Synchronization of dynamical hypernetworks: dimensionality reduction through simultaneous block-diagonalization of matrices

We present a general framework to study stability of the synchronous solution for a hypernetwork of coupled dynamical systems. We are able to reduce the dimensionality of the problem by using simultaneous block-diagonalization of matrices. We obtain necessary and sufficient conditions for stability of the synchronous solution in terms of a set of lower-dimensional problems and test the predictions of our low-dimensional analysis through numerical simulations. Under certain conditions, this technique may yield a substantial reduction of the dimensionality of the problem. For example, for a class of dynamical hypernetworks analyzed in the paper, we discover that arbitrarily large networks can be reduced to a collection of subsystems of dimensionality no more than 2. We apply our reduction techique to a number of different examples, including a class of undirected unweighted hypermotifs of three nodes.Comment: 9 pages, 6 figures, accepted for publication in Phys. Rev.

Limits on Hot Galactic Halo Gas from X-ray Absorption Lines

Although the existence of large-scale hot gaseous halos around massive disk galaxies have been theorized for a long time, there is yet very little observational evidence. We report the Chandra and XMM-Newton grating spectral detection of OVII and NeIX Kalpha absorption lines along the sight-line of 4U 1957+11. The line absorption is consistent with the interstellar medium in origin. Attributing these line absorptions to the hot gas associated with the Galactic disk, we search for the gaseous halo around the Milky Way by comparing this sight-line with more distant ones (toward X-ray binary LMC X-3 and the AGN Mrk 421). We find that all the line absorptions along the LMC X-3 and Mrk 421 sight-lines are attributable to the hot gas in a thick Galactic disk, as traced by the absorption lines in the spectra of 4U~1957+11 after a Galactic latitude dependent correction. We constrain the OVII column density through the halo to be N(OVII) < 5E15 cm^{-2} (95% confidence limit), and conclude that the hot gas contribution to the metal line absorptions, if existing, is negligible.Comment: 4 pages, Accepted for publication in the ApJ Letters, no change except for fixing a typo in an author's nam

Spatially Resolved Chandra HETG Spectroscopy of the NLR Ionization Cone in NGC 1068

We present initial results from a new 440-ks Chandra HETG GTO observation of the canonical Seyfert 2 galaxy NGC 1068. The proximity of NGC 1068, together with Chandra's superb spatial and spectral resolution, allow an unprecedented view of its nucleus and circumnuclear NLR. We perform the first spatially resolved high-resolution X-ray spectroscopy of the `ionization cone' in any AGN, and use the sensitive line diagnostics offered by the HETG to measure the ionization state, density, and temperature at discrete points along the ionized NLR. We argue that the NLR takes the form of outflowing photoionized gas, rather than gas that has been collisionally ionized by the small-scale radio jet in NGC 1068. We investigate evidence for any velocity gradients in the outflow, and describe our next steps in modeling the spatially resolved spectra as a function of distance from the nucleus.Comment: 5 pages, 2 figures, 1 video. To appear in refereed Proceedings of "X-ray Astronomy 2009: Present Status, Multi-Wavelength Approach and Future Perspectives", Bologna, Italy, September 7-11, 2009, AIP, eds. A. Comastri, M. Cappi, and L. Angelin

aCGHViewer: A Generic Visualization Tool For aCGH data

Array-Comparative Genomic Hybridization (aCGH) is a powerful high throughput technology for detecting chromosomal copy number aberrations (CNAs) in cancer, aiming at identifying related critical genes from the affected genomic regions. However, advancing from a dataset with thousands of tabular lines to a few candidate genes can be an onerous and time-consuming process. To expedite the aCGH data analysis process, we have developed a user-friendly aCGH data viewer (aCGHViewer) as a conduit between the aCGH data tables and a genome browser. The data from a given aCGH analysis are displayed in a genomic view comprised of individual chromosome panels which can be rapidly scanned for interesting features. A chromosome panel containing a feature of interest can be selected to launch a detail window for that single chromosome. Selecting a data point of interest in the detail window launches a query to the UCSC or NCBI genome browser to allow the user to explore the gene content in the chromosomal region. Additionally, aCGHViewer can display aCGH and expression array data concurrently to visually correlate the two. aCGHViewer is a stand alone Java visualization application that should be used in conjunction with separate statistical programs. It operates on all major computer platforms and is freely available at http://falcon.roswellpark.org/aCGHview/

Scale-free correlations in the dynamics of a small (N ~ 10000) cortical network

The advent of novel opto-genetics technology allows the recording of brain activity with a resolution never seen before. The characterisation of these very large data sets offers new challenges as well as unique theory-testing opportunities. Here we discuss whether the spatial and temporal correlation of the collective activity of thousands of neurons are tangled as predicted by the theory of critical phenomena. The analysis shows that both, the correlation length $\xi$ and the correlation time $\tau$ scale as predicted as a function of the system size. With some peculiarities that we discuss, the analysis uncovers new evidence consistent with the view that the large scale brain cortical dynamics corresponds to critical phenomena.Comment: 8 pages, 6 figure

Memory Effects in Granular Material

We present a combined experimental and theoretical study of memory effects in vibration-induced compaction of granular materials. In particular, the response of the system to an abrupt change in shaking intensity is measured. At short times after the perturbation a granular analog of aging in glasses is observed. Using a simple two-state model, we are able to explain this short-time response. We also discuss the possibility for the system to obey an approximate pseudo-fluctuation-dissipation theorem relationship and relate our work to earlier experimental and theoretical studies of the problem.Comment: 5 pages, 4 figures, reference list change

Nanoscale chemical imaging by photoinduced force microscopy.

Correlating spatial chemical information with the morphology of closely packed nanostructures remains a challenge for the scientific community. For example, supramolecular self-assembly, which provides a powerful and low-cost way to create nanoscale patterns and engineered nanostructures, is not easily interrogated in real space via existing nondestructive techniques based on optics or electrons. A novel scanning probe technique called infrared photoinduced force microscopy (IR PiFM) directly measures the photoinduced polarizability of the sample in the near field by detecting the time-integrated force between the tip and the sample. By imaging at multiple IR wavelengths corresponding to absorption peaks of different chemical species, PiFM has demonstrated the ability to spatially map nm-scale patterns of the individual chemical components of two different types of self-assembled block copolymer films. With chemical-specific nanometer-scale imaging, PiFM provides a powerful new analytical method for deepening our understanding of nanomaterials

Spatially Resolved Chandra HETG Spectroscopy of the NLR Ionization Cone in NGC 1068

We present initial results from a new 440-ks Chandra HETG GTO observation of the canonical Seyfert 2 galaxy NGC 1068. The proximity of NGC 1068, together with Chandra's superb spatial and spectral resolution, allow an unprecedented view of its nucleus and circumnuclear NLR. We perform the first spatially resolved high-resolution X-ray spectroscopy of the `ionization cone' in any AGN, and use the sensitive line diagnostics offered by the HETG to measure the ionization state, density, and temperature at discrete points along the ionized NLR. We argue that the NLR takes the form of outflowing photoionized gas, rather than gas that has been collisionally ionized by the small-scale radio jet in NGC 1068. We investigate evidence for any velocity gradients in the outflow, and describe our next steps in modeling the spatially resolved spectra as a function of distance from the nucleus

Searching for AGN Outflows: Spatially Resolved Chandra HETG Spectroscopy of the NLR Ionization Cone in NGC 1068

We present initial results from a new 440-ks Chandra HETG GTO observation of the canonical Seyfert 2 galaxy NGC 1068. The proximity of NGC 1068, together with Chandra’s superb spatial and spectral resolution, allow an unprecedented view of its nucleus and circumnuclear NLR. We perform the first spatially resolved high-resolution X-ray spectroscopy of the ‘ionization cone’ in any AGN, and use the sensitive line diagnostics offered by the HETG to measure the ionization state, density, and temperature at discrete points along the ionized NLR. We argue that the NLR takes the form of outflowing photoionized gas, rather than gas that has been collisionally ionized by the small-scale radio jet in NGC 1068. We investigate evidence for any velocity gradients in the outflow, and describe our next steps in modeling the spatially resolved spectra as a function of distance from the nucleus

Social Experiments in the Mesoscale: Humans Playing a Spatial Prisoner's Dilemma

Background: The evolutionary origin of cooperation among unrelated individuals remains a key unsolved issue across several disciplines. Prominent among the several mechanisms proposed to explain how cooperation can emerge is the existence of a population structure that determines the interactions among individuals. Many models have explored analytically and by simulation the effects of such a structure, particularly in the framework of the Prisoner’s Dilemma, but the results of these models largely depend on details such as the type of spatial structure or the evolutionary dynamics. Therefore, experimental work suitably designed to address this question is needed to probe these issues. Methods and Findings: We have designed an experiment to test the emergence of cooperation when humans play Prisoner’s Dilemma on a network whose size is comparable to that of simulations. We find that the cooperation level declines to an asymptotic state with low but nonzero cooperation. Regarding players ’ behavior, we observe that the population is heterogeneous, consisting of a high percentage of defectors, a smaller one of cooperators, and a large group that shares features of the conditional cooperators of public goods games. We propose an agent-based model based on the coexistence of these different strategies that is in good agreement with all the experimental observations. Conclusions: In our large experimental setup, cooperation was not promoted by the existence of a lattice beyond a residual level (around 20%) typical of public goods experiments. Our findings also indicate that both heterogeneity and a ‘‘moody’