Signal-to-noise ratio estimation in digital computer simulation of lowpass and bandpass systems with applications to analog and digital communications, volume 3

Techniques are developed to estimate power gain, delay, signal-to-noise ratio, and mean square error in digital computer simulations of lowpass and bandpass systems. The techniques are applied to analog and digital communications. The signal-to-noise ratio estimates are shown to be maximum likelihood estimates in additive white Gaussian noise. The methods are seen to be especially useful for digital communication systems where the mapping from the signal-to-noise ratio to the error probability can be obtained. Simulation results show the techniques developed to be accurate and quite versatile in evaluating the performance of many systems through digital computer simulation

Periodic solutions of coupled Boussinesq equations and Ostrovsky-type models free from zero-mass contradiction

Coupled Boussinesq equations describe long weakly-nonlinear longitudinal strain waves in a bi-layer with a soft bonding between the layers (e.g. a soft adhesive). From the mathematical viewpoint, a particularly difficult case appears when the linear long-wave speeds in the layers are significantly different (high-contrast case). The traditional derivation of the uni-directional models leads to four uncoupled Ostrovsky equations, for the right- and left-propagating waves in each layer. However, the models impose a ``zero-mass constraint'' i.e. the initial conditions should necessarily have zero mean, restricting the applicability of that description. Here, we bypass the contradiction in this high-contrast case by constructing the solution for the deviation from the evolving mean value, using asymptotic multiple-scale expansions involving two pairs of fast characteristic variables and two slow-time variables. By construction, the Ostrovsky equations emerging within the scope of this derivation are solved for initial conditions with zero mean while initial conditions for the original system may have non-zero mean values. Asymptotic validity of the solution is carefully examined numerically. We apply the models to the description of counter-propagating waves generated by solitary wave initial conditions, or co-propagating waves generated by cnoidal wave initial conditions, as well as the resulting wave interactions, and contrast with the behaviour of the waves in bi-layers when the linear long-wave speeds in the layers are close (low-contrast case). One local (classical) and two non-local (generalised) conservation laws of the coupled Boussinesq equations for strains are derived, and these are used to control the accuracy of the numerical simulations.Comment: 25 pages, 11 figures; previously this version appeared as arXiv:2210.14107 which was submitted as a new work by acciden

Phosphatase activity and organic phosphorus turnover on a high Arctic glacier

Arctic glacier surfaces harbour abundant microbial communities consisting mainly of heterotrophic and photoautotrophic bacteria. The microbes must cope with low concentrations of nutrients and with the fact that both the dissolved and debris-bound nutrient pools are dominated by organic phases. Here we provide evidence that phosphorus (P) is deficient in the supraglacial environment on a Svalbard glacier, we quantify the enzymatic activity of phosphatases in the system and we estimate the contribution of the microbes to the cycling of the dominant organic P in the supraglacial environment. Incubation of cryoconite debris revealed significant phosphatase activity in the samples (19–67 nmol MUP g<sup>−1</sup> h<sup>−1</sup>). It was inhibited by inorganic P during incubations and had its optimum at around 30°C. The phosphatase activity measured at near-in situ temperature and substrate concentration suggests that the available dissolved organic P can be turned over by microbes within ~3–11 h on the glacier surface. By contrast, the amount of potentially bioavailable debris-bound organic P is sufficient for a whole ablation season. However, it is apparent that some of this potentially bioavailable debris-bound P is not accessible to the microbes

pytrax: A simple and efficient random walk implementation for calculating the directional tortuosity of images

Given the huge advances in tomographic imaging capability in recent years, image analysis has become a powerful means of measuring transport and structural properties of porous materials. One of the most important material characteristics is the tortuosity, which is difficult to measure experimentally. We present pytrax: (tortuosity from random axial movements) a simple and efficient random walk method implemented in python to calculate the average tortuosity and orthogonal directional tortuosity components of an image. The code works for both two and three-dimensional images and completes a statistically significant number of walks in parallel for large images in a few minutes using a standard desktop computer. By comparison, a Lattice Boltzmann or finite element simulation on similar sized images can take several hours

A comparison of the Bravyi-Kitaev and Jordan-Wigner transformations for the quantum simulation of quantum chemistry

The ability to perform classically intractable electronic structure calculations is often cited as one of the principal applications of quantum computing. A great deal of theoretical algorithmic development has been performed in support of this goal. Most techniques require a scheme for mapping electronic states and operations to states of and operations upon qubits. The two most commonly used techniques for this are the Jordan-Wigner transformation and the Bravyi-Kitaev transformation. However, comparisons of these schemes have previously been limited to individual small molecules. In this paper we discuss resource implications for the use of the Bravyi-Kitaev mapping scheme, specifically with regard to the number of quantum gates required for simulation. We consider both small systems which may be simulatable on near-future quantum devices, and systems sufficiently large for classical simulation to be intractable. We use 86 molecular systems to demonstrate that the use of the Bravyi-Kitaev transformation is typically at least approximately as efficient as the canonical Jordan-Wigner transformation, and results in substantially reduced gate count estimates when performing limited circuit optimisations.Comment: 46 pages, 11 figure

Periodic solutions of coupled Boussinesq equations and Ostrovsky-type models free from zero-mass contradiction

Coupled Boussinesq equations are used to describe long weakly-nonlinear longitudinal strain waves in a bi-layer with a soft bonding between the layers (e.g. a soft adhesive). From the mathematical viewpoint, a particularly difficult case appears when the linear long-wave speeds in the layers are significantly different (high-contrast case). The traditional derivation of the uni-directional models leads to four uncoupled Ostrovsky equations, for the right-and left-propagating waves in each layer. However, the models impose a "zero-mass constraint" i.e. the initial conditions should necessarily have zero mean, restricting the applicability of that description. Here, we bypass the contradiction in this high-contrast case by constructing the solution for the deviation from the evolving mean value, using asymptotic multiple-scale expansions involving two pairs of fast characteristic variables and two slow-time variables. By construction, the Ostro-vsky equations emerging within the scope of this derivation are solved for initial conditions with zero mean while initial conditions for the original system may have non-zero mean values. Asymptotic validity of the solution is carefully examined numerically. We apply the models to the description of counter-propagating waves generated by solitary wave initial conditions, or co-propagating waves generated by cnoidal wave initial conditions, as well as the resulting wave interactions, and contrast with the behaviour of the waves in bi-layers when the linear long-wave speeds in the layers are close (low-contrast case). One local (classical) and two non-local (generalised) conservation laws of the coupled Boussinesq equations for strains are derived and used to control the accuracy of the numerical simulations. A weakly-nonlinear solution to the coupled Boussinesq equations on a finite interval with periodic boundary conditions is constructed, resolving the zero-mass contradiction. The solution is shown to be asymptotically valid by comparison to direct numerical simulations of the original coupled Boussinesq equations, with the additional control of derived generalised conservation laws. Examples include counter-propagating radiating solitary waves and Ostrovsky-type wave packets when the period of the solution is large compared to the size of a localised initial condition, while decreasing the period of the solution for the localised perturbations and using non-localised initial conditions leads to more complicated scenarios. We observe that, in many cases, the waves appear to interact in a nearly-elastic manner, similarly to that of solitary waves, with small phase shift and amplitude changes compared to the case with no interaction, while in other cases strong interactions lead to formation of new wave structures

Spatial variability in Antarctic surface snow bacterial communities

It was once a long-held view that the Antarctic was a pristine environment with low biomass, low biodiversity and low rates of microbial activity. However, as the intensity of scientific investigation has increased, so these views have started to change. In particular, the role and impact of human activity toward indigenous microbial communities has started to come under more intense scrutiny. During the Subglacial Lake Ellsworth exploration campaign in December 2012, a microbiological survey was conducted to determine the extent and likelihood of exogenous input into the subglacial lake system during the hot-water drilling process. Snow was collected from the surface to represent that used for melt water production for hot-water drilling. The results of this study showed that snow used to provide melt water differed in its microbiological composition from that of the surrounding area and raised the question of how the biogeography of snow-borne microorganisms might influence the potential outcome of scientific analyses. In this study, we investigated the biogeography of microorganisms in snow around a series of Antarctic logistic hubs, where human activity was clearly apparent, and from which scientific investigations have been undertaken. A change in microbial community structure with geographical location was apparent and, notably, a decrease in alpha diversity at more remote southern latitudes. Soil-related microorganisms dominated microbial assemblages suggesting terrestrial input, most likely from long-range aeolian transport into continental Antarctica. We also observed that relic DNA was not a major issue when assessing snow samples. Overall, our observations might have profound implications for future scientific activities in Antarctica, such as the need to establish “no-go” protected areas, the need for better characterization of field sites and improved protocols for sterilization and verification of ice drilling equipment