Diffusion in multiscale spacetimes

We study diffusion processes in anomalous spacetimes regarded as models of quantum geometry. Several types of diffusion equation and their solutions are presented and the associated stochastic processes are identified. These results are partly based on the literature in probability and percolation theory but their physical interpretation here is different since they apply to quantum spacetime itself. The case of multiscale (in particular, multifractal) spacetimes is then considered through a number of examples and the most general spectral-dimension profile of multifractional spaces is constructed.Comment: 23 pages, 5 figures. v2: discussion improved, typos corrected, references adde

Developing and evaluating a five minute phishing awareness video

Confidence tricksters have always defrauded the unwary. The computer era has merely extended their range and made it possible for them to target anyone in the world who has an email address. Nowadays, they send phishing messages that are specially crafted to deceive. Improving user awareness has the potential to reduce their effectiveness. We have previously developed and empirically-validated phishing awareness programmes. Our programmes are specifically designed to neutralize common phish-related misconceptions and teach people how to detect phishes. Many companies and individuals are already using our programmes, but a persistent niggle has been the amount of time required to complete the awareness programme. This paper reports on how we responded by developing and evaluating a condensed phishing awareness video that delivered phishing awareness more efficiently. Having watched our video, participants in our evaluation were able to detect phishing messages significantly more reliably right after watching the video (compared to before watching the video). This ability was also demonstrated after a retention period of eight weeks after first watching the video

On the distance of the Magellanic Clouds using Cepheid NIR and optical-NIR Period Wesenheit Relations

We present the largest near-infrared (NIR) data sets, $JHKs$, ever collected for classical Cepheids in the Magellanic Clouds (MCs). We selected fundamental (FU) and first overtone (FO) pulsators, and found 4150 (2571 FU, 1579 FO) Cepheids for Small Magellanic Cloud (SMC) and 3042 (1840 FU, 1202 FO) for Large Magellanic Cloud (LMC). Current sample is 2--3 times larger than any sample used in previous investigations with NIR photometry. We also discuss optical $VI$ photometry from OGLE-III. NIR and optical--NIR Period-Wesenheit (PW) relations are linear over the entire period range ($0.0<\log P_{\rm FU} \le1.65$) and their slopes are, within the intrinsic dispersions, common between the MCs. These are consistent with recent results from pulsation models and observations suggesting that the PW relations are minimally affected by the metal content. The new FU and FO PW relations were calibrated using a sample of Galactic Cepheids with distances based on trigonometric parallaxes and Cepheid pulsation models. By using FU Cepheids we found a true distance moduli of $18.45\pm0.02{\rm(random)}\pm0.10{\rm(systematic)}$ mag (LMC) and $18.93\pm0.02{\rm(random)}\pm0.10{\rm(systematic)}$ mag (SMC). These estimates are the weighted mean over ten PW relations and the systematic errors account for uncertainties in the zero-point and in the reddening law. We found similar distances using FO Cepheids ($18.60\pm0.03{\rm(random)}\pm0.10{\rm(systematic)}$ mag [LMC] and $19.12\pm0.03{\rm(random)}\pm0.10{\rm(systematic)}$ mag [SMC]). These new MC distances lead to the relative distance, $\Delta\mu=0.48\pm0.03$ mag (FU, $\log P=1$) and $\Delta\mu=0.52\pm0.03$ mag (FO, $\log P=0.5$),which agrees quite well with previous estimates based on robust distance indicators.Comment: 17 pages, 7 figure

The Metallicity of Pre-Galactic Globular Clusters: Observational consequences of the first stars

We explore a scenario where metal-poor globular clusters (GCs) are enriched by the first supernovae in the Universe. If the first stars in a 10^7 Msun dark halo were very massive (>180 Msun), then a pair instability supernova from a single massive star can produce sufficient iron to enrich 10^6 Msun of pristine, primordial gas to [Fe/H] ~ -2. In such a scenario, where a single massive star acts as a seed for halo GCs, the accurate abundance analysis of GC stars would allow a direct measurement of the Population III initial mass. Using the latest theoretical yields for zero metallicity stars in the mass range 140-260 Msun, we find that the metals expelled from a ~230 Msun star are consistent with [Si/Fe] and [Ca/Fe] observed in GC stars. However, no single star in this mass range can simultaneously explain all halo GC heavy-element abundance ratios, such as [V/Fe], [Ti/Fe] and [Ni/Fe]. These require a combination masses for the Population III stellar progenitors. The various observational consequences of this scenario are discussed.Comment: 5 pages, 2 figures, accepted for publication in ApJ Lette

Unsupervised Domain Adaptation through Inter-Modal Rotation for RGB-D Object Recognition

Unsupervised Domain Adaptation (DA) exploits the supervision of a label-rich source dataset to make predictions on an unlabeled target dataset by aligning the two data distributions. In robotics, DA is used to take advantage of automatically generated synthetic data, that come with 'free' annotation, to make effective predictions on real data. However, existing DA methods are not designed to cope with the multi-modal nature of RGB-D data, which are widely used in robotic vision. We propose a novel RGB-D DA method that reduces the synthetic-to-real domain shift by exploiting the inter-modal relation between the RGB and depth image. Our method consists of training a convolutional neural network to solve, in addition to the main recognition task, the pretext task of predicting the relative rotation between the RGB and depth image. To evaluate our method and encourage further research in this area, we define two benchmark datasets for object categorization and instance recognition. With extensive experiments, we show the benefits of leveraging the inter-modal relations for RGB-D DA. The code is available at: 'https://github.com/MRLoghmani/relative-rotation'

Fractional Generalization of Gradient Systems

We consider a fractional generalization of gradient systems. We use differential forms and exterior derivatives of fractional orders. Examples of fractional gradient systems are considered. We describe the stationary states of these systems.Comment: 11 pages, LaTe

Second Overtone Pulsators Among Delta Scuti Stars

We investigate the modal stability of stellar models at masses and luminosity levels corresponding to post main sequence luminous delta scuti pulsators. The envelope models have been computed at fixed mass value, luminosity level and chemical composition (Y=0.28, Z=0.02). According to a nonlinear approach to radial oscillations the present investigation predicts the occurrence of stable second overtone pulsators for the first time. The shape of both light and velocity curves are presented and discussed, providing a useful tool for the identification of second overtone pulsators among the known groups of radially pulsating stars. The period ratios of mixed mode pulsators obtained by perturbing the first and the second overtone radial eigenfunctions are in agreement with observative values. Finally, the physical structure and the dynamical properties of second overtone pulsators are discussed in detail. The role played by the nodal lines in the destabilization of second overtone pulsators is also pointed out.Comment: 20 pages, 11 Postscript figures, uses aaspp4.sty and tighten.st

Retarding Sub- and Accelerating Super-Diffusion Governed by Distributed Order Fractional Diffusion Equations

We propose diffusion-like equations with time and space fractional derivatives of the distributed order for the kinetic description of anomalous diffusion and relaxation phenomena, whose diffusion exponent varies with time and which, correspondingly, can not be viewed as self-affine random processes possessing a unique Hurst exponent. We prove the positivity of the solutions of the proposed equations and establish the relation to the Continuous Time Random Walk theory. We show that the distributed order time fractional diffusion equation describes the sub-diffusion random process which is subordinated to the Wiener process and whose diffusion exponent diminishes in time (retarding sub-diffusion) leading to superslow diffusion, for which the square displacement grows logarithmically in time. We also demonstrate that the distributed order space fractional diffusion equation describes super-diffusion phenomena when the diffusion exponent grows in time (accelerating super-diffusion).Comment: 11 pages, LaTe

Nonholonomic Constraints with Fractional Derivatives

We consider the fractional generalization of nonholonomic constraints defined by equations with fractional derivatives and provide some examples. The corresponding equations of motion are derived using variational principle.Comment: 18 page