Revisiting Complex Moments For 2D Shape Representation and Image Normalization

When comparing 2D shapes, a key issue is their normalization. Translation and scale are easily taken care of by removing the mean and normalizing the energy. However, defining and computing the orientation of a 2D shape is not so simple. In fact, although for elongated shapes the principal axis can be used to define one of two possible orientations, there is no such tool for general shapes. As we show in the paper, previous approaches fail to compute the orientation of even noiseless observations of simple shapes. We address this problem. In the paper, we show how to uniquely define the orientation of an arbitrary 2D shape, in terms of what we call its Principal Moments. We show that a small subset of these moments suffice to represent the underlying 2D shape and propose a new method to efficiently compute the shape orientation: Principal Moment Analysis. Finally, we discuss how this method can further be applied to normalize grey-level images. Besides the theoretical proof of correctness, we describe experiments demonstrating robustness to noise and illustrating the method with real images.Comment: 69 pages, 20 figure

Optimized frequency comb spectrum of parametrically modulated bottle microresonators

The formation of optical frequency combs (OFCs) by the parametric modulation of optical microresonators is commonly described by lumped-parameter models. However, these models do not consider the actual spatial distribution of the parametric modulation (SDPM). Here, we show that the effect of the SDPM becomes of special importance for an elongated SNAP bottle microresonator (SBM) having shallow nanometre-scale effective radius variation along its axial length. The advantage of SBMs compared to microresonators with different shapes (e.g., spherical and toroidal) is that SBMs, remaining miniature, can have resonant spectrum with much smaller free spectral range and no dispersion. Therefore, SBMs can be used to generate OFCs with much lower repetition rates. We consider the resonant and adiabatic modulation of parabolic SBMs and show that it is possible to improve the flatness and increase the bandwidth of the generated OFC spectra by optimising the SDPM. We suggest that the determined optimal SDPM can be experimentally realized using piezoelectric, radiation pressure, and electro-optical excitation of an SBM.Comment: 16 pages, 6 figure

Continuous spectra in high-harmonic generation driven by multicycle laser pulses

We present observations of the emission of XUV continua in the 20-37 eV region by high harmonic generation (HHG) with $4$-$7\ \mathrm{fs}$ pulses focused onto a Kr gas jet. The underlying mechanism relies on coherent control of the relative delays and phases between individually generated attosecond pulse, achievable by adjusting the chirp of the driving pulses and the interaction geometry. Under adequate negative chirp and phase matching conditions, the resulting interpulse interference yields a continuum XUV spectrum, which is due to both microscopic and macroscopic (propagation) contributions. This technique opens the route for modifying the phase of individual attosecond pulses and for the coherent synthesis of XUV continua from multicycle driving laser pulses without the need of an isolated attosecond burst.Comment: 14 pages, 5 figures. Submitted to Physical Review

Is the Cepheus E Outflow driven by a Class 0 Protostar?

New early release observations of the Cepheus E outflow and its embedded source, obtained with the Spitzer Space Telescope, are presented. We show the driving source is detected in all 4 IRAC bands, which suggests that traditional Class 0 classification, although essentially correct, needs to accommodate the new high sensitivity infrared arrays and their ability to detected deeply embedded sources. The IRAC, MIPS 24 and 70 microns new photometric points are consistent with a spectral energy distribution dominated by a cold, dense envelope surrounding the protostar. The Cep E outflow, unlike its more famous cousin the HH 46/47 outflow, displays a very similar morphology in the near and mid-infrared wavelengths, and is detected at 24 microns. The interface between the dense molecular gas (where Cep E lies) and less dense interstellar medium, is well traced by the emission at 8 and 24 microns, and is one of the most exotic features of the new IRAC and MIPS images. IRS observations of the North lobe of the flow confirm that most of the emission is due to the excitation of pure H2 rotational transitions arising from a relatively cold (Tex~700 K) and dense (N{H}~9.6E20 cm-2 molecular gas.Comment: 14 pages (pre-print format), including 6 figures. Published in ApJ Special Spitzer Issue (2004

The ultracool dwarf DENIS-P J104814.7-395606. Chromospheres and coronae at the low-mass end of the main-sequence

We have obtained an XMM-Newton observation and a broad-band spectrum from the ultraviolet to the near infrared with X-Shooter for one of the nearest M9 dwarfs, DENIS-P J1048-3956 (4pc). We integrate these data by a compilation of activity parameters for ultracool dwarfs from the literature with the aim to advance our understanding of these objects by comparing them to early-M type dwarf stars and the Sun. Our deep XMM-Newton observation has led to the first X-ray detection of DENIS-P J1048-3956 (log Lx = 25.1) as well as the first measurement of its V band brightness (V = 17.35mag). Flux-flux relations between X-ray and chromospheric activity indicators are here for the first time extended into the regime of the ultracool dwarfs. The approximate agreement of DENIS-P J1048-3956 and other ultracool dwarfs with flux-flux relations for early-M dwarfs suggests that the same heating mechanisms work in the atmospheres of ultracool dwarfs, albeit weaker as judged from their lower fluxes. The observed Balmer decrements of DENIS-P J1048-3956 are compatible with optically thick plasma in LTE at low, nearly photospheric temperature or optically thin LTE plasma at 20000K. Describing the decrements with CaseB recombination requires different emitting regions for Halpha and the higher Balmer lines. The high observed Halpha/Hbeta flux ratio is also poorly fitted by the optically thin models. We derive a similarly high value for the Halpha/Hbeta ratio of vB10 and LHS2065 and conclude that this may be a characteristic of ultracool dwarfs. We add DENIS-P J1048-3956 to the list of ultracool dwarfs detected in both the radio and the X-ray band. The Benz-Guedel relation between radio and X-ray luminosity of late-type stars is well-known to be violated by ultracool dwarfs. We speculate on the presence of two types of ultracool dwarfs with distinct radio and X-ray behavior.Comment: accepted for publication in Astronomy & Astrophysic

A CRISPR/Cas9-generated mutation in the zebrafish orthologue of PPP2R3B causes idiopathic scoliosis

Idiopathic scoliosis (IS) is the deformation and/or abnormal curvature of the spine that develops progressively after birth. It is a very common condition, affecting approximately 4% of the general population, yet the genetic and mechanistic causes of IS are poorly understood. Here, we focus on PPP2R3B, which encodes a protein phosphatase 2A regulatory subunit. We found that PPP2R3B is expressed at sites of chondrogenesis within human foetuses, including the vertebrae. We also demonstrated prominent expression in myotome and muscle fibres in human foetuses, and zebrafish embryos and adolescents. As there is no rodent orthologue of PPP2R3B, we used CRIPSR/Cas9-mediated gene-editing to generate a series of frameshift mutations in zebrafish ppp2r3b. Adolescent zebrafish that were homozygous for this mutation exhibited a fully penetrant kyphoscoliosis phenotype which became progressively worse over time, mirroring IS in humans. These defects were associated with reduced mineralisation of vertebrae, resembling osteoporosis. Electron microscopy demonstrated abnormal mitochondria adjacent to muscle fibres. In summary, we report a novel zebrafish model of IS and reduced bone mineral density. In future, it will be necessary to delineate the aetiology of these defects in relation to bone, muscle, neuronal and ependymal cilia function

Herschel observations of the Sgr B2 cores: Hydrides, warm CO, and cold dust

Sagittarius B2 (Sgr B2) is one of the most massive and luminous star-forming regions in the Galaxy and shows chemical and physical conditions similar to those in distant extragalactic starbursts. We present large-scale far-IR/submm photometric images and spectroscopic maps taken with the PACS and SPIRE instruments onboard Herschel. The spectra towards the Sgr B2 star-forming cores, B2(M) and B2(N), are characterized by strong CO line emission, emission lines from high-density tracers (HCN, HCO+, and H2S), [N II] 205 um emission from ionized gas, and absorption lines from hydride molecules (OH+, H2O+, H2O, CH+, CH, SH+, HF, NH, NH2, and NH3). The rotational population diagrams of CO suggest the presence of two gas temperature components: an extended warm component, which is associated with the extended envelope, and a hotter component, which is seen towards the B2(M) and B2(N) cores. As observed in other Galactic Center clouds, the gas temperatures are significantly higher than the dust temperatures inferred from photometric images. We determined far-IR and total dust masses in the cores. Non-local thermodynamic equilibrium models of the CO excitation were used to constrain the averaged gas density in the cores. A uniform luminosity ratio is measured along the extended envelope, suggesting that the same mechanism dominates the heating of the molecular gas at large scales. The detection of high-density molecular tracers and of strong [N II] 205 um line emission towards the cores suggests that their morphology must be clumpy to allow UV radiation to escape from the inner HII regions. Together with shocks, the strong UV radiation field is likely responsible for the heating of the hot CO component. At larger scales, photodissociation regions models can explain both the observed CO line ratios and the uniform L(CO)/LFIR luminosity ratios

The X-ray Luminosities of HH Objects

The recent detection of X-ray emission from HH 2 and HH 154 with the Chandra and XMM-Newton satellites (respectively) have opened up an interesting, new observational possibility in the field of Herbig-Haro objects. In order to be able to plan further X-ray observations of other HH objects, it is now of interest to be able to estimate their X-ray luminosities in order to choose which objects to observe. This paper describes a simple, analytic model for predicting the X-ray luminosity of a bow shock from the parameters of the flow (i.e., the size of the bow shock, its velocity, and the pre-shock density). The accuracy of the analytic model is analyzed through a comparison with the predictions obtained from axisymmetric, gasdynamic simulations of the leading working surface of an HH jet. We find that our analytic model reproduces the observed X-ray luminosities of HH 2 and HH 154, and we propose that HH~80/81 is a good candidate for future observations with Chandra.Comment: 10 pages (8 text, 2 figures