The square root law and structure of finite rings

Let $R$ be a finite ring and define the hyperbola $H=\{(x,y) \in R \times R: xy=1 \}$. Suppose that for a sequence of finite odd order rings of size tending to infinity, the following "square root law" bound holds with a constant $C>0$ for all non-trivial characters $\chi$ on $R^2$: $$\left| \sum_{(x,y)\in H}\chi(x,y)\right|\leq C\sqrt{|H|}.$$ Then, with a finite number of exceptions, those rings are fields. For rings of even order we show that there are other infinite families given by Boolean rings and Boolean twists which satisfy this square-root law behavior. We classify the extremal rings, those for which the left hand side of the expression above satisfies the worst possible estimate. We also describe applications of our results to problems in graph theory and geometric combinatorics. These results provide a quantitative connection between the square root law in number theory, Salem sets, Kloosterman sums, geometric combinatorics, and the arithmetic structure of the underlying rings

Dynamics of coreless vortices and rotation-induced dissipation peak in superfluid films on rotating porous substrates

We analyze dynamics of 3D coreless vortices in superfluid films covering porous substrates. The 3D vortex dynamics is derived from the 2D dynamics of the film. The motion of a 3D vortex is a sequence of jumps between neighboring substrate cells, which can be described, nevertheless, in terms of quasi-continuous motion with average vortex velocity. The vortex velocity is derived from the dissociation rate of vortex-antivortex pairs in a 2D film, which was developed in the past on the basis of the Kosterlitz-Thouless theory. The theory explains the rotation-induced dissipation peak in torsion-oscillator experiments on $^4$He films on rotating porous substrates and can be used in the analysis of other phenomena related to vortex motion in films on porous substrates.Comment: 8 pages, 3 figures submitted to Phys. Rev.

PassGAN: A Deep Learning Approach for Password Guessing

State-of-the-art password guessing tools, such as HashCat and John the Ripper, enable users to check billions of passwords per second against password hashes. In addition to performing straightforward dictionary attacks, these tools can expand password dictionaries using password generation rules, such as concatenation of words (e.g., "password123456") and leet speak (e.g., "password" becomes "p4s5w0rd"). Although these rules work well in practice, expanding them to model further passwords is a laborious task that requires specialized expertise. To address this issue, in this paper we introduce PassGAN, a novel approach that replaces human-generated password rules with theory-grounded machine learning algorithms. Instead of relying on manual password analysis, PassGAN uses a Generative Adversarial Network (GAN) to autonomously learn the distribution of real passwords from actual password leaks, and to generate high-quality password guesses. Our experiments show that this approach is very promising. When we evaluated PassGAN on two large password datasets, we were able to surpass rule-based and state-of-the-art machine learning password guessing tools. However, in contrast with the other tools, PassGAN achieved this result without any a-priori knowledge on passwords or common password structures. Additionally, when we combined the output of PassGAN with the output of HashCat, we were able to match 51%-73% more passwords than with HashCat alone. This is remarkable, because it shows that PassGAN can autonomously extract a considerable number of password properties that current state-of-the art rules do not encode.Comment: This is an extended version of the paper which appeared in NeurIPS 2018 Workshop on Security in Machine Learning (SecML'18), see https://github.com/secml2018/secml2018.github.io/raw/master/PASSGAN_SECML2018.pd

Five-dimensional Monopole Equation with Hedge-Hog Ansatz and Abel's Differential Equation

We review the generalized monopole in the five-dimensional Euclidean space. A numerical solution with the Hedge-Hog ansatz is studied. The Bogomol'nyi equation becomes a second order autonomous non-linear differential equation. The equation can be translated into the Abel's differential equation of the second kind and is an algebraic differential equation.Comment: 4 pages, 4 figures, typos correcte

The Molonglo Galactic Plane Survey (MGPS-2): Compact Source Catalogue

We present the first data release from the second epoch Molonglo Galactic Plane Survey (MGPS-2). MGPS-2 was carried out with the Molonglo Observatory Synthesis Telescope at a frequency of 843 MHz and with a restoring beam of 45 arcsec x 45 arcsec cosec(dec), making it the highest resolution large scale radio survey of the southern Galactic plane. It covers the range |b| < 10 deg and 245 deg < l < 365 deg and is the Galactic counterpart to the Sydney University Molonglo Sky Survey (SUMSS) which covers the whole southern sky with dec 10 deg). In this paper we present the MGPS-2 compact source catalogue. The catalogue has 48,850 sources above a limiting peak brightness of 10 mJy/beam. Positions in the catalogue are accurate to 1 arcsec - 2 arcsec. A full catalogue including extended sources is in preparation. We have carried out an analysis of the compact source density across the Galactic plane and find that the source density is not statistically higher than the density expected from the extragalactic source density alone. We also present version 2.0 of the SUMSS image data and catalogue which are now available online. The data consists of 629 4.3 deg x 4.3 deg mosaic images covering the 8100 deg^2 of sky with dec 10 deg. The catalogue contains 210,412 radio sources to a limiting peak brightness of 6 mJy/beam at dec -50 deg. We describe the updates and improvements made to the SUMSS cataloguing process.Comment: 12 pages, 9 figures, to be published in MNRAS Note that Figures 8 and 9 are much lower resolution than in the published versio

Statistical region based active contour using a fractional entropy descriptor: Application to nuclei cell segmentation in confocal microscopy images

We propose an unsupervised statistical region based active contour approach integrating an original fractional entropy measure for image segmentation with a particular application to single channel actin tagged fluorescence confocal microscopy image segmentation. Following description of statistical based active contour segmentation and the mathematical definition of the proposed fractional entropy descriptor, we demonstrate comparative segmentation results between the proposed approach and standard Shannon’s entropy on synthetic and natural images. We also show that the proposed unsupervised statistical based approach, integrating the fractional entropy measure, leads to very satisfactory segmentation of the cell nuclei from which shape characterization can be calculated

Exact 1-D Model for Coherent Synchrotron Radiation with Shielding and Bunch Compression

Coherent Synchrotron Radiation has been studied effectively using a 1-dimensional model for the charge distribution in the realm of small angle approximations and high energies. Here we use Jefimenko's form of Maxwell's equations, without such approximations, to calculate the exact wake-fields due to this effect in multiple bends and drifts. It has been shown before that the influence of a drift can propagate well into a subsequent bend. We show, for reasonable parameters, that the influence of a previous bend can also propagate well into a subsequent bend, and that this is especially important at the beginning of a bend. Shielding by conducting parallel plates is simulated using the image charge method. We extend the formalism to situations with compressing and decompressing distributions, and conclude that simpler approximations to bunch compression usually overestimates the effect. Additionally, an exact formula for the coherent power radiated by a Gaussian bunch is derived by considering the coherent synchrotron radiation spectrum, and is used to check the accuracy of wake-field calculations