Statistical properties of Lorenz like flows, recent developments and perspectives

We comment on mathematical results about the statistical behavior of Lorenz equations an its attractor, and more generally to the class of singular hyperbolic systems. The mathematical theory of such kind of systems turned out to be surprisingly difficult. It is remarkable that a rigorous proof of the existence of the Lorenz attractor was presented only around the year 2000 with a computer assisted proof together with an extension of the hyperbolic theory developed to encompass attractors robustly containing equilibria. We present some of the main results on the statisitcal behavior of such systems. We show that for attractors of three-dimensional flows, robust chaotic behavior is equivalent to the existence of certain hyperbolic structures, known as singular-hyperbolicity. These structures, in turn, are associated to the existence of physical measures: \emph{in low dimensions, robust chaotic behavior for flows ensures the existence of a physical measure}. We then give more details on recent results on the dynamics of singular-hyperbolic (Lorenz-like) attractors.Comment: 40 pages; 10 figures; Keywords: sensitive dependence on initial conditions, physical measure, singular-hyperbolicity, expansiveness, robust attractor, robust chaotic flow, positive Lyapunov exponent, large deviations, hitting and recurrence times. Minor typos corrected and precise acknowledgments of financial support added. To appear in Int J of Bif and Chaos in App Sciences and Engineerin

Cluster spacecraft observations of a ULF wave enhanced by Space Plasma Exploration by Active Radar (SPEAR)

Space Plasma Exploration by Active Radar (SPEAR) is a high-latitude ionospheric heating facility capable of exciting ULF waves on local magnetic field lines. We examine an interval from 1 February 2006 when SPEAR was transmitting a 1 Hz modulation signal with a 10 min on-off cycle. Ground magnetometer data indicated that SPEAR modulated currents in the local ionosphere at 1 Hz, and enhanced a natural field line resonance with a 10 min period. During this interval the Cluster spacecraft passed over the heater site. Signatures of the SPEAR-enhanced field line resonance were present in the magnetic field data measured by the magnetometer on-board Cluster-2. These are the first joint ground- and space-based detections of field line tagging by SPEAR

Modelling spatial biodiversity in the world’s largest mangrove ecosystem-The Bangladesh Sundarbans: a baseline for conservation

Aim: Mangrove forests are among the most threatened and rapidly vanishing, but poorly understood ecosystems. We aim to uncover the variables driving mangrove biodiversity and produce baseline biodiversity maps for the Sundarbans world heritage site—the Earth's largest contiguous mangrove ecosystem. Location: The Bangladesh Sundarbans, South Asia. Methods: We collected species abundance, environmental and disturbance data from 110 permanent sample plots (PSPs) covering the entire Bangladesh Sundarbans (6,017 km2). We applied generalized additive models to determine the key variables shaping the spatial distributions of mangrove diversity and community composition. Biodiversity maps were constructed using covariate‐driven habitat models, and their predictive performances were compared with covariate‐free (i.e., direct interpolation) approaches to see whether the inclusion of habitat variables bolster spatial predictions of biodiversity or whether we can rely on direct interpolation approaches when environmental data are not available. Results: Historical forest exploitation, disease, siltation and soil alkalinity were the key stressors causing loss of alpha and gamma diversity in mangrove communities. Both alpha and gamma diversity increased along the downstream‐to‐upstream and riverbank‐to‐forest interior gradients. Mangrove communities subjected to intensive past tree harvesting, disease outbreaks and siltation were more homogeneous in species composition (beta diversity). In contrast, heterogeneity in species composition increased along decreasing salinity and downstream‐to‐upstream gradients. We find that the surviving biodiversity hotspots (comprising many globally endangered tree species) are located outside the established protected area network and hence open to human exploitation. We therefore suggest bringing them immediately under protected area management. Main Conclusions: We provide the first habitat‐based modelling and mapping of alpha, beta and gamma diversity in threatened mangrove communities. In general, habitat‐based models showed better predictive ability than the covariate‐free approach. Nevertheless, the small margin of differences between the approaches demonstrates the utility of direct interpolation approaches when environmental data are unavailable

A nonstationary generalization of the Kerr congruence

Making use of the Kerr theorem for shear-free null congruences and of Newman's representation for a virtual charge ``moving'' in complex space-time, we obtain an axisymmetric time-dependent generalization of the Kerr congruence, with a singular ring uniformly contracting to a point and expanding then to infinity. Electromagnetic and complex eikonal field distributions are naturally associated with the obtained congruence, with electric charge being necesssarily unit (``elementary''). We conjecture that the corresponding solution to the Einstein-Maxwell equations could describe the process of continious transition of the naked ringlike singularitiy into a rotating black hole and vice versa, under a particular current radius of the singular ring.Comment: 6 pages, twocolum

On two-dimensional surface attractors and repellers on 3-manifolds

We show that if $f: M^3\to M^3$ is an $A$-diffeomorphism with a surface two-dimensional attractor or repeller $\mathcal B$ and $M^2_ \mathcal B$ is a supporting surface for $\mathcal B$, then $\mathcal B = M^2_{\mathcal B}$ and there is $k\geq 1$ such that: 1) $M^2_{\mathcal B}$ is a union $M^2_1\cup...\cup M^2_k$ of disjoint tame surfaces such that every $M^2_i$ is homeomorphic to the 2-torus $T^2$. 2) the restriction of $f^k$ to $M^2_i$ $(i\in\{1,...,k\})$ is conjugate to Anosov automorphism of $T^2$

String amplitudes in arbitrary dimensions

We calculate gravitational dressed tachyon correlators in non critcal dimensions. The 2D gravity part of our theory is constrained to constant curvature. Then scaling dimensions of gravitational dressed vertex operators are equal to their bare conformal dimensions. Considering the model as d+2 dimensional critical string we calculate poles of generalized Shapiro-Virasoro amplitudes.Comment: 14 page

Radio Observations of the Hubble Deep Field South Region III: The 2.5, 5.2 and 8.7 GHz Catalogues and Radio Source Properties

Deep radio observations of a wide region centred on the Hubble Deep Field South have been performed, providing one of the most sensitive set of radio observations acquired on the Australia Telescope Compact Array to date. A central rms of ~10 microJy is reached at four frequencies (1.4, 2.5, 5.2 and 8.7 GHz). In this paper the full source catalogues from the 2.5, 5.2 and 8.7 GHz observations are presented to complement Paper II, along with a detailed analysis of image quality and noise. We produce a consolidated catalogue by matching sources across all four frequencies of our survey. Radio spectral indices are used to investigate the nature of the radio sources and identify a number of sources with flat or inverted radio spectra, which indicates AGN activity. We also find several other interesting sources, including a broadline emitting radio galaxy, a giant radio galaxy and three Gigahertz Peaked Spectrum sources.Comment: Accepted by AJ. 13 figures and 13 table

BATSE observations of BL Lac Objects

The Burst and Transient Source Experiment (BATSE) on the Compton Gamma-Ray Observatory has been shown to be sensitive to non-transient hard X-ray sources in our galaxy, down to flux levels of 100 mCrab for daily measurements, 3 mCrab for integrations over several years. We use the continuous BATSE database and the Earth Occultation technique to extract average flux values between 20 and 200 keV from complete radio- and X-ray- selected BL Lac samples over a 2 year period

On the Hardness of SAT with Community Structure

Recent attempts to explain the effectiveness of Boolean satisfiability (SAT) solvers based on conflict-driven clause learning (CDCL) on large industrial benchmarks have focused on the concept of community structure. Specifically, industrial benchmarks have been empirically found to have good community structure, and experiments seem to show a correlation between such structure and the efficiency of CDCL. However, in this paper we establish hardness results suggesting that community structure is not sufficient to explain the success of CDCL in practice. First, we formally characterize a property shared by a wide class of metrics capturing community structure, including "modularity". Next, we show that the SAT instances with good community structure according to any metric with this property are still NP-hard. Finally, we study a class of random instances generated from the "pseudo-industrial" community attachment model of Gir\'aldez-Cru and Levy. We prove that, with high probability, instances from this model that have relatively few communities but are still highly modular require exponentially long resolution proofs and so are hard for CDCL. We also present experimental evidence that our result continues to hold for instances with many more communities. This indicates that actual industrial instances easily solved by CDCL may have some other relevant structure not captured by the community attachment model.Comment: 23 pages. Full version of a SAT 2016 pape