Convex integration for Lipschitz mappings and counterexamples to regularity

We study Lispchitz solutions of partial differential relations $\nabla u\in K$, where $u$ is a vector-valued function in an open subset of $R^n$. In some cases the set of solutions turns out to be surprisingly large. The general theory is then used to construct counter-examples to regularity of solutions of Euler-Lagrange systems satisfying classical ellipticity conditions.Comment: 28 pages published versio

Submillimeter polarization and variability of quasar PKS 1830-211

Polarization from active galactic nuclei is interpreted as a signpost of the role of magnetic fields in the launch and collimation of their relativistic radio jets. Here, we report the detection of a clear polarization signal from ALMA observations of the gravitationally lensed quasar PKS 1830-211 at submillimeter wavelengths (Band 9, 650 GHz). Applying a differential-polarimetry technique to the two compact lensed images of the quasar, we estimate a fractional polarization of ~5% for one lensed image, while the other appears nearly unpolarized, which implies that the polarization activity varies on a timescale of a few weeks. With additional ALMA Band 7 and 8 (between 300-500 GHz) concomitant data, we constrain a Faraday rotation of a few $10^5$ rad m$^{-2}$. We also observe flux-density variability of ~10% within one hour in Band 9. This work illustrates that a differential analysis can extract high-accuracy information (flux-density ratio and polarimetry) free of calibration issues from resolved sources in the submillimeter domain.Comment: 7 pages, 6 figures, accepted for publications in A&

Using gravitational lensed images to investigate the intrinsic AGN variability

We discuss about how the relative flux densities among the images of gravitationally-lensed active galactic nuclei, AGN, can be used to study the intrinsic AGN variability with high accuracy. Multi-frequency monitoring observations of resolved gravitational lenses can allow us to detect signals of very weak variability and also provide information about the jet opacity and structure. As an example, we investigate the variability of the flux-density ratio between the two lensed images of the blazar B0218+357, using dual-frequency cm-wave observations. Similar to our previously reported submm-wave observations of the lensed blazar PKS1830-211, we observe a clear chromatic variability, starting short before an increase in the flux-density of the blazar. The evolution of the flux-density ratios between the blazar images shows a more clear and rich structure than that of the mere lightcurves of each individual image. The accuracy in the ratio measurements is allowing us to see variability episodes in the blazar that are weaker than the natural scatter in the absolute flux-density measurements. A simple opacity model in the jet is used to consistently explain the difference between the flux-density-ratio evolution at the two frequencies.Comment: 5 pages, 2 figures. Accepted for publication in A&A. Final versio

Sequential Sparsening by Successive Adaptation in Neural Populations

In the principal cells of the insect mushroom body, the Kenyon cells (KC), olfactory information is represented by a spatially and temporally sparse code. Each odor stimulus will activate only a small portion of neurons and each stimulus leads to only a short phasic response following stimulus onset irrespective of the actual duration of a constant stimulus. The mechanisms responsible for the sparse code in the KCs are yet unresolved. Here, we explore the role of the neuron-intrinsic mechanism of spike-frequency adaptation (SFA) in producing temporally sparse responses to sensory stimulation in higher processing stages. Our single neuron model is defined through a conductance-based integrate-and-fire neuron with spike-frequency adaptation [1]. We study a fully connected feed-forward network architecture in coarse analogy to the insect olfactory pathway. A first layer of ten neurons represents the projection neurons (PNs) of the antenna lobe. All PNs receive a step-like input from the olfactory receptor neurons, which was realized by independent Poisson processes. The second layer represents 100 KCs which converge onto ten neurons in the output layer which represents the population of mushroom body extrinsic neurons (ENs). Our simulation result matches with the experimental observations. In particular, intracellular recordings of PNs show a clear phasic-tonic response that outlasts the stimulus [2] while extracellular recordings from KCs in the locust express sharp transient responses [3]. We conclude that the neuron-intrinsic mechanism is can explain a progressive temporal response sparsening in the insect olfactory system. Further experimental work is needed to test this hypothesis empirically. [1] Muller et. al., Neural Comput, 19(11):2958-3010, 2007. [2] Assisi et. al., Nat Neurosci, 10(9):1176-1184, 2007. [3] Krofczik et. al. Front. Comput. Neurosci., 2(9), 2009.Comment: 5 pages, 2 figures, This manuscript was submitted for review to the Eighteenth Annual Computational Neuroscience Meeting CNS*2009 in Berlin and accepted for oral presentation at the meetin

Isotopic ratios at z=0.68 from molecular absorption lines toward B 0218+357

Isotopic ratios of heavy elements are a key signature of the nucleosynthesis processes in stellar interiors. The contribution of successive generations of stars to the metal enrichment of the Universe is imprinted on the evolution of isotopic ratios over time. We investigate the isotopic ratios of carbon, nitrogen, oxygen, and sulfur through millimeter molecular absorption lines arising in the z=0.68 absorber toward the blazar B 0218+357. We find that these ratios differ from those observed in the Galactic interstellar medium, but are remarkably close to those in the only other source at intermediate redshift for which isotopic ratios have been measured to date, the z=0.89 absorber in front of PKS1830-211. The isotopic ratios in these two absorbers should reflect enrichment mostly from massive stars, and they are indeed close to the values observed toward local starburst galaxies. Our measurements set constraints on nucleosynthesis and chemical evolution models.Comment: Accepted for publication in Astronomy & Astrophysics; 10 pages, 9 figure

What is the temperature in heavy ion collisions?

We consider the Tsallis distribution as the source of the apparent slope of one-particle spectra in heavy-ion collisions and investigate the equation of state of this special quark matter in the framework of non-extensive thermodynamics.Comment: Talk given by T.S.Biro at RHIC School 2003, Dec.8-11, 2003, Budapest, Hungar

Void Scaling and Void Profiles in CDM Models

An analysis of voids using cosmological N-body simulations of cold dark matter models is presented. It employs a robust statistics of voids, that was recently applied to discriminate between data from the Las Campanas Redshift Survey and different cosmological models. Here we extend the analysis to 3D and show that typical void sizes D in the simulated galaxy samples obey a linear scaling relation with the mean galaxy separation lambda: D=D_0+nu*lambda. It has the same slope nu as in 2D, but with lower absolute void sizes. The scaling relation is able to discriminate between different cosmologies. For the best standard LCDM model, the slope of the scaling relation for voids in the dark matter halos is too steep as compared to the LCRS, with too small void sizes for well sampled data sets. The scaling relation of voids for dark matter halos with increasing mass thresholds is even steeper than that for samples of galaxy-mass halos where we sparse sample the data. This shows the stronger clustering of more massive halos. Further, we find a correlation of the void size to its central and environmental average density. While there is little sign of an evolution in samples of small DM halos with v_{circ} ~ 90 km/s, voids in halos with circular velocity over 200 km/s are larger at redshift z = 3 due to the smaller halo number density. The flow of dark matter from the underdense to overdense regions in an early established network of large scale structure is also imprinted in the evolution of the density profiles with a relative density decrease in void centers by 0.18 per redshift unit between z=3 and z=0.Comment: 12 pages, 9 eps figures, submitted to MNRA