple source points. The proposed solutions exploit the Continuous Riccati Equation (CRE) to calculate observer gains yielding global uniform exponential stability of zero estimation errors, also when the measured velocity is biased by an unknown constant vector or when direction measurements are corrupted by an unknown constant bias. With respect to prior contributions on these subjects they provide a coherent generalization of existing solutions with the preoccupation of pointing out general and explicit persistent excitation (p.e.) conditions whose satisfaction ensures uniform exponential stability of the observers

Riccati observers for position and velocity bias estimation from either direction or range measurements

This paper revisits the problems of estimating the position of an object moving in n (≥ 2)-dimensional Euclidean space using velocity measurements and either direction or range measurements of one or multiple source points. The proposed solutions exploit the Continuous Riccati Equation (CRE) to calculate observer gains yielding global exponential stability of zero estimation errors, even in the case where the measured velocity is biased by an unknown constant perturbation. These results are obtained under persistent excitation (p.e.) conditions depending on the number of source points and body motion that ensure both uniform observability and good conditioning of the CRE solutions. With respect to prior contributions on these subjects some of the proposed solutions are entirely novel while others are adapted from existing ones with the preoccupation of stating simpler and more explicit conditions under which uniform exponential stability is achieved. A complementary contribution, related to the delicate tuning of the observers gains, is the derivation of a lower-bound of the exponential rate of convergence specified as a function of the amount of persistent excitation. Simulation results illustrate the performance of the proposed observers

Wave transport in parity-time symmetric, time-varying, and quasi-periodic systems

The past several decades have witnessed a rapid growth of research interest in the fields of artificial materials and systems, in particular in the areas of parity-time symmetric systems, time-varying systems and quasi-periodic systems. These newly developed material platforms have been enabling many exotic wave-matter interaction phenomena unavailable in nature. In this context, I investigated a series of wave transport and scattering phenomena in parity-time symmetric, time-varying and quasi periodic systems in this dissertation. First, I proposed a sensing circuit based on sixth-order exceptional point (EP), which supports high sensitivity, resolution, and nondegraded thermal noise performance compared with conventional diabolic point (DP) sensing system. I also studied the influence of thermal noise in a general two-level sensing platform based on EP. Second, I demonstrated a robust microwave tunneling device operating in the extreme case in which the transmission channel is shorted through a small reactance. We observed full restoration of information and overall transparency to an external observer through use of a pair of parity-time-symmetric emitter and absorber. Third, I studied the effects of realistic switching parameters and synchronization in a series of nonreciprocal devices based on synchronized loss modulation. The research showed that the nonreciprocal response of these systems experiences a linear regression of insertion loss and isolation with respect to the timing error among switches. Remarkably, impedance matching, and nonreciprocal phase shifts are immune from synchronization issues, and reasonable levels of synchronization errors still guarantee low insertion loss and good isolation. Fourth, I studied wave scattering phenomena in static and dynamic quasi-periodic LC resonator array, which provides an easily accessible and reconfigurable platform to study fractal energy band and topological edge state. Overall, my explorations have been enabling a new degree of control of waves in circuits and metamaterials, pushing forward the opportunities for extreme wave-matter interactions using gain and time modulations.Electrical and Computer Engineerin