Loss of lamin A function increases chromatin dynamics in the nuclear interior.

Chromatin is organized in a highly ordered yet dynamic manner in the cell nucleus, but the principles governing this organization remain unclear. Similarly, it is unknown whether, and how, various proteins regulate chromatin motion and as a result influence nuclear organization. Here by studying the dynamics of different genomic regions in the nucleus of live cells, we show that the genome has highly constrained dynamics. Interestingly, depletion of lamin A strikingly alters genome dynamics, inducing a dramatic transition from slow anomalous diffusion to fast and normal diffusion. In contrast, depletion of LAP2α, a protein that interacts with lamin A and chromatin, has no such effect on genome dynamics. We speculate that chromosomal inter-chain interactions formed by lamin A throughout the nucleus contribute to chromatin dynamics, and suggest that the molecular regulation of chromatin diffusion by lamin A in the nuclear interior is critical for the maintenance of genome organization.

Coupled lasers: phase versus chaos synchronization.

The synchronization of chaotic lasers and the optical phase synchronization of light originating in multiple coupled lasers have both been extensively studied. However, the interplay between these two phenomena, especially at the network level, is unexplored. Here, we experimentally compare these phenomena by controlling the heterogeneity of the coupling delay times of two lasers. While chaotic lasers exhibit deterioration in synchronization as the time delay heterogeneity increases, phase synchronization is found to be independent of heterogeneity. The experimental results are found to be in agreement with numerical simulations for semiconductor lasers.

Random symmetry breaking and freezing in chaotic networks.

Parameter space of a driven damped oscillator in a double well potential presents either a chaotic trajectory with sign oscillating amplitude or a nonchaotic trajectory with a fixed sign amplitude. A network of such delay coupled damped oscillators is shown to present chaotic dynamics while the sign amplitude of each damped oscillator is randomly frozen. This phenomenon of random broken global symmetry of the network simultaneous with random freezing of each degree of freedom is accompanied by the existence of exponentially many randomly frozen chaotic attractors with the size of the network. Results are exemplified by a network of modified Duffing oscillators with infinite range pseudoinverse delayed interactions.

Sensitivity of global network dynamics to local parameters versus motif structure in a cortexlike neuronal model.

In the field of network dynamics it has been suggested that statistical information of motifs, small subnetworks, can help in understanding global activity of the entire network. We present a counterexample where the relation between the stable synchronized activity modes and network connectivity was studied using the Hodgkin-Huxley brain dynamics model. Simulations indicate that small motifs of three nodes exhibit different synchronization modes depending on their local parameters such as delays, synaptic strength, and external drives. Thus the activity of a complex network composed of interconnected motifs cannot be extracted from the activity mode of each individual motif and is governed by local parameters. Finally, we exemplify how local dynamics ultimately enriches the ability of a network to generate diverse modes with a given motif structure.

Synchronization in small networks of time-delay coupled chaotic diode lasers.

Topologies of two, three and four time-delay-coupled chaotic semiconductor lasers are experimentally and theoretically found to show new types of synchronization. Generalized zero-lag synchronization is observed for two lasers separated by long distances even when their self-feedback delays are not equal. Generalized sub-lattice synchronization is observed for quadrilateral geometries while the equilateral triangle is zero-lag synchronized. Generalized zero-lag synchronization, without the limitation of precisely matched delays, opens possibilities for advanced multi-user communication protocols.

Synchronization of chaotic networks with time-delayed couplings: an analytic study.

Networks of nonlinear units with time-delayed couplings can synchronize to a common chaotic trajectory. Although the delay time may be very large, the units can synchronize completely without time shift. For networks of coupled Bernoulli maps, analytic results are derived for the stability of the chaotic synchronization manifold. For a single delay time, chaos synchronization is related to the spectral gap of the coupling matrix. For networks with multiple delay times, analytic results are obtained from the theory of polynomials. Finally, the analytic results are compared with networks of iterated tent maps and Lang-Kobayashi equations, which imitate the behavior of networks of semiconductor lasers.

Coexistence of exponentially many chaotic spin-glass attractors.

A chaotic network of size N with delayed interactions which resembles a pseudoinverse associative memory neural network is investigated. For a load α = P/N < 1, where P stands for the number of stored patterns, the chaotic network functions as an associative memory of 2P attractors with macroscopic basin of attractions which decrease with α. At finite α, a chaotic spin-glass phase exists, where the number of distinct chaotic attractors scales exponentially with N. Each attractor is characterized by a coexistence of chaotic behavior and freezing of each one of the N chaotic units or freezing with respect to the P patterns. Results are supported by large scale simulations of networks composed of Bernoulli map units and Mackey-Glass time delay differential equations.

Zero lag synchronization of chaotic systems with time delayed couplings.

Zero-lag synchronization (ZLS) between chaotic units, which do not have self-feedback or a relay unit connecting them, is experimentally demonstrated for two mutually coupled chaotic semiconductor lasers. The mechanism is based on two mutual coupling delay times with certain allowed integer ratios, whereas for a single mutual delay time ZLS cannot be achieved. This mechanism is also found numerically for mutually coupled chaotic maps where its stability is analyzed using the Schur-Cohn theorem for the roots of polynomials. The symmetry of the polynomials allows only specific integer ratios for ZLS. In addition, we present a general argument for ZLS when several mutual coupling delay times are present.

On chaos synchronization and secure communication.

Chaos synchronization, in particular isochronal synchronization of two chaotic trajectories to each other, may be used to build a means of secure communication over a public channel. In this paper, we give an overview of coupling schemes of Bernoulli units deduced from chaotic laser systems, different ways to transmit information by chaos synchronization and the advantage of bidirectional over unidirectional coupling with respect to secure communication. We present the protocol for using dynamical private commutative filters for tap-proof transmission of information that maps the task of a passive attacker to the class of non-deterministic polynomial time-complete problems.

Ultrahigh-speed random number generation based on a chaotic semiconductor laser.

The fluctuating intensity of a chaotic semiconductor laser is used for generating random sequences at rates up to 12.5 Gbits/s. The conversion of the fluctuating intensity to a random bit sequence can be implemented in either software or hardware and the overall rate of generation is much faster than any previously reported random number generator based on a physical mechanism. The generator's simplicity, robustness, and insensitivity to control parameters should enable its application to tasks of secure communication and calculation procedures requiring ultrahigh-speed generation of random bit sequences.

Synchronization of networks of chaotic units with time-delayed couplings.

A network of chaotic units is investigated where the units are coupled by signals with a transmission delay. Any arbitrary finite network is considered where the chaotic trajectories of the uncoupled units are a solution of the dynamic equations of the network. It is shown that chaotic trajectories cannot be synchronized if the transmission delay is larger than the time scales of the individual units. For several models the master stability function is calculated which determines the maximal delay time for which synchronization is possible.

Phase synchronization in mutually coupled chaotic diode lasers.

Semiconductor lasers with optical feedback have chaotically pulsating output behavior. When two similar chaotic lasers are optically coupled, they can become synchronized in their optical fluctuations. Here we show that the synchronization is not only in the amplitude and in the timing of the pulses but that the short pulses are also phase coherent with each other. This is true even when the lasers are separated by distances much larger than their coherence length.

Influence of intraventricular fibrinolytic therapy with rt-PA on the long-term outcome of treated patients with spontaneous basal ganglia hemorrhage: a case-control study.

Over the recent years, fibrinolytic agents have been tested for intraventricular clot fibrinolysis (IVF). Compared with patients who did not receive IVF, administration of rt-PA induces rapid resorption of intraventricular blood and normalization of cerebrospinal fluid (CSF) circulation resulting in a reduced 30-day mortality and beneficial short-term outcome after 3 months. Our objective was to analyze possible influences of IVF on the long-term outcome after 12 months. Based on a prospective data base, patients with ganglionic supratentorial hematoma with additional intraventricular hemorrhage and occlusive hydrocephalus (n = 135) were isolated. Twenty-seven patients received IVF. To design a case-control study, we carefully matched 22 controls without IVF with regard to hematoma volume, Graeb score, Glasgow Coma Scale on admission and age (five patients remained unmatchable). We determined clinical and imaging parameters by reviewing the medical records and CT scans of all included patients. Outcome after 12 months was evaluated using the modified Rankin scale (mRS). One multivariate regression analysis was performed to determine predisposing factors for outcome. IVF significantly reduced Graeb score during treatment (eight on admission, three after IVF, one prior to discharge in the treated group versus 8/6/2 in patients without IVF). In patients with IVF requirement, a second external ventricular drainage (EVD) and a ventriculoperitoneal (VP) shunt were reduced (P = 0.08) and the incidence of a lumbar drainage was significantly higher (P < 0.01), whilst the overall time of extra-corporal CSF drainage was comparable. EVD associated complications were equal in both groups. Overall long-term outcome was poor but no significant differences were found between patients with and without IVF (mRS 4-6: 12/22 (54%) in patients with and 13/22 (59%) in patients without IVF; P = 0.81). The five excluded patients with IVF were similar to the 22 included ones with respect to imaging findings and outcome. The multivariate analysis revealed age and baseline hematoma volume, but not IVF to significantly impact the outcome. In accordance with previous studies, IVF hastened clot lysis and reduced the need for repeated EVD exchanges and permanent shunting. However, despite these advantages, IVF did not influence long-term outcome after 12 months. The results of the prospective randomized trial (Clot Lysis: Evaluating Accelerated Resolution of Intraventricular Hemorrhage) need to be awaited.

Statistical properties of contact vectors.

We study the statistical properties of contact vectors, a construct to characterize a protein's structure. The contact vector of an N-residue protein is a list of N integers n(i), representing the number of residues in contact with residue i. We study analytically (at mean-field level) and numerically the amount of structural information contained in a contact vector. Analytical calculations reveal that a large variance in the contact numbers reduces the degeneracy of the mapping between contact vectors and structures. Exact enumeration for lengths up to N=16 on the three-dimensional cubic lattice indicates that the growth rate of number of contact vectors as a function of N is only 3% less than that for contact maps. In particular, for compact structures we present numerical evidence that, practically, each contact vector corresponds to only a handful of structures. We discuss how this information can be used for better structure prediction.

Secure key-exchange protocol with an absence of injective functions.

The security of neural cryptography is investigated. A key-exchange protocol over a public channel is studied where the parties exchanging secret messages use multilayer neural networks which are trained by their mutual output bits and synchronize to a time dependent secret key. The weights of the networks have integer values between +/-L. Recently an algorithm for an eavesdropper which could break the key was introduced by [A. Shamir, A. Mityagin, and A. Klimov, Ramp Session (Eurocrypt, Amsterdam, 2002)]. We show that the synchronization time increases with L2 while the probability to find a successful attacker decreases exponentially with L. Hence for large L we find a secure key-exchange protocol which depends neither on number theory nor on injective trapdoor functions used in conventional cryptography.

Training a perceptron in a discrete weight space.

Learning in a perceptron having a discrete weight space, where each weight can take 2L+1 different values, is examined analytically and numerically. The learning algorithm is based on the training of the continuous perceptron and prediction following the clipped weights. The learning is described by a new set of order parameters, composed of the overlaps between the teacher and the continuous/clipped students. Different scenarios are examined, among them on-line learning with discrete and continuous transfer functions. The generalization error of the clipped weights decays asymptotically as exp(-Kalpha(2)) in the case of on-line learning with binary activation functions and exp(-e(|lambda|alpha)) in the case of on-line learning with continuous one, where alpha is the number of examples divided by N, the size of the input vector and K is a positive constant. For finite N and L, perfect agreement between the discrete student and the teacher is obtained for alpha~Lsqrt[ln(NL)]. A crossover to the generalization error approximately 1/alpha, characterizing continuous weights with binary output, is obtained for synaptic depth L>O(sqrt[N]).

Multilayer neural networks with extensively many hidden units.

The information processing abilities of a multilayer neural network with a number of hidden units scaling as the input dimension are studied using statistical mechanics methods. The mapping from the input layer to the hidden units is performed by general symmetric Boolean functions, whereas the hidden layer is connected to the output by either discrete or continuous couplings. Introducing an overlap in the space of Boolean functions as order parameter, the storage capacity is found to scale with the logarithm of the number of implementable Boolean functions. The generalization behavior is smooth for continuous couplings and shows a discontinuous transition to perfect generalization for discrete ones.

Generation of unpredictable time series by a neural network.

A perceptron that "learns" the opposite of its own output is used to generate a time series. We analyze properties of the weight vector and the generated sequence, such as the cycle length and the probability distribution of generated sequences. A remarkable suppression of the autocorrelation function is explained, and connections to the Bernasconi model are discussed. If a continuous transfer function is used, the system displays chaotic and intermittent behavior, with the product of the learning rate and amplification as a control parameter.

Multichoice minority game.

The generalization of the problem of adaptive competition, known as the minority game, to the case of K possible choices for each player, is addressed, and applied to a system of interacting perceptrons with input and output units of a type of K-state Potts spins. An optimal solution of this minority game, as well as the dynamic evolution of the adaptive strategies of the players, are solved analytically for a general K and compared with numerical simulations.