Periodic nonlinear Fourier transform for fiber-optic communications, Part I:theory and numerical methods

In this work, we introduce the periodic nonlinear Fourier transform (PNFT) method as an alternative and efficacious tool for compensation of the nonlinear transmission effects in optical fiber links. In the Part I, we introduce the algorithmic platform of the technique, describing in details the direct and inverse PNFT operations, also known as the inverse scattering transform for periodic (in time variable) nonlinear Schrödinger equation (NLSE). We pay a special attention to explaining the potential advantages of the PNFT-based processing over the previously studied nonlinear Fourier transform (NFT) based methods. Further, we elucidate the issue of the numerical PNFT computation: we compare the performance of four known numerical methods applicable for the calculation of nonlinear spectral data (the direct PNFT), in particular, taking the main spectrum (utilized further in Part II for the modulation and transmission) associated with some simple example waveforms as the quality indicator for each method. We show that the Ablowitz-Ladik discretization approach for the direct PNFT provides the best performance in terms of the accuracy and computational time consumption.

Periodic nonlinear Fourier transform for fiber-optic communications, Part II:eigenvalue communication

In this paper we propose the design of communication systems based on using periodic nonlinear Fourier transform (PNFT), following the introduction of the method in the Part I. We show that the famous "eigenvalue communication" idea [A. Hasegawa and T. Nyu, J. Lightwave Technol. 11, 395 (1993)] can also be generalized for the PNFT application: In this case, the main spectrum attributed to the PNFT signal decomposition remains constant with the propagation down the optical fiber link. Therefore, the main PNFT spectrum can be encoded with data in the same way as soliton eigenvalues in the original proposal. The results are presented in terms of the bit-error rate (BER) values for different modulation techniques and different constellation sizes vs. the propagation distance, showing a good potential of the technique.

Physics of Hexagonal Limit-Periodic Phases: Thermodynamics, Formation and Vibrational Modes

Limit-periodic (LP) structures exhibit a type of nonperiodic order yet to be found in a natural material. A recent result in tiling theory, however, has shown that LP order can spontaneously emerge in a two-dimensional (2D) lattice model with nearest-and next-nearest-neighbor interactions. In this dissertation, we explore the question of what types of interactions can lead to a LP state and address the issue of whether the formation of a LP structure in experiments is possible. We study emergence of LP order in three-dimensional (3D) tiling models and bring the subject into the physical realm by investigating systems with realistic Hamiltonians and low energy LP states. Finally, we present studies of the vibrational modes of a simple LP ball and spring model whose results indicate that LP materials would exhibit novel physical properties.

A 2D lattice model defined on a triangular lattice with nearest- and next-nearest-neighbor interactions based on the Taylor-Socolar (TS) monotile is known to have a LP ground state. The system reaches that state during a slow quench through an infinite sequence of phase transitions. Surprisingly, even when the strength of the next-nearest-neighbor interactions is zero, in which case there is a large degenerate class of both crystalline and LP ground states, a slow quench yields the LP state. The first study in this dissertation introduces 3D models closely related to the 2D models that exhibit LP phases. The particular 3D models were designed such that next-nearest-neighbor interactions of the TS type are implemented using only nearest-neighbor interactions. For one of the 3D models, we show that the phase transitions are first order, with equilibrium structures that can be more complex than in the 2D case.

In the second study, we investigate systems with physical Hamiltonians based on one of the 2D tiling models with the goal of stimulating attempts to create a LP structure in experiments. We explore physically realizable particle designs while being mindful of particular features that may make the assembly of a LP structure in an experimental system difficult. Through Monte Carlo (MC) simulations, we have found that one particle design in particular is a promising template for a physical particle; a 2D system of identical disks with embedded dipoles is observed to undergo the series of phase transitions which leads to the LP state.

LP structures are well ordered but nonperiodic, and hence have nontrivial vibrational modes. In the third section of this dissertation, we study a ball and spring model with a LP pattern of spring stiffnesses and identify a set of extended modes with arbitrarily low participation ratios, a situation that appears to be unique to LP systems. The balls that oscillate with large amplitude in these modes live on periodic nets with arbitrarily large lattice constants. By studying periodic approximants to the LP structure, we present numerical evidence for the existence of such modes, and we give a heuristic explanation of their structure.

Experimental analysis of novel telecom source materials and devices

Incumbent telecommunication lasers emitting at 1.5 µm are fabricated on InP substrates and consist of multiple strained quantum well layers of the ternary alloy InGaAs, with barriers of InGaAsP or InGaAlAs. These lasers have been seen to exhibit very strong temperature dependence of the threshold current. This strong temperature dependence leads to a situation where external cooling equipment is required to stabilise the optical output power of these lasers. This results in a significant increase in the energy bill associated with telecommunications, as well as a large increase in equipment budgets. If the exponential growth trend of end user bandwidth demand associated with the internet continues, these inefficient lasers could see the telecommunications industry become the dominant consumer of world energy. For this reason there is strong interest in developing new, much more efficient telecommunication lasers. One avenue being investigated is the development of quantum dot lasers on InP. The confinement experienced in these low dimensional structures leads to a strong perturbation of the density of states at the band edge, and has been predicted to result in reduced temperature dependence of the threshold current in these devices. The growth of these structures is difficult due to the large lattice mismatch between InP and InAs; however, recently quantum dots elongated in one dimension, known as quantum dashes, have been demonstrated. Chapter 4 of this thesis provides an experimental analysis of one of these quantum dash lasers emitting at 1.5 µm along with a numerical investigation of threshold dynamics present in this device. Another avenue being explored to increase the efficiency of telecommunications lasers is bandstructure engineering of GaAs-based materials to emit at 1.5 µm. The cause of the strong temperature sensitivity in InP-based quantum well structures has been shown to be CHSH Auger recombination. Calculations have shown and experiments have verified that the addition of bismuth to GaAs strongly reduces the bandgap and increases the spin orbit splitting energy of the alloy GaAs1−xBix. This leads to a bandstructure condition at x = 10 % where not only is 1.5 µm emission achieved on GaAs-based material, but also the bandstructure of the material can naturally suppress the costly CHSH Auger recombination which plagues InP-based quantum-well-based material. It has been predicted that telecommunications lasers based on this material system should operate in the absence of external cooling equipment and offer electrical and optical benefits over the incumbent lasers. Chapters 5, 6, and 7 provide a first analysis of several aspects of this material system relevant to the development of high bismuth content telecommunication lasers.

Periodic Breathing and Behavioral Awakenings at High Altitude.

Objectives. To study the relationship between nocturnal periodic breathing episodes and behavioral awakenings at high altitude. Methods. Observational study. It is 6-day ascent of 4 healthy subjects from Besisahar (760 meters) to Manang (3540 meters) in Nepal in March 2012. A recording pulse oximeter was worn by each subject to measure their oxygen saturation and the presence of periodic breathing continuously through the night. An actigraph was simultaneously worn in order to determine nocturnal behavioral awakenings. There were no interventions. Results. 187-hour sleep at high altitude was analyzed, and of this, 145 hours (78%) had at least one PB event. At high altitude, 10.5% (95% CI 6.5-14.6%) of total sleep time was spent in PB while 15 out of 50 awakenings (30%, 95% CI: 18-45%) occurring at high altitudes were associated with PB (P < 0.001). Conclusions. Our data reveals a higher than expected number of behavioral awakenings associated with PB compared to what would be expected by chance. This suggests that PB likely plays a role in behavioral awakenings at high altitude.

THE DESIGN AND SYNTHESIS OF SILOXANE PRECURSORS FOR CHIRAL PERIODIC MESOPOROUS ORGANOSILICA MATERIALS

The development of cost-effective and reliable methods for the synthesis and separation of asymmetric compounds is paramount in helping to meet society’s ever-growing demand for chiral small molecules. Of these methods, chiral heterogeneous supports are particularly appealing as they allow for the reuse of the chiral source. One such support, based on the synergy between chiral organic units and structurally stable inorganic silicon scaffolds are periodic mesoporous organosilicas (PMOs). In the work described herein, I examine some of the factors governing the transmission of chirality between chiral dopants and prochiral bulk phases in chiral PMO materials. In particular, the exploration of 1,1’-binaphthalene-bridged chiral dopants with a focus on the point of attachment into the materials. Moreover, the effects of ordering in the materials are examined and reveal that chirality transfer is more facile in materials with molecular-scale order then those containing amorphous walls. Secondly, the issues surrounding the synthesis and purification of aryl-triethoxysilanes as siloxane precursors are addressed. Both the introduction of a two-carbon linker and the direct attachment of allyl and mixed allyldiethoxysilane species are explored. This work demonstrates that allyldiethoxysilanes are ideal, in that they are stable enough to permit facile synthesis, while still being able to hydrolyze completely to produce well-ordered materials. Lastly, the production of new bulk phases for chiral PMO materials is examined by introducing new prochiral nitrogen-containing siloxane precursors. Biphenyldiamine and bipyridine-bridged siloxane precursors are readily synthesized on reasonable scales. Their use as the bulk siloxane precursor in the production of PMO materials however, is precluded by insufficient gelation and additional siloxane precursors are necessary for the production of ordered materials. In addition to the research detailed above that forms the body of this thesis, two short works are appended. The first details the production of polythiophene assemblies mediated through coordination nanospaces, while the second explores the production of N-heterocyclic carbene functionalized gold nanoparticles through ligand exchange.

UPTAKE OF THE PERIODIC HEALTH EXAM AMONG ADULTS WITH INTELLECTUAL AND DEVELOPMENTAL DISABILITIES FROM 2003 TO 2015

Background: Over the past decade, annual heath exams have been de-emphasized for the general population but emphasized for adults with intellectual and developmental disabilities (IDD). The purpose of this project was to determine if there has been an increase in the uptake of the health exam among adults with IDD in Ontario, to what extent, and the effect on the quality of preventive care provided. Methods: Using administrative health data, the proportion of adults (18-64 years old) with IDD who received a health exam (long appointment, general assessment, and “true” health exam), a high value on the primary care quality composite score (PCQS), and a health exam or high PCQS each year was compared to the proportion in a propensity score matched sample of the general population. Negative binomial and segmented negative binomial regression controlling for age and sex were used to determine the relative risk of having a health exam/high PCQS/health exam or PCQS over time. Results: Pre joinpoint, the long appointment and general assessment health exam definitions saw a decrease and the “true” health exam saw an increase in the likelihood of adults having a health exam. Post joinpoint, all health exam definitions saw a decrease in the likelihood of adults having a health exam. Pre joinpoint, all PCQS measures (high PCQS, long appointment or high PCQS, “true” health exam or high PCQS) saw an increase in the likelihood for adults to achieve a high PCQS or high PCQS/have a health exam. Post joinpoint, all PCQS measures saw a decrease in the likelihood for adults to achieve a high PCQS or high PCQS/have a health exam. Achieving a high PCQS was strongly associated with having a health exam regardless of health exam definition or IDD status. Conclusions: Despite the publication of guidelines, only a small proportion of adults with IDD are receiving health exams. This indicates that the publication of guidelines alone was not sufficient to change practice. More targeted measures, such as the implementation of an IDD-specific health exam fee code, should be considered to increase the uptake of the health exam among adults with IDD.

Discrete-time positive periodic systems with state and control constraints

The aim of this paper is to provide an efficient control design technique for discrete-time positive periodic systems. In particular, stability, positivity and periodic invariance of such systems are studied. Moreover, the concept of periodic invariance with respect to a collection of boxes is introduced and investigated with connection to stability. It is shown how such concept can be used for deriving a stabilizing state-feedback control that maintains the positivity of the closed-loop system and respects states and control signals constraints. In addition, all the proposed results can be efficiently solved in terms of linear programming.

Report on the Status of Findings and Recommendations from the City of Lambs Grove Periodic Examination Report dated September 4, 2014 for the period June 1, 2015 through February 29, 2016

Report on the Status of Findings and Recommendations from the City of Lambs Grove Periodic Examination Report dated September 4, 2014 for the period June 1, 2015 through February 29, 2016

SYSTEMS OF DIFFERENTIAL EQUATIONSTHAT ARE COMPETITIVE OR COOPERATIVE II:CONVERGENCE ALMOST EVERYWHERE*MORRIS W. HIRSCH

A vector field in n-space determines a competitive (or cooperative) system of differential equations provided all of the off-diagonal terms of its Jacobian matrix are nonpositive (or nonnegative). The main results in this article are the following. A cooperative system cannot have nonconstant attracting periodic solutions. In a cooperative system whose Jacobian matrices are irreducible the forward orbit converges for almost every point having compact forward orbit closure. In a cooperative system in 2 dimensions, every solution is eventually monotone.  Applications are made to generalizations of positive feedback loops.

A Periodic State Space Model to Monthly Long-term Temperature Data

This work presents a periodic state space model to model monthly temperature data. Additionally, some issues are discussed, as the parameter estimation or the Kalman filter recursions adapted to a periodic model. This framework is applied to monthly long-term temperature time series of Lisbon.

Produção científica gaúcha em ciências da saúde: estudo cientométrico

Estudo cientométrico sobre a produção científica na área das ciências da saúde, de pesquisadores vinculados com instituições localizadas no estado do Rio Grande do Sul. Foram analisados os artigos publicados em periódicos indexados pela base de dados bibliográfica Medline entre os anos de 1987 e 2012. Os resultados mostraram que 23.442 autores vinculados com 34 instituições, publicaram 12.423 artigos em 1.912 diferentes periódicos. As análises temporais revelaram que houve um crescimento constante na produção científica que passou de 16 artigos no ano de 1987 para 12.423 em 2012. A média geométrica deste crescimento foi de 22,755% ao ano. Comparado com um estudo anterior que utilizou a mesma fonte de dados, verificou-se que a produção científica do Rio Grande do Sul apresentou uma média maior que a brasileira. Sete instituições lideram o ranking das mais produtivas concentrando 83,64% de todos os artigos publicados no período, sendo cinco universidades públicas e duas privadas. Na área das ciências da saúde, a Universidade Federal do Rio Grande do Sul foi a líder de produtividade, seguida da Universidade de Santa Maria e Federal de Pelotas. Verificou-se que os autores mais prolíferos foram aqueles vinculados com instituições públicas. A Unidade Integrada Vale do Taquari de Ensino Superior, ocupou o primeiro lugar no grau de colaboração. O periódico “Cadernos de Saúde Pública”, foi o mais utilizado pelos pesquisadores das instituições gaúchas.