Stability of Soft Quasicrystals in a Coupled-Mode Swift-Hohenberg Model for Three-Component Systems

In this article, we discuss the stability of soft quasicrystalline phases in a coupled-mode Swift-Hohenberg model for three-component systems, where the characteristic length scales are governed by the positive-definite gradient terms. Classic two-mode approximation method and direct numerical minimization are applied to the model. In the latter approach, we apply the projection method to deal with the potentially quasiperiodic ground states. A variable cell method of optimizing the shape and size of higher-dimensional periodic cell is developed to minimize the free energy with respect to the order parameters. Based on the developed numerical methods, we rediscover decagonal and dodecagonal quasicrystalline phases, and find diverse periodic phases and complex modulated phases. Furthermore, phase diagrams are obtained in various phase spaces by comparing the free energies of different candidate structures. It does show not only the important roles of system parameters, but also the effect of optimizing computational domain. In particular, the optimization of computational cell allows us to capture the ground states and phase behavior with higher fidelity. We also make some discussions on our results and show the potential of applying our numerical methods to a larger class of mean-field free energy functionals.Comment: 26 pages, 13 figures; accepted by Communications in Computational Physic

NBLDA: Negative Binomial Linear Discriminant Analysis for RNA-Seq Data

RNA-sequencing (RNA-Seq) has become a powerful technology to characterize gene expression profiles because it is more accurate and comprehensive than microarrays. Although statistical methods that have been developed for microarray data can be applied to RNA-Seq data, they are not ideal due to the discrete nature of RNA-Seq data. The Poisson distribution and negative binomial distribution are commonly used to model count data. Recently, Witten (2011) proposed a Poisson linear discriminant analysis for RNA-Seq data. The Poisson assumption may not be as appropriate as negative binomial distribution when biological replicates are available and in the presence of overdispersion (i.e., when the variance is larger than the mean). However, it is more complicated to model negative binomial variables because they involve a dispersion parameter that needs to be estimated. In this paper, we propose a negative binomial linear discriminant analysis for RNA-Seq data. By Bayes' rule, we construct the classifier by fitting a negative binomial model, and propose some plug-in rules to estimate the unknown parameters in the classifier. The relationship between the negative binomial classifier and the Poisson classifier is explored, with a numerical investigation of the impact of dispersion on the discriminant score. Simulation results show the superiority of our proposed method. We also analyze four real RNA-Seq data sets to demonstrate the advantage of our method in real-world applications

Stability of Two-Dimensional Soft Quasicrystals

The relative stability of two-dimensional soft quasicrystals is examined using a recently developed projection method which provides a unified numerical framework to compute the free energy of periodic crystal and quasicrystals. Accurate free energies of numerous ordered phases, including dodecagonal, decagonal and octagonal quasicrystals, are obtained for a simple model, i.e. the Lifshitz-Petrich free energy functional, of soft quasicrystals with two length-scales. The availability of the free energy allows us to construct phase diagrams of the system, demonstrating that, for the Lifshitz-Petrich model, the dodecagonal and decagonal quasicrystals can become stable phases, whereas the octagonal quasicrystal stays as a metastable phase.Comment: 11 pages, 7 figure

On observations of artificial light at night from ground and space

To assess the negative effects of artificial light at night, measurement data are often necessary. These can be acquired from ground or satellite-based measurements. Satellite-based observations of artificial light have an advantage of global coverage. Since the launch of the Suomi National Polar-orbiting Partnership (S-NPP) satellite, the Visible Infrared Imaging Radiometer Suite (VIIRS) Day-Night Band (DNB) provides a tool for worldwide night time remote sensing for various applications, including artificial light. We used the data in year 2015 from the VIIRS-DNB sensor to study the angular distribution of artificial light in major cities and metropoles in Europe. Despite encountering some issues, for example low overflight rate with cloud-free sky condition, we are able to investigate the angular distributions of upwelling artificial light emission for 74 regions, almost all of which emit more light near the horizon. In comparison to satellite-based observations, ground-based measurements can acquire data more frequently. An international campaign studying variations of night sky at 44 worldwide locations was conducted in 2011 and 2012, measuring the night sky using broadband radiometers, the Sky Quality Meters (SQMs), and was the first time comparing ground-based night sky measurement in a unified analysis procedure. The presence of artificial light reverses the variation pattern of sky brightness at cloudy nights. Instead of darkening of night sky by blockage of extraterrestrial light sources, clouds backscatter the artificial light emitted from ground, brighting the night sky. Comparison with daytime aerosol measurement data did not yield a consistent relationship between the aerosol content and night sky brightness for the rural site in Cabauw, the Netherlands, but found the brightening of the night sky of Madrid with increasing atmospheric aerosol load. Long-term monitoring of the night sky enables us to observe the change in skyglow pattern over a long period. Two SQMs have been set up in a suburban site and a rural site in Bremen, Germany since December 2011. The night sky of the suburban site is found to be brighter during cloudy nights and becomes darker during the course of the night, which is typical for a light-polluted location. While instrumental issues cannot be ruled out, we found a decrease of sky brightness over a span of about 4.5 years, with a stronger decreasing trend at late hours of the night. For the rural site, the local public and domestic lightings are the dominating light source, contributing to the larger skyglow in the early hours of the night. However, with domestic and public lighting switched off as the night progresses, the variation pattern of the night sky is typical for a location with less light pollution, where the overcast sky is only slightly different in brightness from clear sky. It is suspected that this trend in the change of sky brightness originates from the gradual decrease of output of the public lighting system due to aging, while the progress replacing the public lighting to light-emitting diode (LED) devices is slow. An improvement in terms of ecological impacts in the future is therefore not guaranteed

Performance Limits of Fluid Antenna Systems

Fluid antenna represents a concept where a mechanically flexible antenna can switch its location freely within a given space. Recently, it has been reported that even with a tiny space, a single-antenna fluid antenna system (FAS) can outperform an L-antenna maximum ratio combining (MRC) system in terms of outage probability if the number of locations (or ports) the fluid antenna can be switched to, is large enough. This letter aims to study if extraordinary capacity can also be achieved by FAS with a small space. We do this by deriving the ergodic capacity, and a capacity lower bound. This letter also derives the level crossing rate (LCR) and average fade duration (AFD) for the FAS.Comment: 4 pages, 5 figure

Fluid Antenna Systems

Over the past decades, multiple antenna technologies have appeared in many different forms, most notably as multiple-input multiple-output (MIMO), to transform wireless communications for extraordinary diversity and multiplexing gains. The variety of technologies has been based on placing a number of antennas at fixed locations which dictates the fundamental limit on the achievable performance. By contrast, this paper envisages the scenario where the physical position of an antenna can be switched freely to one of the N positions over a fixed-length line space to pick up the strongest signal in the manner of traditional selection combining. We refer to this system as a fluid antenna system (FAS) for tremendous flexibility in its possible shape and position. The aim of this paper is to study the achievable performance of a single-antenna FAS system with a fixed length and N in arbitrarily correlated Rayleigh fading channels. Our contributions include exact and approximate closed-form expressions for the outage probability of FAS. We also derive an upper bound for the outage probability, from which it is shown that a single-antenna FAS given any arbitrarily small space can outperform an L-antenna maximum ratio combining (MRC) system if N is large enough. Our analysis also reveals the minimum required size of the FAS, and how large N is considered enough for the FAS to surpass MRC.Comment: 26 pages, 5 figure