Channel model and lower capacity bound for the transmission based on nonlinear Fourier transform

The integrability of the nonlinear Schräodinger equation (NLSE) by the inverse scattering transform shown in a seminal work [1] gave an interesting opportunity to treat the corresponding nonlinear channel similar to a linear one by using the nonlinear Fourier transform. Integrability of the NLSE is in the background of the old idea of eigenvalue communications [2] that was resurrected in recent works [3{7]. In [6, 7] the new method for the coherent optical transmission employing the continuous nonlinear spectral data | nonlinear inverse synthesis was introduced. It assumes the modulation and detection of data using directly the continuous part of nonlinear spectrum associated with an integrable transmission channel (the NLSE in the case considered). Although such a transmission method is inherently free from nonlinear impairments, the noisy signal corruptions, arising due to the ampli¯er spontaneous emission, inevitably degrade the optical system performance. We study properties of the noise-corrupted channel model in the nonlinear spectral domain attributed to NLSE. We derive the general stochastic equations governing the signal evolution inside the nonlinear spectral domain and elucidate the properties of the emerging nonlinear spectral noise using well-established methods of perturbation theory based on inverse scattering transform [8]. It is shown that in the presence of small noise the communication channel in the nonlinear domain is the additive Gaussian channel with memory and signal-dependent correlation matrix. We demonstrate that the effective spectral noise acquires colouring", its autocorrelation function becomes slow decaying and non-diagonal as a function of \frequencies", and the noise loses its circular symmetry, becoming elliptically polarized. Then we derive a low bound for the spectral effiency for such a channel. Our main result is that by using the nonlinear spectral techniques one can significantly increase the achievable spectral effiency compared to the currently available methods [9]. REFERENCES 1. Zakharov, V. E. and A. B. Shabat, Sov. Phys. JETP, Vol. 34, 62{69, 1972. 2. Hasegawa, A. and T. Nyu, J. Lightwave Technol., Vol. 11, 395{399, 1993. 3. Yousefi, M. I. and F. R. Kschischang, IEEE Trans. Inf. Theory, Vol. 60, 4312{4328, 2014. 4. Yousefi, M. I. and F. R. Kschischang, IEEE Trans. Inf. Theory, Vol. 60, 4329{4345 2014. 5. Yousefi, M. I. and F. R. Kschischang, IEEE Trans. Inf. Theory, Vol. 60, 4346{4369, 2014. 6. Prilepsky, J. E., S. A. Derevyanko, K. J. Blow, I. Gabitov, and S. K. Turitsyn, Phys. Rev. Lett., Vol. 113, 013901, 2014. 7. Le, S. T., J. E. Prilepsky, and S. K. Turitsyn, Opt. Express, Vol. 22, 26720{26741, 2014. 8. Kaup, D. J. and A. C. Newell, Proc. R. Soc. Lond. A, Vol. 361, 413{446, 1978. 9. Essiambre, R.-J., G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, J. Lightwave Technol., Vol. 28, 662{701, 2010.

Early warnings of heart rate deterioration

Hospitals can experience difficulty in detecting and responding to early signs of patient deterioration leading to late intensive care referrals, excess mortality and morbidity, and increased hospital costs. Our study aims to explore potential indicators of physiological deterioration by the analysis of vital-signs. The dataset used comprises heart rate (HR) measurements from MIMIC II waveform database, taken from six patients admitted to the Intensive Care Unit (ICU) and diagnosed with severe sepsis. Different indicators were considered: 1) generic early warning indicators used in ecosystems analysis (autocorrelation at-1-lag (ACF1), standard deviation (SD), skewness, kurtosis and heteroskedasticity) and 2) entropy analysis (kernel entropy and multi scale entropy). Our preliminary findings suggest that when a critical transition is approaching, the equilibrium state changes what is visible in the ACF1 and SD values, but also by the analysis of the entropy. Entropy allows to characterize the complexity of the time series during the hospital stay and can be used as an indicator of regime shifts in a patient’s condition. One of the main problems is its dependency of the scale used. Our results demonstrate that different entropy scales should be used depending of the level of entropy verified.

Spatiotemporal patterns in community structure of macroinvertebrates inhabiting calcareous periphyton mats

Calcareous floating periphyton mats in the southern Everglades provide habitat for a diverse macroinvertebrate community that has not been well characterized. Our study described this community in an oligotrophic marsh, compared it with the macroinvertebrate community associated with adjacent epiphytic algae attached to macrophytes in the water column, and detected spatial patterns in density and community structure. The floating periphyton mat (floating mat) and epiphytic algae in the water column (submerged epiphyton) were sampled at 4 sites (1 km apart) in northern Shark River Slough, Everglades National Park (ENP), in the early (July) and late (November) wet season. Two perpendicular 90-m transects were established at each site and 100 samples were taken in a nested design. Sites were located in wet-prairie spikerush-dominated sloughs with similar water depths and emergent macrophyte communities. Floating mats were sampled by taking cores (6-cm diameter) that were sorted under magnification to enumerate infauna retained on a 250-μm-mesh sieve and with a maximum dimension >1 mm. Our results showed that floating mats provide habitat for a macroinvertebrate community with higher densities (no. animals/g ash-free dry mass) of Hyalella azteca, Dasyhelea spp., and Cladocera, and lower densities of Chironomidae and Planorbella spp. than communities associated with submerged epiphyton. Densities of the most common taxa increased 3× to 15× from early to late wet season, and community differences between the 2 habitat types became more pronounced. Floating-mat coverage and estimated floating-mat biomass increased 20 to 30% and 30 to 110%, respectively, at most sites in the late wet season. Some intersite variation was observed in individual taxa, but no consistent spatial pattern in any taxon was detected at any scale (from 0.2 m to 3 km). Floating mats and their resident macroinvertebrate communities are important components in the Everglades food web. This community should be included in environmental monitoring programs because degradation and eventual loss of the calcareous periphyton mat is associated with P enrichment in this ecosystem.

Gráfico de controle modificado para processos com estruturas complexas de autocorrelação

This work proposes a modified control chart incorporating concepts of time series analysis. Specifically, we considerer Gaussian mixed transition distribution (GMTD) models. The GMTD models are a more general class than the autorregressive (AR) family, in the sense that the autocorrelated processes may present flat stretches, bursts or outliers. In this scenario traditional Shewhart charts are no longer appropriate tools to monitoring such processes. Therefore, Vasilopoulos and Stamboulis (1978) proposed a modified version of those charts, considering proper control limits based on autocorrelated processes. In order to evaluate the efficiency of the proposed technique a comparison with a traditional Shewhart chart (which ignores the autocorrelation structure of the process), a AR(1) Shewhart control chart and a GMTD Shewhart control chart was made. An analytical expression for the process variance, as well as control limits were developed for a particular GMTD model. The ARL was used as a criteria to measure the efficiency of control charts. The comparison was made based on a series generated according to a GMTD model. The results point to the direction that the modified Shewhart GMTD charts have a better performance than the AR(1) Shewhart and the traditional Shewhart.

Influência das condições ambientais no verdor da vegetação da caatinga frente às mudanças climáticas

The Caatinga biome, a semi-arid climate ecosystem found in northeast Brazil, presents low rainfall regime and strong seasonality. It has the most alarming climate change projections within the country, with air temperature rising and rainfall reduction with stronger trends than the global average predictions. Climate change can present detrimental results in this biome, reducing vegetation cover and changing its distribution, as well as altering all ecosystem functioning and finally influencing species diversity. In this context, the purpose of this study is to model the environmental conditions (rainfall and temperature) that influence the Caatinga biome productivity and to predict the consequences of environmental conditions in the vegetation dynamics under future climate change scenarios. Enhanced Vegetation Index (EVI) was used to estimate vegetation greenness (presence and density) in the area. Considering the strong spatial and temporal autocorrelation as well as the heterogeneity of the data, various GLS models were developed and compared to obtain the best model that would reflect rainfall and temperature influence on vegetation greenness. Applying new climate change scenarios in the model, environmental determinants modification, rainfall and temperature, negatively influenced vegetation greenness in the Caatinga biome. This model was used to create potential vegetation maps for current and future of Caatinga cover considering 20% decrease in precipitation and 1 °C increase in temperature until 2040, 35% decrease in precipitation and 2.5 °C increase in temperature in the period 2041-2070 and 50% decrease in precipitation and 4.5 °C increase in temperature in the period 2071-2100. The results suggest that the ecosystem functioning will be affected on the future scenario of climate change with a decrease of 5.9% of the vegetation greenness until 2040, 14.2% until 2070 and 24.3% by the end of the century. The Caatinga vegetation in lower altitude areas (most of the biome) will be more affected by climatic changes.

Uso de correntropia na generalização de funções cicloestacionárias e aplicações para a extração de características de sinais modulados

Information extraction is a frequent and relevant problem in digital signal processing. In the past few years, different methods have been utilized for the parameterization of signals and the achievement of efficient descriptors. When the signals possess statistical cyclostationary properties, the Cyclic Autocorrelation Function (CAF) and the Spectral Cyclic Density (SCD) can be used to extract second-order cyclostationary information. However, second-order cyclostationary information is poor in nongaussian signals, as the cyclostationary analysis in this case should comprise higher-order statistical information. This paper proposes a new mathematical tool for the higher-order cyclostationary analysis based on the correntropy function. Specifically, the cyclostationary analysis is revisited focusing on the information theory, while the Cyclic Correntropy Function (CCF) and Cyclic Correntropy Spectral Density (CCSD) are also defined. Besides, it is analytically proven that the CCF contains information regarding second- and higher-order cyclostationary moments, being a generalization of the CAF. The performance of the aforementioned new functions in the extraction of higher-order cyclostationary characteristics is analyzed in a wireless communication system where nongaussian noise exists.

Improved damage detectability in a wind turbine blade by optimal selection of vibration signal correlation coefficients

Piotr Omenzetter and Simon Hoell’s work within the Lloyd’s Register Foundation Centre for Safety and Reliability Engineering at the University of Aberdeen is supported by Lloyd’s Register Foundation. The Foundation helps to protect life and property by supporting engineering-related education, public engagement and the application of research.

Temporal scaling of optical rogue waves in unidirectional ring fiber laser

A fiber mode-lock laser allows generation of the optical rogue wave (ORW) at different time scales. The criteria for distinguishing between them is a comparison of the event lifetime with the main characteristic time of the system. The characteristic time can be estimated from the decay of an autocorrelation function (AF). Thus, in comparison with AF characteristic time, fast optical rogue wave (FORW) events have duration less than the AF decay time and it appeared due to pulse-pulse interaction and nonlinear pulses dynamics. While slow optical rogue wave (SORW) have a duration much more longer than the decay time of the AF which it papered due to hopping between different attractors. Switching between regimes can be managed by change the artificial birefringence that induced in a laser cavity. For understanding the role playing by the periodical amplification and the resonator, we have performed an unidirectional fiber laser experiments without a saturable absorber. This laser experiment allowed to generate of most of the RW patterns which were either observed experimentally or predicted theoretically. In this way, we have observed the generation of an FORW along with SORW under similar conditions. Most of the patterns were found to be mutually exclusive which means that only one RW mechanism was realized in each regime of generation.

Advances in Dynamic Modeling and Computation for Count Data

A class of multi-process models is developed for collections of time indexed count data. Autocorrelation in counts is achieved with dynamic models for the natural parameter of the binomial distribution. In addition to modeling binomial time series, the framework includes dynamic models for multinomial and Poisson time series. Markov chain Monte Carlo (MCMC) and Po ́lya-Gamma data augmentation (Polson et al., 2013) are critical for fitting multi-process models of counts. To facilitate computation when the counts are high, a Gaussian approximation to the P ́olya- Gamma random variable is developed.

Three applied analyses are presented to explore the utility and versatility of the framework. The first analysis develops a model for complex dynamic behavior of themes in collections of text documents. Documents are modeled as a “bag of words”, and the multinomial distribution is used to characterize uncertainty in the vocabulary terms appearing in each document. State-space models for the natural parameters of the multinomial distribution induce autocorrelation in themes and their proportional representation in the corpus over time.

The second analysis develops a dynamic mixed membership model for Poisson counts. The model is applied to a collection of time series which record neuron level firing patterns in rhesus monkeys. The monkey is exposed to two sounds simultaneously, and Gaussian processes are used to smoothly model the time-varying rate at which the neuron’s firing pattern fluctuates between features associated with each sound in isolation.

The third analysis presents a switching dynamic generalized linear model for the time-varying home run totals of professional baseball players. The model endows each player with an age specific latent natural ability class and a performance enhancing drug (PED) use indicator. As players age, they randomly transition through a sequence of ability classes in a manner consistent with traditional aging patterns. When the performance of the player significantly deviates from the expected aging pattern, he is identified as a player whose performance is consistent with PED use.

All three models provide a mechanism for sharing information across related series locally in time. The models are fit with variations on the P ́olya-Gamma Gibbs sampler, MCMC convergence diagnostics are developed, and reproducible inference is emphasized throughout the dissertation.

Math 412 - Topology with Applications

Highlights of Data Expedition: • Students explored daily observations of local climate data spanning the past 35 years. • Topological Data Analysis, or TDA for short, provides cutting-edge tools for studying the geometry of data in arbitrarily high dimensions. • Using TDA tools, students discovered intrinsic dynamical features of the data and learned how to quantify periodic phenomenon in a time-series. • Since nature invariably produces noisy data which rarely has exact periodicity, students also considered the theoretical basis of almost-periodicity and even invented and tested new mathematical definitions of almost-periodic functions. Summary The dataset we used for this data expedition comes from the Global Historical Climatology Network. “GHCN (Global Historical Climatology Network)-Daily is an integrated database of daily climate summaries from land surface stations across the globe.” Source: https://www.ncdc.noaa.gov/oa/climate/ghcn-daily/ We focused on the daily maximum and minimum temperatures from January 1, 1980 to April 1, 2015 collected from RDU International Airport. Through a guided series of exercises designed to be performed in Matlab, students explore these time-series, initially by direct visualization and basic statistical techniques. Then students are guided through a special sliding-window construction which transforms a time-series into a high-dimensional geometric curve. These high-dimensional curves can be visualized by projecting down to lower dimensions as in the figure below (Figure 1), however, our focus here was to use persistent homology to directly study the high-dimensional embedding. The shape of these curves has meaningful information but how one describes the “shape” of data depends on which scale the data is being considered. However, choosing the appropriate scale is rarely an obvious choice. Persistent homology overcomes this obstacle by allowing us to quantitatively study geometric features of the data across multiple-scales. Through this data expedition, students are introduced to numerically computing persistent homology using the rips collapse algorithm and interpreting the results. In the specific context of sliding-window constructions, 1-dimensional persistent homology can reveal the nature of periodic structure in the original data. I created a special technique to study how these high-dimensional sliding-window curves form loops in order to quantify the periodicity. Students are guided through this construction and learn how to visualize and interpret this information. Climate data is extremely complex (as anyone who has suffered from a bad weather prediction can attest) and numerous variables play a role in determining our daily weather and temperatures. This complexity coupled with imperfections of measuring devices results in very noisy data. This causes the annual seasonal periodicity to be far from exact. To this end, I have students explore existing theoretical notions of almost-periodicity and test it on the data. They find that some existing definitions are also inadequate in this context. Hence I challenged them to invent new mathematics by proposing and testing their own definition. These students rose to the challenge and suggested a number of creative definitions. While autocorrelation and spectral methods based on Fourier analysis are often used to explore periodicity, the construction here provides an alternative paradigm to quantify periodic structure in almost-periodic signals using tools from topological data analysis.

Droplet etching of deep nanoholes for filling with self-aligned complex quantum structures

Strain-free epitaxial quantum dots (QDs) are fabricated by a combination of Al local droplet etching (LDE) of nanoholes in AlGaAs surfaces and subsequent hole filling with GaAs. The whole process is performed in a conventional molecular beam epitaxy (MBE) chamber. Autocorrelation measurements establish single-photon emission from LDE QDs with a very small correlation function g (2)(0)≃ 0.01 of the exciton emission. Here, we focus on the influence of the initial hole depth on the QD optical properties with the goal to create deep holes suited for filling with more complex nanostructures like quantum dot molecules (QDM). The depth of droplet etched nanoholes is controlled by the droplet material coverage and the process temperature, where a higher coverage or temperature yields deeper holes. The requirements of high quantum dot uniformity and narrow luminescence linewidth, which are often found in applications, set limits to the process temperature. At high temperatures, the hole depths become inhomogeneous and the linewidth rapidly increases beyond 640 °C. With the present process technique, we identify an upper limit of 40-nm hole depth if the linewidth has to remain below 100 μeV. Furthermore, we study the exciton fine-structure splitting which is increased from 4.6 μeV in 15-nm-deep to 7.9 μeV in 35-nm-deep holes. As an example for the functionalization of deep nanoholes, self-aligned vertically stacked GaAs QD pairs are fabricated by filling of holes with 35 nm depth. Exciton peaks from stacked dots show linewidths below 100 μeV which is close to that from single QDs.

Multivariate analysis of regional-scale geochemical data for environmental monitoring

A compositional multivariate approach is used to analyse regional scale soil geochemical data obtained as part of the Tellus Project generated by the Geological Survey Northern Ireland (GSNI). The multi-element total concentration data presented comprise XRF analyses of 6862 rural soil samples collected at 20cm depths on a non-aligned grid at one site per 2 km2. Censored data were imputed using published detection limits. Using these imputed values for 46 elements (including LOI), each soil sample site was assigned to the regional geology map provided by GSNI initially using the dominant lithology for the map polygon. Northern Ireland includes a diversity of geology representing a stratigraphic record from the Mesoproterozoic, up to and including the Palaeogene. However, the advance of ice sheets and their meltwaters over the last 100,000 years has left at least 80% of the bedrock covered by superficial deposits, including glacial till and post-glacial alluvium and peat. The question is to what extent the soil geochemistry reflects the underlying geology or superficial deposits. To address this, the geochemical data were transformed using centered log ratios (clr) to observe the requirements of compositional data analysis and avoid closure issues. Following this, compositional multivariate techniques including compositional Principal Component Analysis (PCA) and minimum/maximum autocorrelation factor (MAF) analysis method were used to determine the influence of underlying geology on the soil geochemistry signature. PCA showed that 72% of the variation was determined by the first four principal components (PC’s) implying “significant” structure in the data. Analysis of variance showed that only 10 PC’s were necessary to classify the soil geochemical data. To consider an improvement over PCA that uses the spatial relationships of the data, a classification based on MAF analysis was undertaken using the first 6 dominant factors. Understanding the relationship between soil geochemistry and superficial deposits is important for environmental monitoring of fragile ecosystems such as peat. To explore whether peat cover could be predicted from the classification, the lithology designation was adapted to include the presence of peat, based on GSNI superficial deposit polygons and linear discriminant analysis (LDA) undertaken. Prediction accuracy for LDA classification improved from 60.98% based on PCA using 10 principal components to 64.73% using MAF based on the 6 most dominant factors. The misclassification of peat may reflect degradation of peat covered areas since the creation of superficial deposit classification. Further work will examine the influence of underlying lithologies on elemental concentrations in peat composition and the effect of this in classification analysis.

Modelling the influence of biotic factors on species distribution patterns

Biotic interactions can have large effects on species distributions yet their role in shaping species ranges is seldom explored due to historical difficulties in incorporating biotic factors into models without a priori knowledge on interspecific interactions. Improved SDMs, which account for biotic factors and do not require a priori knowledge on species interactions, are needed to fully understand species distributions. Here, we model the influence of abiotic and biotic factors on species distribution patterns and explore the robustness of distributions under future climate change. We fit hierarchical spatial models using Integrated Nested Laplace Approximation (INLA) for lagomorph species throughout Europe and test the predictive ability of models containing only abiotic factors against models containing abiotic and biotic factors. We account for residual spatial autocorrelation using a conditional autoregressive (CAR) model. Model outputs are used to estimate areas in which abiotic and biotic factors determine species’ ranges. INLA models containing both abiotic and biotic factors had substantially better predictive ability than models containing abiotic factors only, for all but one of the four species. In models containing abiotic and biotic factors, both appeared equally important as determinants of lagomorph ranges, but the influences were spatially heterogeneous. Parts of widespread lagomorph ranges highly influenced by biotic factors will be less robust to future changes in climate, whereas parts of more localised species ranges highly influenced by the environment may be less robust to future climate. SDMs that do not explicitly include biotic factors are potentially misleading and omit a very important source of variation. For the field of species distribution modelling to advance, biotic factors must be taken into account in order to improve the reliability of predicting species distribution patterns both presently and under future climate change.

Urban Ponds as an Aquatic Biodiversity Resource in Modified Landscapes

Urbanization is a global process contributing to the loss and fragmentation of natural habitats. Many studies have focused on the biological response of terrestrial taxa and habitats to urbanization. However, little is known regarding the consequences of urbanization on freshwater habitats, especially small lentic systems. In this study we examined aquatic macroinvertebrate diversity (family and species level) and variation in community composition between 240 urban and 782 non-urban ponds distributed across the UK. Contrary to predictions, urban ponds supported similar numbers of invertebrate species and families compared to non-urban ponds. Similar gamma diversity was found between the two groups at both family and species taxonomic levels. The biological communities of urban ponds were markedly different to those of non-urban ponds and the variability in urban pond community composition was greater than that in non-urban ponds, contrary to previous work showing homogenisation of communities in urban areas. Positive spatial autocorrelation was recorded for urban and non-urban ponds at 0-50 km (distance between pond study sites) and negative spatial autocorrelation was observed at 100-150 km, and was stronger in urban ponds in both cases. Ponds do not follow the same ecological patterns as terrestrial and lotic habitats (reduced taxonomic richness) in urban environments; in contrast they support high taxonomic richness and contribute significantly to regional faunal diversity. Individual cities are complex structural mosaics which evolve over long periods of time and are managed in diverse ways, promoting the development of a wide-range of environmental conditions and habitat niches in urban ponds which can promote greater heterogeneity between pond communities at larger scales. Ponds provide an opportunity for managers and environmental regulators to conserve and enhance freshwater biodiversity in urbanized landscapes whilst also facilitating key ecosystem services including storm water storage and water treatment.

Análise do contributo das acessibilidades rodoviárias para o desenvolvimento regional: o caso da Nut II do Centro

Trabalho Final de Mestrado para obtenção do grau de Mestre em Engenharia Civil na Área de Especialização em Vias de Comunicação e Transportes