Wavelike patterns in precessing elliptical rings for swarming systems

A continuum model for a swarm of devices is investigated with the devices moving along precessing elliptical Earth-centered orbits. Wavelike patterns in these precessing elliptical rings with peaks in swarm density are found that can be used to provide enhanced coverage for Earth observation and space science. Two orbital models are considered for the purpose of comparison: perturbed by J2J2 and solar radiation pressure, and perturbed by J2J2 and J3J3, respectively, each with a different frozen eccentricity. By removing osculating orbital elements, only the long-period orbit eccentricity and argument of perigee are chosen to derive closed-form solutions to the continuum model for the swarm density. Zero-density lines in the swarm density are found, as well as infinite density at certain boundaries. Comparison between the analytic and numerical number density evolutions is made to yield the range of applicable eccentricity based on the maximum error tolerance, as well as the minimum number of swarm members required to approximate continuous evolution. Closed-form solutions are then derived to predict the number density of swarm devices for magnetic-tail measurement and Earth-observation applications

Variational wave functions of a vortex in cyclotron motion

In two dimensions the microscopic theory, which provides a basis for the naive analogy between a quantized vortex in a superfluid and an electron in an uniform magnetic field, is presented. A one-to-one correspondence between the rotational states of a vortex in a cylinder and the cyclotron states of an electron in the central gauge is found. Like the Landau levels of an electron, the energy levels of a vortex are highly degenerate. However, the gap between two adjacent energy levels does not only depend on the quantized circulation, but also increases with the energy, and scales with the size of the vortex.Comment: LaTeX, 4 pages, 2 EPS figures, To appear in ``Series on Advances in Quantum Many-Body Theory'' ed. by R.F. Bishop, C.E. Campbell, J.W. Clark and S. Fantoni (World Scientific, 2000

Compensatory Proliferation Induced by Cell Death in the Drosophila Wing Disc Requires Activity of the Apical Cell Death Caspase Dronc in a Nonapoptotic Role

Achieving proper organ size requires a balance between proliferation and cell death. For example, at least 40%–60% of cells in the Drosophila wing disc can be lost, yet these discs go on to give rise to normal-looking adult wings as a result of compensatory proliferation 1, 2, 3. The signals that drive this proliferation are unknown. One intriguing possibility is that they derive, at least in part, from the dying cells. To explore this hypothesis, we activated cell death signaling in specific populations of cells in the developing wing but prevented these cells from dying through expression of the baculovirus p35 protein, which inhibits the activity of effector caspases that mediate apoptosis [4]. This allowed us to uncouple the activation steps of apoptosis from death itself. Here we report that stimulation of cell death signaling in the wing disc—in the absence of cell death—results in increased proliferation and ectopic expression of Wingless, a known mitogen in the wing. Activation of the apical cell death caspase Dronc is necessary and sufficient to drive both of these processes. Our results demonstrate an unanticipated function, the nonautonomous induction of proliferation, of an apical cell death caspase. This activity is likely to contribute to tissue homeostasis by promoting local compensatory proliferation in response to cell death. We speculate that dying cells may communicate cell fate or behavior instructions to their neighbors in other contexts as well

Cooperative hunting in a discrete predator-prey system

We propose and investigate a discrete-time predator-prey system with cooperative hunting in the predator population. The model is constructed from the classical Nicholson-Bailey host-parasitoid system with density dependent growth rate. A sufficient condition based on the model parameters for which both populations can coexist is derived, namely that the predator's maximal reproductive number exceeds one. We study existence of interior steady states and their stability in certain parameter regimes. It is shown that the system behaves asymptotically similar to the model with no cooperative hunting if the degree of cooperation is small. Large cooperative hunting, however, may promote persistence of the predator for which the predator would otherwise go extinct if there were no cooperation

Sparse Codes for Speech Predict Spectrotemporal Receptive Fields in the Inferior Colliculus

We have developed a sparse mathematical representation of speech that minimizes the number of active model neurons needed to represent typical speech sounds. The model learns several well-known acoustic features of speech such as harmonic stacks, formants, onsets and terminations, but we also find more exotic structures in the spectrogram representation of sound such as localized checkerboard patterns and frequency-modulated excitatory subregions flanked by suppressive sidebands. Moreover, several of these novel features resemble neuronal receptive fields reported in the Inferior Colliculus (IC), as well as auditory thalamus and cortex, and our model neurons exhibit the same tradeoff in spectrotemporal resolution as has been observed in IC. To our knowledge, this is the first demonstration that receptive fields of neurons in the ascending mammalian auditory pathway beyond the auditory nerve can be predicted based on coding principles and the statistical properties of recorded sounds.Comment: For Supporting Information, see PLoS website: http://www.ploscompbiol.org/article/info%3Adoi%2F10.1371%2Fjournal.pcbi.100259

Local Density of States and Angle-Resolved Photoemission Spectral Function of an Inhomogeneous D-wave Superconductor

Nanoscale inhomogeneity seems to be a central feature of the d-wave superconductivity in the cuprates. Such a feature can strongly affect the local density of states (LDOS) and the spectral weight functions. Within the Bogoliubov-de Gennes formalism we examine various inhomogeneous configurations of the superconducting order parameter to see which ones better agree with the experimental data. Nanoscale large amplitude oscillations in the order parameter seem to fit the LDOS data for the underdoped cuprates. The one-particle spectral function for a general inhomogeneous configuration exhibits a coherent peak in the nodal direction. In contrast, the spectral function in the antinodal region is easily rendered incoherent by the inhomogeneity. This throws new light on the dichotomy between the nodal and antinodal quasiparticles in the underdoped cuprates.Comment: 5 pages, 9 pictures. Phys. Rev. B (in press

Epidemic Variability in Hierarchical Geographical Networks with Human Activity Patterns

Recently, some studies have revealed that non-Poissonian statistics of human behaviors stem from the hierarchical geographical network structure. On this view, we focus on epidemic spreading in the hierarchical geographical networks, and study how two distinct contact patterns (i. e., homogeneous time delay (HOTD) and heterogeneous time delay (HETD) associated with geographical distance) influence the spreading speed and the variability of outbreaks. We find that, compared with HOTD and null model, correlations between time delay and network hierarchy in HETD remarkably slow down epidemic spreading, and result in a upward cascading multi-modal phenomenon. Proportionately, the variability of outbreaks in HETD has the lower value, but several comparable peaks for a long time, which makes the long-term prediction of epidemic spreading hard. When a seed (i. e., the initial infected node) is from the high layers of networks, epidemic spreading is remarkably promoted. Interestingly, distinct trends of variabilities in two contact patterns emerge: high-layer seeds in HOTD result in the lower variabilities, the case of HETD is opposite. More importantly, the variabilities of high-layer seeds in HETD are much greater than that in HOTD, which implies the unpredictability of epidemic spreading in hierarchical geographical networks