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

The impact of victim-perpetrator relationship, reputation, and initial point of resistance on officers’ responsibility and authenticity ratings towards hypothetical rape cases

Purpose: Previous studies suggest that judgments of responsibility and authenticity made towards hypothetical rape cases differ when specific case factors are varied. However, few studies have examined whether police officers exhibit similar variations in judgment. Methods: Sixteen vignettes depicting a hypothetical rape scenario were created. Vignettes varied on victim-perpetrator relationship, victim reputation, and initial point of resistance. Police officers from a large police force in the United Kingdom (n = 808) provided judgments of victim and perpetrator responsibility, as well as rape authenticity. Results: Officers rated perpetrators as less responsible and gave lower rape authenticity ratings when a partner was the perpetrator, and in ‘late’ resistance scenarios. Officers rated victims as more responsible in ‘bad’ reputation conditions and in ‘late’ resistance conditions. Additional effects of officer sex and receipt of specialist training were also found (i.e., male officers rated the victim as more responsible than female officers), as were several interactions between factors. Conclusions: Results suggest that police officers in the UK may judge victims of rape differentially based on extra-legal case factors. The potential impact on the investigation of rape cases is discussed, and a recommendation for thorough and prompt review of specialist and non-specialist training is made

Investigating the demographic and attitudinal predictors of rape myth acceptance in U.K. Police officers: developing an evidence-base for training and professional development

Efforts to understand rape myth acceptance (RMA) as a cognitive framework in police, unifying key cognitive/attitudinal and demographic factors into one coherent model, are lacking. Using a cross-sectional survey design, predictors of RMA were assessed by linear hierarchical regression, including demographic (age, length of service, gender, experience of specialist rape investigation training) and attitudinal factors (hostility towards women, sexist attitudes, and explicit power/sex beliefs) among officers from a large U.K. police force (N = 912). The final model explained 44% of variance in RMA. Gender and previous specialist training significantly predicted RMA, but to a much lesser extent than attitudinal variables, which explain 42% of RMA variance. Only specialist rape investigation training remained significant when attitudinal variables were added. The greater contribution from attitudinal variables suggests that efforts to address RMA in officers must consider the broader attitudinal structures underpinning RMA. Findings highlight implications for evidence- based training for rape investigators

The Influence of ‘high’ vs. ‘low’ rape myth acceptance on police officers’ judgements of victim and perpetrator responsibility, and rape authenticity

Purpose: Previous studies suggest that officers’ level of rape myth acceptance (RMA) is predictive of their case decision making and judgements towards victim-survivors. However, few studies have directly assessed the relationship between RMA and responsibility and authenticity judgments. Methods: 808 UK police officers categorised as ‘high’ or ‘low’ in rape myth acceptance made judgements of victim and perpetrator responsibility, and case authenticity, towards one of 16 vignettes depicting a hypothetical rape scenario varying on victim-perpetrator relationship, victim reputation, and initial point of resistance. Results: Officers categorised as ‘high’ in RMA rated victims as more responsible, perpetrators as less responsible, and cases as less authentic than those deemed to be ‘low’ in RMA. When rape-myth related factors were present, both individually and in combination, judgements by officers ‘high’ in RMA were more negative than those ‘low’ in RMA. Conclusions: Results suggest that officers ‘high’ in RMA may judge victims of rape differently to those ‘low’ in RMA, particularly when rape myth-related extra-legal case factors are present. The potential implications for training and selection are discussed

Proof of Stanley's conjecture about irreducible character values of the symmetric group

R. Stanley has found a nice combinatorial formula for characters of irreducible representations of the symmetric group of rectangular shape. Then, he has given a conjectural generalisation for any shape. Here, we will prove this formula using shifted Schur functions and Jucys-Murphy elements.Comment: 9 page

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