Search Results (12 total)

We study a locally nonconservative self-organized branching process (SOBP) in an open system of excitable agents exhibiting spontaneous excitation and deexcitation. The SOBP achieves criticality even in the absence of energy conservation as the population relaxes to a stable state with no overexcited agent. Criticality is widely thought to happen only in a locally conservative SOBP. Our model explains the observed characteristic size in the size distribution of tuna fish schools and the neuronal avalanches in cortical networks.

Animal and human clusters are complex adaptive systems and many organize in cluster sizes s that obey the frequency distribution D(s)∝s^−τ. The exponent τ describes the relative abundance of the cluster sizes in a given system. Data analyses reveal that real-world clusters exhibit a broad spectrum of τ values, 0.7 (tuna fish schools) ≤τ≤4.61 (T4 bacteriophage gene family sizes). Allelomimesis is proposed as an underlying mechanism for adaptation that explains the observed broad τ spectrum. Allelomimesis is the tendency of an individual to imitate the actions of others and two cluster systems have different τ values when their component agents display unequal degrees of allelomimetic tendencies. Cluster formation by allelomimesis is shown to be of three general types: namely, blind copying, information-use copying, and noncopying. Allelomimetic adaptation also reveals that the most stable cluster size is formed by three strongly allelomimetic individuals. Our finding is consistent with available field data taken from killer whales and marmots.

Via the Richards-Wolf vector diffraction theory, we analyze the three-dimensional intensity distribution of the focal volume that is produced by a strongly focused 750-nm beam of ultrafast, Gaussian-shaped optical pulses (10^-9 s>~ pulse width τ>~1 fs=10^-15 s). Knowledge of the three-dimensional distribution near focus is essential in determining the diffraction-limited resolution of an optical microscope. The optical spectrum of a short pulse is characterized by side frequencies about the carrier frequency. The effect of spectral broadening on the focused intensity distribution is evaluated via the Linfoot’s criteria of fidelity, structural content, and correlation quality and with reference to a 750-nm cw focused beam. Different values are considered for τ and numerical aperture of the focusing lens (0.1<~X_NA<~1.2). At X_NA=0.8, rapid deterioration of the focused intensity distribution is observed at τ=1.2 fs. This happens because a 750-nm optical pulse with τ=1.2 fs has an associated coherence length of 359.7 nm which is less than the Nyquist sampling interval of 375 nm that is required to sample 750 nm sinusoid without loss of information. The ill-effects of spectral broadening is weaker in two-photon excitation microscope than in its single-photon counterpart for the same focusing lens and light source.

High-resolution segregation is demonstrated for elastic granular materials of the same mass and size. Each grain starts at a randomly selected position in the entrance facet of a cylinder, accelerates downwards due to gravity, and then bounces against a massive obstacle with a collision cross section that is proportional to the facet size. Bounce dynamics of the falling grain is a function of its relative elasticity with the obstacle. Subsequent collisions of the grain with the wall are assumed to be perfectly elastic. In the absence of interparticle collisions, grain focusing occurs at points along the cylinder axis. In the absence of rotation, focusing occurs regardless of the initial locations and (downward) velocities of the grains at the entrance facet. The focus location depends only on the coefficient of restitution of the falling particle and the obstacle size. Grains arrive at the focus in temporally localized bursts even if released simultaneously from the facet. Efficient segregation is, therefore, achieved without additional mechanical work (e.g., shaking, spinning) on the system configuration.

We show that the generalization capability of a mature thresholding neural network to process above-threshold disturbances in a noise-free environment is extended to subthreshold disturbances by ambient noise without retraining. The ability to benefit from noise is intrinsic and does not have to be learned separately. Nonlinear dependence of sensitivity with noise strength is significantly narrower than in individual threshold systems. Noise has a minimal effect on network performance for above-threshold signals. We resolve two seemingly contradictory responses of trained networks to noise—their ability to benefit from its presence and their robustness against noisy strong disturbances.

We model the emergence of hysteresis as a collective behavior in a lattice network of individually nonhysteretic agents with continuous responses. The emergence, which depends on the agent’s characteristic response to an external input, is optimized at a finite interaction size of the Moore neighborhood. The network also exhibits rich behavior including power-law variations, chaos, and system saturation. Our model is used to describe the hysteresis and high-frequency fluctuations in the oxygen isotope variation ( δ¹⁸O) data of ice (Greenland Ice Core Project) that exhibit the Younger Dryas cold event.

We show a new approach for solving the N-body problems based on neural networks. Without loss of generality, we derived a network solution for the time-dependent positions of N bodies in self-gravitating systems. The simulation is limited to a system of collisionless disks—a case for determining the spatial distributions of dark matter and in reproducing global effects such as formation of spiral galaxies. Our approach yields a solution that is analytic with time-reversed path-tracing capabilities that could lead to new findings in the study of the collective behavior of N-body systems.

We present a method for directly obtaining the 2M equally sampled amplitude values of the analog input signal s(t) from the 2M locations {t_i} where it intersects with a reference signal r(t)=A cos(2πf_rt). Until now, high-accuracy signal recovery in sinusoid-crossing sampling had been achieved only indirectly using spectral methods. The recovery requirements are (1) |s(t)|<A and (2) W<~2 f_r where W is the bandwidth of s(t). The recovery method is evaluated as a function of the accuracy in which the crossings are located, and the sampling period T=2MΔ, where Δ=1/2 f_r. Its performance is also compared with other direct interpolation schemes.

The detection threshold B of a sinusoid-crossing (SC) detector is improved using a new dithering technique. In a real SC detector, B is always greater than zero because the crossings could be located only with finite accuracy. Dithering is employed to determine the frequency f_s and the amplitude A_s of the subthreshold oscillation s(t)=A_s cos(2πf_st), where A_s<B. The data representation of an analog input signal of bandlimit W, consists of locations {t₁,t₂,…,t_2M}={t_i} where the signal intersects with the reference sinusoid r(t)=A cos(2πf_rt). A crossing exists within each interval Δ=1/2 f_r=T/2M, where T is the sampling period. If W/2<~f_r, and the signal amplitude is less than A for all t values within T, then SC sampling satisfies the Nyquist sampling theorem. The unknown f_s value is determined from the power spectrum of the crossing locations of [s(t)+n_σ(t)], where n_σ(t) is the noise of variance σ². The A_s value is approximated from the signal-to-noise ratio (R) vs σ plot. The performance of the technique is studied from the R plots for different A_s, f_s, and T values.

The method of Lagrange multipliers is utilized in the unsupervised training of a three-layer, single-output, feed-forward neural network for characterizing the dynamics of constrained physical systems. Training aims at minimizing the energy function that is obtained from the equations of state which are generated using the method of Lagrange multipliers. The approach is illustrated (1) to solve an inverse problem in nuclear reactor design, (2) to determine how competing biological entities organized (cells in a tissue, Eucalyptus trees), and (3) to solve an ill-posed differential equation.

A three-layer network that utilizes Hopfield encoding neurons [J. J Hopfield, Nature 376, 33 (1995)], is designed to compute the Fourier spectrum of an analog input signal of duration T. Each of the 2M (integer M≳0) Hopfield neurons in the input layer, is linked to an exclusive decoder with its output connected to all the 4M neurons present in the output layer. The connection strength between a decoder and a target neuron in the output layer (hereby called the output neuron), is characterized by a coupling constant which attenuates the decoder output that reaches the output neuron. All the attenuated 2M decoder signals reaching an output neuron are summed up within an integration time given by the period of the oscillatory drive of the Hopfield neuron. The frequency resolution and bandwidth of the analyzer network are given by 1/T and 2M/T, respectively. The first 2M output neurons yield the amplitudes of the real components of the Fourier spectrum, while the next 2M output neurons give the amplitudes of the corresponding imaginary components. Experiments show that the network exhibits an exponentially decaying learning error, and is capable of learning the general properties of Fourier transform from a limited set of examples. © 1996 The American Physical Society.

We show that the wavelet transforms of an analog signal f_a(t) can be computed directly and efficiently from a data representation consisting only of locations {t_i}, where f_a(t) intersects with the reference sinusoid r(t) of frequency W and amplitude A. To achieve a measurement bandwidth of W, one crossing must occur within each interval Δ=1/2W. This is satisfied when A≥‖f_a(t)‖ for all f_a(t) values within the sampling period T. A total of 2M sinusoid crossings occur within T. Crossing-based wavelet analysis is demonstrated with respect to the sombrero-shaped wavelet, using 256 crossings of an interferogram signal. © 1996 The American Physical Society.