Abstract:
In this report, we describe the system integration of a complementary metal oxide semiconductor (CMOS) integrated circuit (IC) chip, capable of both stimulation and recording of neurons or neural tissues, to investigate electrical signal propagation within cellular networks in vitro. The overall system consisted of three major subunits: a 5.0 × 5.0 mm CMOS IC chip, a reconfigurable logic device (field-programmable gate array, FPGA), and a PC. To test the system, microelectrode arrays (MEAs) were used to extracellularly measure the activity of cultured rat cortical neurons and mouse cortical slices. The MEA had 64 bidirectional (stimulation and recording) electrodes. In addition, the CMOS IC chip was equipped with dedicated analog filters, amplification stages, and a stimulation buffer. Signals from the electrodes were sampled at 15.6 kHz with 16-bit resolution. The measured input-referred circuitry noise was 10.1 μ V root mean square (10 Hz to 100 kHz), which allowed reliable detection of neural signals ranging from several millivolts down to approximately 33 μ Vpp. Experiments were performed involving the stimulation of neurons with several spatiotemporal patterns and the recording of the triggered activity. An advantage over current MEAs, as demonstrated by our experiments, includes the ability to stimulate (voltage stimulation, 5-bit resolution) spatiotemporal patterns in arbitrary subsets of electrodes. Furthermore, the fast stimulation reset mechanism allowed us to record neuronal signals from a stimulating electrode around 3 ms after stimulation. We demonstrate that the system can be directly applied to, for example, auditory neural prostheses in conjunction with an acoustic sensor and a sound processing system.

Abstract:
Fractalization of torus and its transition to chaos in a quasi-periodically forced logistic map is re-investigated in relation with a strange nonchaotic attractor, with the aid of functional equation for the invariant curve. Existence of fractal torus in an interval in parameter space is confirmed by the length and the number of extrema of the torus attractor, as well as the Fourier mode analysis. Mechanisms of the onset of fractal torus and the transition to chaos are studied in connection with the intermittency.

Abstract:
Slow parameter drift is common in many systems (e.g., the amount of greenhouse gases in the terrestrial atmosphere is increasing). In such situations, the attractor on which the system trajectory lies can be destroyed, and the trajectory will then go to another attractor of the system. We consider the case where there are more than one of these possible final attractors, and we ask whether we can control the outcome (i.e., the attractor that ultimately captures the trajectory) using only small controlling perturbations. Specifically, we consider the problem of controlling a noisy system whose parameter slowly drifts through a saddle-node bifurcation taking place on a fractal boundary between the basins of multiple attractors. We show that, when the noise level is low, a small perturbation of size comparable to the noise amplitude applied at a single point in time can ensure that the system will evolve toward a target attracting state with high probability. For a range of noise levels, we find that the minimum size of perturbation required for control is much smaller within a time period that starts some time after the bifurcation, providing a "window of opportunity" for driving the system toward a desirable state. We refer to this procedure as tipping point control.

Abstract:
We investigate linear parabolic maps on the torus. In a generic case these maps are non-invertible and discontinuous. Although the metric entropy of these systems is equal to zero, their dynamics is non-trivial due to folding of the image of the unit square into the torus. We study the structure of the maximal invariant set, and in a generic case we prove the sensitive dependence on the initial conditions. We study the decay of correlations and the diffusion in the corresponding system on the plane. We also demonstrate how the rationality of the real numbers defining the map influences the dynamical properties of the system.

Abstract:
Introduction: Although inhalational anesthesia and nitrousoxide (N_{2}O) are known to affect the intraocular pressure (IOP), little is known about the effect of nitrousoxide on the IOP during sevoflurane and remifentanil anesthesia. In the present study, we examined the effect of balanced anesthesia on the IOP. Materials and Methods: After obtaining informed consent, the patients undergoing abdominal surgery under general anesthesia were divided into two groups: N_{2}O group (n = 10) and control group (n = 12). General anesthesia was maintained with remifentanil (0.05 - 0.3 μg/kg/min), 33% O_{2} and 1.2% sevoflurane to keep ETCO_{2} of 35 - 40 mmHg following tracheal intubation. After baseline measurement of IOP (T0, 20 minutes after injection of anesthesia), the patients in the N_{2}O group received 67% nitrousoxide, and the patients in the control group received air, with O_{2} and 1.2% sevoflurane. Then, IOP was measured at 1 hour (T1), 2 hours (T2), and 3 hours (T3) after anesthesia induction in the supineposition. Blood pressure and heart rate were recorded at the same time interval. Results: There was no significant difference in the IOP at any period between the two groups. In both groups, the IOP at the T3 was significantly higher than that at T0. Conclusion: These results suggest that N2O does not affect the IOP in patients undergoing abdominal surgery under sevoflurane and remifentanil anesthesia.

Abstract:
To understand the formation, evolution, and function of complex systems, it is crucial to understand the internal organization of their interaction networks. Partly due to the impossibility of visualizing large complex networks, resolving network structure remains a challenging problem. Here we overcome this difficulty by combining the visual pattern recognition ability of humans with the high processing speed of computers to develop an exploratory method for discovering groups of nodes characterized by common network properties, including but not limited to communities of densely connected nodes. Without any prior information about the nature of the groups, the method simultaneously identifies the number of groups, the group assignment, and the properties that define these groups. The results of applying our method to real networks suggest the possibility that most group structures lurk undiscovered in the fast-growing inventory of social, biological, and technological networks of scientific interest.

Abstract:
The dynamics of power-grid networks is becoming an increasingly active area of research within the physics and network science communities. The results from such studies are typically insightful and illustrative, but are often based on simplifying assumptions that can be either difficult to assess or not fully justified for realistic applications. Here we perform a comprehensive comparative analysis of three leading models recently used to study synchronization dynamics in power-grid networks -- a fundamental problem of practical significance given that frequency synchronization of all power generators in the same interconnection is a necessary condition for a power grid to operate. We show that each of these models can be derived from first principles within a common framework based on the classical model of a generator, thereby clarifying all assumptions involved. This framework allows us to view power grids as complex networks of coupled second-order phase oscillators with both forcing and damping terms. Using simple illustrative examples, test systems, and real power-grid datasets, we study the inherent frequencies of the oscillators as well as their coupling structure, comparing across the different models. We demonstrate, in particular, that if the network structure is not homogeneous, generators with identical parameters need to be modeled as non-identical oscillators in general. We also discuss an approach to estimate the required (dynamical) parameters that are unavailable in typical power-grid datasets, their use for computing the constants of each of the three models, and an open-source MATLAB toolbox that we provide for these computations.

Abstract:
Synchronization, in which individual dynamical units keep in pace with each other in a decentralized fashion, depends both on the dynamical units and on the properties of the interaction network. Yet, the role played by the network has resisted comprehensive characterization within the prevailing paradigm that interactions facilitating pair-wise synchronization also facilitate collective synchronization. Here we challenge this paradigm and show that networks with best complete synchronization, least coupling cost, and maximum dynamical robustness, have arbitrary complexity but quantized total interaction strength that constrains the allowed number of connections. It stems from this characterization that negative interactions as well as link removals can be used to systematically improve and optimize synchronization properties in both directed and undirected networks. These results extend the recently discovered compensatory perturbations in metabolic networks to the realm of oscillator networks and demonstrate why "less can be more" in network synchronization.

Abstract:
We consider two optimization problems on synchronization of oscillator networks: maximization of synchronizability and minimization of synchronization cost. We first develop an extension of the well-known master stability framework to the case of non-diagonalizable Laplacian matrices. We then show that the solution sets of the two optimization problems coincide and are simultaneously characterized by a simple condition on the Laplacian eigenvalues. Among the optimal networks, we identify a subclass of hierarchical networks, characterized by the absence of feedback loops and the normalization of inputs. We show that most optimal networks are directed and non-diagonalizable, necessitating the extension of the framework. We also show how oriented spanning trees can be used to explicitly and systematically construct optimal networks under network topological constraints. Our results may provide insights into the evolutionary origin of structures in complex networks for which synchronization plays a significant role.

Abstract:
We consider the problem of maximizing the synchronizability of oscillator networks by assigning weights and directions to the links of a given interaction topology. We first extend the well-known master stability formalism to the case of non-diagonalizable networks. We then show that, unless some oscillator is connected to all the others, networks of maximum synchronizability are necessarily non-diagonalizable and can always be obtained by imposing unidirectional information flow with normalized input strengths. The extension makes the formalism applicable to all possible network structures, while the maximization results provide insights into hierarchical structures observed in complex networks in which synchronization plays a significant role.