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.

Influence of Outlet Boundary Conditions on Cerebrovascular Aneurysm Hemodynamics

Computational fluid dynamic (CFD) studies of blood flow in cerebrovascular aneurysms have potential to improve patient treatment planning by enabling clinicians and engineers to model patient-specific geometries and compute predictors and risks prior to neurovascular intervention. However, the use of patient-specific computational models in clinical settings is unfeasible due to their complexity, computationally intensive and time-consuming nature. An important factor contributing to this challenge is the choice of outlet boundary conditions, which often involves a trade-off between physiological accuracy, patient-specificity, simplicity and speed. In this study, we analyze how resistance and impedance outlet boundary conditions affect blood flow velocities, wall shear stresses and pressure distributions in a patient-specific model of a cerebrovascular aneurysm. We also use geometrical manipulation techniques to obtain a model of the patient’s vasculature prior to aneurysm development, and study how forces and stresses may have been involved in the initiation of aneurysm growth. Our CFD results show that the nature of the prescribed outlet boundary conditions is not as important as the relative distributions of blood flow through each outlet branch. As long as the appropriate parameters are chosen to keep these flow distributions consistent with physiology, resistance boundary conditions, which are simpler, easier to use and more practical than their impedance counterparts, are sufficient to study aneurysm pathophysiology, since they predict very similar wall shear stresses, time-averaged wall shear stresses, time-averaged pressures, and blood flow patterns and velocities. The only situations where the use of impedance boundary conditions should be prioritized is if pressure waveforms are being analyzed, or if local pressure distributions are being evaluated at specific time points, especially at peak systole, where the use of resistance boundary conditions leads to unnaturally large pressure pulses. In addition, we show that in this specific patient, the region of the blood vessel where the neck of the aneurysm developed was subject to abnormally high wall shear stresses, and that regions surrounding blebs on the aneurysmal surface were subject to low, oscillatory wall shear stresses. Computational models using resistance outlet boundary conditions may be suitable to study patient-specific aneurysm progression in a clinical setting, although several other challenges must be addressed before these tools can be applied clinically.

Quantitative Analysis of Kilohertz-Frequency Neurostimulation

Mainstream electrical stimulation therapies, e.g., spinal cord stimulation (SCS) and deep brain stimulation, use pulse trains that are delivered at rates no higher than 200 Hz. In recent years, stimulation of nerve fibers using kilohertz-frequency (KHF) signals has received increased attention due to the potential to penetrate deeper in the tissue and to the ability to block conduction of action potentials. As well, there are a growing number of clinical applications that use KHF waveforms, including transcutaneous electrical stimulation (TES) for overactive bladder and SCS for chronic pain. However, there is a lack of fundamental understanding of the mechanisms of action of KHF stimulation. The goal of this research was to analyze quantitatively KHF neurostimulation.

We implemented a multilayer volume conductor model of TES including dispersion and capacitive effects, and we validated the model with in vitro measurements in a phantom constructed from dispersive materials. We quantified the effects of frequency on the distribution of potentials and fiber excitation. We also quantified the effects of a novel transdermal amplitude modulated signal (TAMS) consisting of a non-zero offset sinusoidal carrier modulated by a square-pulse train. The model revealed that high-frequency signals generated larger potentials at depth than did low frequencies, but this did not translate into lower stimulation thresholds. Both TAMS and conventional rectangular pulses activated more superficial fibers in addition to the deeper, target fibers, and at no frequency did we observe an inversion of the strength-distance relationship. In addition, we performed in vivo experiments and applied direct stimulation to the sciatic nerve of cats and rats. We measured electromyogram and compound action potential activity evoked by pulses, TAMS and modified versions of TAMS in which we varied the amplitude of the carrier. Nerve fiber activation using TAMS showed no difference with respect to activation with conventional pulse for carrier frequencies of 20 kHz and higher, regardless the size of the carrier. Therefore, TAMS with carrier frequencies >20 kHz does not offer any advantage over conventional pulses, even with larger amplitudes of the carrier, and this has implications for design of waveforms for efficient and effective TES.

We developed a double cable model of a dorsal column (DC) fiber to quantify the responses of DC fibers to a novel KHF-SCS signal. We validated the model using in vivo recordings of the strength-duration relationship and the recovery cycle of single DC fibers. We coupled the fiber model to a model of SCS in human and applied the KHF-SCS signal to quantify thresholds for activation and conduction block for different fiber diameters at different locations in the DCs. Activation and block thresholds increased sharply as the fibers were placed deeper in the DCs, and decreased for larger diameter fibers. Activation thresholds were > 5 mA in all cases and up to five times higher than for conventional (~ 50 Hz) SCS. For fibers exhibiting persistent activation, the degree of synchronization of the firing activity to the KHF-SCS signal, as quantified using the vector strength, was low for a broad amplitude range, and the dissimilarity between the activities in pairs of fibers, as quantified using the spike time distance, was high and decreased for more closely positioned fibers. Conduction block thresholds were higher than 30 mA for all fiber diameters at any depth and well above the amplitudes used clinically (0.5 – 5 mA). KHF-SCS appears to activate few, large, superficial fibers, and the activated fibers fire asynchronously to the stimulation signal and to other activated fibers.

The outcomes of this work contribute to the understanding of KHF neurostimulation by establishing the importance of the tissue filtering properties on the distribution of potentials, assessing quantitatively the impact of KHF stimulation on nerve fiber excitation, and developing and validating a detailed model of a DC fiber to characterize the effects of KHF stimulation on DC axons. The results have implications for design of waveforms for efficient and effective nerve fiber stimulation in the peripheral and central nervous system.

Time-resolved dosimetric verification of respiratory-gated radiotherapy exposures using a high-resolution 2D ionisation chamber array

The aim of this work was to track and verify the delivery of respiratory-gated irradiations, performed with three versions of TrueBeam linac, using a novel phantom arrangement that combined the OCTAVIUS® SRS 1000 array with a moving platform. The platform was programmed to generate sinusoidal motion of the array. This motion was tracked using the real-time position management (RPM) system and four amplitude gating options were employed to interrupt MV beam delivery when the platform was not located within set limits. Time-resolved spatial information extracted from analysis of x-ray fluences measured by the array was compared to the programmed motion of the platform and to the trace recorded by the RPM system during the delivery of the x-ray field. Temporal data recorded by the phantom and the RPM system were validated against trajectory log files, recorded by the linac during the irradiation, as well as oscilloscope waveforms recorded from the linac target signal. Gamma analysis was employed to compare time-integrated 2D x-ray dose fluences with theoretical fluences derived from the probability density function for each of the gating settings applied, where gamma criteria of 2%/2 mm, 1%/1 mm and 0.5%/0.5 mm were used to evaluate the limitations of the RPM system. Excellent agreement was observed in the analysis of spatial information extracted from the SRS 1000 array measurements. Comparisons of the average platform position with the expected position indicated absolute deviations of  <0.5 mm for all four gating settings. Differences were observed when comparing time-resolved beam-on data stored in the RPM files and trajectory logs to the true target signal waveforms. Trajectory log files underestimated the cycle time between consecutive beam-on windows by 10.0  ±  0.8 ms. All measured fluences achieved 100% pass-rates using gamma criteria of 2%/2 mm and 50% of the fluences achieved pass-rates  >90% when criteria of 0.5%/0.5 mm were used. Results using this novel phantom arrangement indicate that the RPM system is capable of accurately gating x-ray exposure during the delivery of a fixed-field treatment beam.

Using the interaural time difference and cross-correlation to localise short-term complex noises

The mammalian binaural cue of interaural time difference (ITD) and cross-correlation have long been used to determine the point of origin of a sound source. The ITD can be defined as the different points in time at which a sound from a single location arrives at each individual ear [1]. From this time difference, the brain can calculate the angle of the sound source in relation to the head [2]. Cross-correlation compares the similarity of each channel of a binaural waveform producing the time lag or offset required for both channels to be in phase with one another. This offset corresponds to the maximum value produced by the cross-correlation function and can be used to determine the ITD and thus the azimuthal angle θ of the original sound source. However, in indoor environments, cross-correlation has been known to have problems with both sound reflections and reverberations. Additionally, cross-correlation has difficulties with localising short-term complex noises when they occur during a longer duration waveform, i.e. in the presence of background noise. The crosscorrelation algorithm processes the entire waveform and the short-term complex noise can be ignored. This paper presents a technique using thresholding which enables higher-localisation abilities for short-term complex sounds in the midst of background noise. To determine the success of this thresholding technique, twenty-five sounds were recorded in a dynamic and echoic environment. The twenty-five sounds consist of hand-claps, finger-clicks and speech. The proposed technique was compared to the regular cross-correlation function for the same waveforms, and an average of the azimuthal angles determined for each individual sample. The sound localisation ability for all twenty-five sound samples is as follows: average of the sampled angles using cross-correlation: 44%; cross-correlation technique with thresholding: 84%. From these results, it is clear that this proposed technique is very successful for the localisation of short-term complex sounds in the midst of background noise and in a dynamic and echoic indoor environment.

OFDM-based schemes for next generation wireless systems

The purpose of this study is to investigate two candidate waveforms for next generation wireless systems, filtered Orthogonal Frequency Division Multiplexing (f-OFDM) and Unified Filtered Multi-Carrier (UFMC). The evaluation is done based on the power spectral density analysis of the signal and performance measurements in synchronous and asynchronous transmission. In f-OFDM we implement a soft truncated filter with length 1/3 of OFDM symbol. In UFMC we use the Dolph-Chebyshev filter, limited to the length of zero padding (ZP). The simulation results demonstrates that both waveforms have a better spectral behaviour compared with conventional OFDM. However, the induced inter-symbol interference (ISI) caused by the filter in f-OFDM, and the inter-carrier interference (ICI) induced in UFMC due to cyclic prefix (CP) reduction , should be kept under control. In addition, in a synchronous transmission case with ideal parameters, f-OFDM and UFMC appear to have similar performance with OFDM. When carrier frequency offset (CFO) is imposed in the transmission, UFMC outperforms OFDM and f-OFDM.

Event-related potential effects of object repetition depend on attention and part-whole configuration

The effects of spatial attention and part-whole configuration on recognition of repeated objects were investigated with behavioral and event-related potential (ERP) measures. Short-term repetition effects were measured for probe objects as a function of whether a preceding prime object was shown as an intact image or coarsely scrambled (split into two halves) and whether or not it had been attended during the prime display. In line with previous behavioral experiments, priming effects were observed from both intact and split primes for attended objects, but only from intact (repeated same-view) objects when they were unattended. These behavioral results were reflected in ERP waveforms at occipital-temporal locations as more negative-going deflections for repeated items in the time window between 220 and 300 ms after probe onset (N250r). Attended intact images showed generally more enhanced repetition effects than split ones. Unattended images showed repetition effects only when presented in an intact configuration, and this finding was limited to the right-hemisphere electrodes. Repetition effects in earlier (before 200 ms) time-windows were limited to attended conditions at occipito-temporal sites (N1), a component linked to the encoding of object structure, while repetition effects at central locations during the same time window (P150) were found only from objects repeated in the same intact configuration—both previously attended and unattended probe objects. The data indicate that view-generalization is mediated by a combination of analytic (part-based) representations and automatic view-dependent representations.

Orthogonal chirp division multiplexing for coherent optical fiber communications

In this paper, we propose an orthogonal chirp division multiplexing (OCDM) technique for coherent optical communication. OCDM is the principle of orthogonally multiplexing a group of linear chirped waveforms for high-speed data communication, achieving the maximum spectral efficiency (SE) for chirp spread spectrum, in a similar way as the orthogonal frequency division multiplexing (OFDM) does for frequency division multiplexing. In the coherent optical (CO)-OCDM, Fresnel transform formulates the synthesis of the orthogonal chirps; discrete Fresnel transform (DFnT) realizes the CO-OCDM in the digital domain. As both the Fresnel and Fourier transforms are trigonometric transforms, the CO-OCDM can be easily integrated into the existing CO-OFDM systems. Analyses and numerical results are provided to investigate the transmission of CO-OCDM signals over optical fibers. Moreover, experiments of 36-Gbit/s CO-OCDM signal are carried out to validate the feasibility and confirm the analyses. It is shown that the CO-OCDM can effectively compensate the dispersion and is more resilient to fading and noise impairment than OFDM.

Fadiga e conforto do quadricípite femoral gerados por estimulação eléctrica neuromuscular com modulação da forma de onda

Mestrado em Fisioterapia

Seismic waveform inversion for core-mantle boundary topography

International audience

Asymptotic analysis of combined breather-kink modes in a Fermi-Pasta-Ulam chain

We find approximations to travelling breather solutions of the one-dimensional Fermi-Pasta-Ulam (FPU) lattice. Both bright breather and dark breather solutions are found. We find that the existence of localised (bright) solutions depends upon the coefficients of cubic and quartic terms of the potential energy, generalising an earlier inequality derived by James [CR Acad Sci Paris 332, 581, (2001)]. We use the method of multiple scales to reduce the equations of motion for the lattice to a nonlinear Schr{\"o}dinger equation at leading order and hence construct an asymptotic form for the breather. We show that in the absence of a cubic potential energy term, the lattice supports combined breathing-kink waveforms. The amplitude of breathing-kinks can be arbitrarily small, as opposed to traditional monotone kinks, which have a nonzero minimum amplitude in such systems. We also present numerical simulations of the lattice, verifying the shape and velocity of the travelling waveforms, and confirming the long-lived nature of all such modes.

Time-Reversal Massive Multipath Effect and Bandwidth Heterogeneity

The proliferation of new mobile communication devices, such as smartphones and tablets, has led to an exponential growth in network traffic. The demand for supporting the fast-growing consumer data rates urges the wireless service providers and researchers to seek a new efficient radio access technology, which is the so-called 5G technology, beyond what current 4G LTE can provide. On the other hand, ubiquitous RFID tags, sensors, actuators, mobile phones and etc. cut across many areas of modern-day living, which offers the ability to measure, infer and understand the environmental indicators. The proliferation of these devices creates the term of the Internet of Things (IoT). For the researchers and engineers in the field of wireless communication, the exploration of new effective techniques to support 5G communication and the IoT becomes an urgent task, which not only leads to fruitful research but also enhance the quality of our everyday life. Massive MIMO, which has shown the great potential in improving the achievable rate with a very large number of antennas, has become a popular candidate. However, the requirement of deploying a large number of antennas at the base station may not be feasible in indoor scenarios. Does there exist a good alternative that can achieve similar system performance to massive MIMO for indoor environment? In this dissertation, we address this question by proposing the time-reversal technique as a counterpart of massive MIMO in indoor scenario with the massive multipath effect. It is well known that radio signals will experience many multipaths due to the reflection from various scatters, especially in indoor environments. The traditional TR waveform is able to create a focusing effect at the intended receiver with very low transmitter complexity in a severe multipath channel. TR's focusing effect is in essence a spatial-temporal resonance effect that brings all the multipaths to arrive at a particular location at a specific moment. We show that by using time-reversal signal processing, with a sufficiently large bandwidth, one can harvest the massive multipaths naturally existing in a rich-scattering environment to form a large number of virtual antennas and achieve the desired massive multipath effect with a single antenna. Further, we explore the optimal bandwidth for TR system to achieve maximal spectral efficiency. Through evaluating the spectral efficiency, the optimal bandwidth for TR system is found determined by the system parameters, e.g., the number of users and backoff factor, instead of the waveform types. Moreover, we investigate the tradeoff between complexity and performance through establishing a generalized relationship between the system performance and waveform quantization in a practical communication system. It is shown that a 4-bit quantized waveforms can be used to achieve the similar bit-error-rate compared to the TR system with perfect precision waveforms. Besides 5G technology, Internet of Things (IoT) is another terminology that recently attracts more and more attention from both academia and industry. In the second part of this dissertation, the heterogeneity issue within the IoT is explored. One of the significant heterogeneity considering the massive amount of devices in the IoT is the device heterogeneity, i.e., the heterogeneous bandwidths and associated radio-frequency (RF) components. The traditional middleware techniques result in the fragmentation of the whole network, hampering the objects interoperability and slowing down the development of a unified reference model for the IoT. We propose a novel TR-based heterogeneous system, which can address the bandwidth heterogeneity and maintain the benefit of TR at the same time. The increase of complexity in the proposed system lies in the digital processing at the access point (AP), instead of at the devices' ends, which can be easily handled with more powerful digital signal processor (DSP). Meanwhile, the complexity of the terminal devices stays low and therefore satisfies the low-complexity and scalability requirement of the IoT. Since there is no middleware in the proposed scheme and the additional physical layer complexity concentrates on the AP side, the proposed heterogeneous TR system better satisfies the low-complexity and energy-efficiency requirement for the terminal devices (TDs) compared with the middleware approach.

Probabilistic Imaging and Dynamic Modeling of Earthquake Source Processes

Investigation of large, destructive earthquakes is challenged by their infrequent occurrence and the remote nature of geophysical observations. This thesis sheds light on the source processes of large earthquakes from two perspectives: robust and quantitative observational constraints through Bayesian inference for earthquake source models, and physical insights on the interconnections of seismic and aseismic fault behavior from elastodynamic modeling of earthquake ruptures and aseismic processes.

To constrain the shallow deformation during megathrust events, we develop semi-analytical and numerical Bayesian approaches to explore the maximum resolution of the tsunami data, with a focus on incorporating the uncertainty in the forward modeling. These methodologies are then applied to invert for the coseismic seafloor displacement field in the 2011 Mw 9.0 Tohoku-Oki earthquake using near-field tsunami waveforms and for the coseismic fault slip models in the 2010 Mw 8.8 Maule earthquake with complementary tsunami and geodetic observations. From posterior estimates of model parameters and their uncertainties, we are able to quantitatively constrain the near-trench profiles of seafloor displacement and fault slip. Similar characteristic patterns emerge during both events, featuring the peak of uplift near the edge of the accretionary wedge with a decay toward the trench axis, with implications for fault failure and tsunamigenic mechanisms of megathrust earthquakes.

To understand the behavior of earthquakes at the base of the seismogenic zone on continental strike-slip faults, we simulate the interactions of dynamic earthquake rupture, aseismic slip, and heterogeneity in rate-and-state fault models coupled with shear heating. Our study explains the long-standing enigma of seismic quiescence on major fault segments known to have hosted large earthquakes by deeper penetration of large earthquakes below the seismogenic zone, where mature faults have well-localized creeping extensions. This conclusion is supported by the simulated relationship between seismicity and large earthquakes as well as by observations from recent large events. We also use the modeling to connect the geodetic observables of fault locking with the behavior of seismicity in numerical models, investigating how a combination of interseismic geodetic and seismological estimates could constrain the locked-creeping transition of faults and potentially their co- and post-seismic behavior.

Exploration of Ground Penetrating Radar and Time Domain Reflectometry Methods for the Determination of Pavement Dielectric Constant

Traditionally, densities of newly built roadways are checked by direct sampling (cores) or by nuclear density gauge measurements. For roadway engineers, density of asphalt pavement surfaces is essential to determine pavement quality. Unfortunately, field measurements of density by direct sampling or by nuclear measurement are slow processes. Therefore, I have explored the use of rapidly-deployed ground penetrating radar (GPR) as an alternative means of determining pavement quality. The dielectric constant of pavement surface may be a substructure parameter that correlates with pavement density, and can be used as a proxy when density of asphalt is not known from nuclear or destructive methods. The dielectric constant of the asphalt can be determined using ground penetrating radar (GPR). In order to use GPR for evaluation of road surface quality, the relationship between dielectric constants of asphalt and their densities must be established. Field measurements of GPR were taken at four highway sites in Houghton and Keweenaw Counties, Michigan, where density values were also obtained using nuclear methods in the field. Laboratory studies involved asphalt samples taken from the field sites and samples created in the laboratory. These were tested in various ways, including, density, thickness, and time domain reflectometry (TDR). In the field, GPR data was acquired using a 1000 MHz air-launched unit and a ground-coupled unit at 200 and 500 MHz. The equipment used was owned and operated by the Michigan Department of Transportation (MDOT) and available for this study for a total of four days during summer 2005 and spring 2006. The analysis of the reflected waveforms included “routine” processing for velocity using commercial software and direct evaluation of reflection coefficients to determine a dielectric constant. The dielectric constants computed from velocities do not agree well with those obtained from reflection coefficients. Perhaps due to the limited range of asphalt types studied, no correlation between density and dielectric constant was evident. Laboratory measurements were taken with samples removed from the field and samples created for this study. Samples from the field were studied using TDR, in order to obtain dielectric constant directly, and these correlated well with the estimates made from reflection coefficients. Samples created in the laboratory were measured using 1000 MHz air-launched GPR, and 400 MHz ground-coupled GPR, each under both wet and dry conditions. On the basis of these observations, I conclude that dielectric constant of asphalt can be reliably measured from waveform amplitude analysis of GJPR data, based on the consistent agreement with that obtained in the laboratory using TDR. Because of the uniformity of asphalts studied here, any correlation between dielectric constant and density is not yet apparent.

The effect of notch filtering on the waveform of the newborn auditory brainstem response

OBJECTIVE: To identify whether the use of a notch filter significantly affects the morphology or characteristics of the newborn auditory brainstem response (ABR) waveform and so inform future guidance for clinical practice. DESIGN: Waveforms with and without the application of a notch filter were recorded from babies undergoing routine ABR tests at 4000, 1000 and 500 Hz. Any change in response morphology was judged subjectively. Response latency, amplitude, and measurements of response quality and residual noise were noted. An ABR simulator was also used to assess the effect of notch filtering in conditions of low and high mains interference. RESULTS: The use of a notch filter changed waveform morphology for 500 Hz stimuli only in 15% of tests in newborns. Residual noise was lower when 4000 Hz stimuli were used. Response latency, amplitude, and quality were unaffected regardless of stimulus frequency. Tests with the ABR stimulator suggest that these findings can be extended to conditions of high level mains interference. CONCLUSIONS: A notch filter should be avoided when testing at 500 Hz, but at higher frequencies appears to carry no penalty.