Nested Sampling and its Applications in Stable Compressive Covariance Estimation and Phase Retrieval with Near-Minimal Measurements

Compressed covariance sensing using quadratic samplers is gaining increasing interest in recent literature. Covariance matrix often plays the role of a sufficient statistic in many signal and information processing tasks. However, owing to the large dimension of the data, it may become necessary to obtain a compressed sketch of the high dimensional covariance matrix to reduce the associated storage and communication costs. Nested sampling has been proposed in the past as an efficient sub-Nyquist sampling strategy that enables perfect reconstruction of the autocorrelation sequence of Wide-Sense Stationary (WSS) signals, as though it was sampled at the Nyquist rate. The key idea behind nested sampling is to exploit properties of the difference set that naturally arises in quadratic measurement model associated with covariance compression. In this thesis, we will focus on developing novel versions of nested sampling for low rank Toeplitz covariance estimation, and phase retrieval, where the latter problem finds many applications in high resolution optical imaging, X-ray crystallography and molecular imaging. The problem of low rank compressive Toeplitz covariance estimation is first shown to be fundamentally related to that of line spectrum recovery. In absence if noise, this connection can be exploited to develop a particular kind of sampler called the Generalized Nested Sampler (GNS), that can achieve optimal compression rates. In presence of bounded noise, we develop a regularization-free algorithm that provably leads to stable recovery of the high dimensional Toeplitz matrix from its order-wise minimal sketch acquired using a GNS. Contrary to existing TV-norm and nuclear norm based reconstruction algorithms, our technique does not use any tuning parameters, which can be of great practical value. The idea of nested sampling idea also finds a surprising use in the problem of phase retrieval, which has been of great interest in recent times for its convex formulation via PhaseLift, By using another modified version of nested sampling, namely the Partial Nested Fourier Sampler (PNFS), we show that with probability one, it is possible to achieve a certain conjectured lower bound on the necessary measurement size. Moreover, for sparse data, an l1 minimization based algorithm is proposed that can lead to stable phase retrieval using order-wise minimal number of measurements.

Evolution of classifiers for pitch estimation of piano music using cartesian genetic programming

Pitch Estimation, also known as Fundamental Frequency (F0) estimation, has been a popular research topic for many years, and is still investigated nowadays. The goal of Pitch Estimation is to find the pitch or fundamental frequency of a digital recording of a speech or musical notes. It plays an important role, because it is the key to identify which notes are being played and at what time. Pitch Estimation of real instruments is a very hard task to address. Each instrument has its own physical characteristics, which reflects in different spectral characteristics. Furthermore, the recording conditions can vary from studio to studio and background noises must be considered. This dissertation presents a novel approach to the problem of Pitch Estimation, using Cartesian Genetic Programming (CGP).We take advantage of evolutionary algorithms, in particular CGP, to explore and evolve complex mathematical functions that act as classifiers. These classifiers are used to identify piano notes pitches in an audio signal. To help us with the codification of the problem, we built a highly flexible CGP Toolbox, generic enough to encode different kind of programs. The encoded evolutionary algorithm is the one known as 1 + , and we can choose the value for . The toolbox is very simple to use. Settings such as the mutation probability, number of runs and generations are configurable. The cartesian representation of CGP can take multiple forms and it is able to encode function parameters. It is prepared to handle with different type of fitness functions: minimization of f(x) and maximization of f(x) and has a useful system of callbacks. We trained 61 classifiers corresponding to 61 piano notes. A training set of audio signals was used for each of the classifiers: half were signals with the same pitch as the classifier (true positive signals) and the other half were signals with different pitches (true negative signals). F-measure was used for the fitness function. Signals with the same pitch of the classifier that were correctly identified by the classifier, count as a true positives. Signals with the same pitch of the classifier that were not correctly identified by the classifier, count as a false negatives. Signals with different pitch of the classifier that were not identified by the classifier, count as a true negatives. Signals with different pitch of the classifier that were identified by the classifier, count as a false positives. Our first approach was to evolve classifiers for identifying artifical signals, created by mathematical functions: sine, sawtooth and square waves. Our function set is basically composed by filtering operations on vectors and by arithmetic operations with constants and vectors. All the classifiers correctly identified true positive signals and did not identify true negative signals. We then moved to real audio recordings. For testing the classifiers, we picked different audio signals from the ones used during the training phase. For a first approach, the obtained results were very promising, but could be improved. We have made slight changes to our approach and the number of false positives reduced 33%, compared to the first approach. We then applied the evolved classifiers to polyphonic audio signals, and the results indicate that our approach is a good starting point for addressing the problem of Pitch Estimation.

Estimation of Convective Extreme Events over Germany based on Large Scale Parameters

Strong convective events can produce extreme precipitation, hail, lightning or gusts, potentially inducing severe socio-economic impacts. These events have a relatively small spatial extension and, in most cases, a short lifetime. In this study, a model is developed for estimating convective extreme events based on large scale conditions. It is shown that strong convective events can be characterized by a Weibull distribution of radar-based rainfall with a low shape and high scale parameter value. A radius of 90km around a station reporting a convective situation turned out to be suitable. A methodology is developed to estimate the Weibull parameters and thus the occurrence probability of convective events from large scale atmospheric instability and enhanced near-surface humidity, which are usually found on a larger scale than the convective event itself. Here, the probability for the occurrence of extreme convective events is estimated from the KO-index indicating the stability, and relative humidity at 1000hPa. Both variables are computed from ERA-Interim reanalysis. In a first version of the methodology, these two variables are applied to estimate the spatial rainfall distribution and to estimate the occurrence of a convective event. The developed method shows significant skill in estimating the occurrence of convective events as observed at synoptic stations, lightning measurements, and severe weather reports. In order to take frontal influences into account, a scheme for the detection of atmospheric fronts is implemented. While generally higher instability is found in the vicinity of fronts, the skill of this approach is largely unchanged. Additional improvements were achieved by a bias-correction and the use of ERA-Interim precipitation. The resulting estimation method is applied to the ERA-Interim period (1979-2014) to establish a ranking of estimated convective extreme events. Two strong estimated events that reveal a frontal influence are analysed in detail. As a second application, the method is applied to GCM-based decadal predictions in the period 1979-2014, which were initialized every year. It is shown that decadal predictive skill for convective event frequencies over Germany is found for the first 3-4 years after the initialization.

Estimation of water use and crop coefficients for an intensive olive orchard using sap flow measurements and modeled data

Olive tree sap flow measurements were collected in an intensive orchard near Évora, Portugal, during the irrigation seasons of 2013 and 2014, to calculate daily tree transpiration rates (T_SF). Meteorological variables were also collected to calculate reference evapotranspiration (ETo). Both data were used to assess values of basal crop coefficient (Kcb) for the period of the sap flow observations. The soil water balance model SIMDualKc was calibrated with soil, biophysical ground data and sap flow measurements collected in 2013. Validated in 2014 with collected sap flow observations, the model was used to provide estimates of dual e single crop coefficients for 2014 crop growing season. Good agreement between model simulated daily transpiration rates and those obtained with sapflow measurements was observed for 2014 (R2=0.76, RMSE=0.20 mm d-1), the year of validation, with an estimation average absolute error (AAE) of 0.20 mm d-1. Olive modeled daily actual evapotranspiration resulted in atual ETc values of 0.87, 2.05 and 0.77 mm d-1 for 2014 initial, mid- and end-season, respectively. Actual crop coefficient (Kc act) values of 0.51, 0.43 and 0.67 were also obtained for the same periods, respectively. Higher Kc values during spring (initial stage) and autumn (end-stage) were published in FAO56, varying between 0.65 for Kc ini and 0.70 for Kc end. The lower Kc mid value of 0.43 obtained for the summer (mid-season) is also inconsistent with the FAO56 expected Kc mid value of 0.70 for the period. The modeled Kc results are more consistent with the ones published by Allen & Pereira [1] for olive orchards with effective ground cover of 0.25 to 0.5, which vary between 0.40 and 0.80 for Kc ini, 0.40–0.60 for Kc mid with no active ground cover, and 0.35–0.75 for Kc end, depending on ground cover. The SIMDualKc simulation model proved to be appropriate for obtaining evapotranspiration and crop coefficient values for our intensive olive orchard in southern Portugal.

Annual Average Value of Solar Radiation and its Variability in Portugal

Solar resource assessment is essential for the different phases of solar energy projects, such as preliminary design engineering, financing including due diligence and, later, insurance phases. An important aspect is the long term resource estimation. This kind of estimation can only be obtained through the statistical analysis of long-term data series of solar radiation measurements, preferably ground measurements. This paper is a first step in this direction, with an initial statistical analysis performed over the radiation data from a national measurement network, consisting of eighty-nine meteorological stations. These preliminary results are presented in figures that represent the annual average values of Global Horizontal Irradiation (GHI) and its Variability in the Portuguese continental territory. These results show that the South of Portugal is the most suitable area for the implementation of medium to large scale solar plants.

ABOVE-GROUND BIOMASS ESTIMATION OF OPUNTIA FICUS-INDICA (L.) MILL. FOR FORAGE CROP IN A MEDITERRANEAN ENVIRONMENT BY USING NON-DESTRUCTIVE METHODS

In marginal lands Opuntia ficus-indica (OFI) could be used as an alternative fruit and forage crop. The plant vigour and the biomass production were evaluated in Portuguese germplasm (15 individuals from 16 ecotypes) by non-destructive methods, 2 years following planting in a marginal soil and dryland conditions. Two Italian cultivars (Gialla and Bianca) were included in the study for comparison purposes. The biomass production and the plant vigour were estimated by measuring the cladodes number and area, and the fresh (FW) and dry weight (DW) per plant. We selected linear models by using the biometric data from 60 cladodes to predict the cladode area, the FW and the DW per plant. Among ecotypes, significant differences were found in the studied biomass-related parameters and several homogeneous groups were established. Four Portuguese ecotypes had higher biomass production than the others, 3.20 Mg ha−1 on average, a value not significantly different to the improved ‘Gialla’ cultivar, which averaged 3.87 Mg ha−1. Those ecotypes could be used to start a breeding program and to deploy material for animal feeding and fruit production.

Customer Loyalty toward grocery retailing service: a multidimensional approach to costumer perceived value

Structured abstract Purpose: To deepen, in grocery retail context, the roles of consumer perceived value and consumer satisfaction, as antecedents’ dimensions of customer loyalty intentions. Design/Methodology/approach: Also employing a short version (12-items) of the original 19-item PERVAL scale of Sweeney & Soutar (2001), a structural equation modeling approach was applied to investigate statistical properties of the indirect influence on loyalty of a reflective second order customer perceived value model. The performance of three alternative estimation methods was compared through bootstrapping techniques. Findings: Results provided i) support for the use of the short form of the PERVAL scale in measuring consumer perceived value; ii) the influence of the four highly correlated independent latent predictors on satisfaction was well summarized by a higher-order reflective specification of consumer perceived value; iii) emotional and functional dimensions were determinants for the relationship with the retailer; iv) parameter’s bias with the three methods of estimation was only significant for bootstrap small sample sizes. Research limitations:/implications: Future research is needed to explore the use of the short form of the PERVAL scale in more homogeneous groups of consumers. Originality/value: Firstly, to indirectly explain customer loyalty mediated by customer satisfaction it was adopted a recent short form of PERVAL scale and a second order reflective conceptualization of value. Secondly, three alternative estimation methods were used and compared through bootstrapping and simulation procedures.

Joint value at risk: a new conditional risk measure

In this PhD thesis a new firm level conditional risk measure is developed. It is named Joint Value at Risk (JVaR) and is defined as a quantile of a conditional distribution of interest, where the conditioning event is a latent upper tail event. It addresses the problem of how risk changes under extreme volatility scenarios. The properties of JVaR are studied based on a stochastic volatility representation of the underlying process. We prove that JVaR is leverage consistent, i.e. it is an increasing function of the dependence parameter in the stochastic representation. A feasible class of nonparametric M-estimators is introduced by exploiting the elicitability of quantiles and the stochastic ordering theory. Consistency and asymptotic normality of the two stage M-estimator are derived, and a simulation study is reported to illustrate its finite-sample properties. Parametric estimation methods are also discussed. The relation with the VaR is exploited to introduce a volatility contribution measure, and a tail risk measure is also proposed. The analysis of the dynamic JVaR is presented based on asymmetric stochastic volatility models. Empirical results with S&P500 data show that accounting for extreme volatility levels is relevant to better characterize the evolution of risk. The work is complemented by a review of the literature, where we provide an overview on quantile risk measures, elicitable functionals and several stochastic orderings.

Novel methods of state estimation and parameter identification for high-performance motorcycles

This research activity aims at providing a reliable estimation of particular state variables or parameters concerning the dynamics and performance optimization of a MotoGP-class motorcycle, integrating the classical model-based approach with new methodologies involving artificial intelligence. The first topic of the research focuses on the estimation of the thermal behavior of the MotoGP carbon braking system. Numerical tools are developed to assess the instantaneous surface temperature distribution in the motorcycle's front brake discs. Within this application other important brake parameters are identified using Kalman filters, such as the disc convection coefficient and the power distribution in the disc-pads contact region. Subsequently, a physical model of the brake is built to estimate the instantaneous braking torque. However, the results obtained with this approach are highly limited by the knowledge of the friction coefficient (μ) between the disc rotor and the pads. Since the value of μ is a highly nonlinear function of many variables (namely temperature, pressure and angular velocity of the disc), an analytical model for the friction coefficient estimation appears impractical to establish. To overcome this challenge, an innovative hybrid solution is implemented, combining the benefit of artificial intelligence (AI) with classical model-based approach. Indeed, the disc temperature estimated through the thermal model previously implemented is processed by a machine learning algorithm that outputs the actual value of the friction coefficient thus improving the braking torque computation performed by the physical model of the brake. Finally, the last topic of this research activity regards the development of an AI algorithm to estimate the current sideslip angle of the motorcycle's front tire. While a single-track motorcycle kinematic model and IMU accelerometer signals theoretically enable sideslip calculation, the presence of accelerometer noise leads to a significant drift over time. To address this issue, a long short-term memory (LSTM) network is implemented.

Bayesian Linear Regression for estimation of the Fractal Dimension of the Cerebral Cortex

The cerebral cortex presents self-similarity in a proper interval of spatial scales, a property typical of natural objects exhibiting fractal geometry. Its complexity therefore can be characterized by the value of its fractal dimension (FD). In the computation of this metric, it has usually been employed a frequentist approach to probability, with point estimator methods yielding only the optimal values of the FD. In our study, we aimed at retrieving a more complete evaluation of the FD by utilizing a Bayesian model for the linear regression analysis of the box-counting algorithm. We used T1-weighted MRI data of 86 healthy subjects (age 44.2 ± 17.1 years, mean ± standard deviation, 48% males) in order to gain insights into the confidence of our measure and investigate the relationship between mean Bayesian FD and age. Our approach yielded a stronger and significant (P < .001) correlation between mean Bayesian FD and age as compared to the previous implementation. Thus, our results make us suppose that the Bayesian FD is a more truthful estimation for the fractal dimension of the cerebral cortex compared to the frequentist FD.

The Value Of The 2005 International Society Of Urological Pathology (isup) Modified Gleason Grading System As A Predictor Of Biochemical Recurrence After Radical Prostatectomy.

To compare time and risk to biochemical recurrence (BR) after radical prostatectomy of two chronologically different groups of patients using the standard and the modified Gleason system (MGS). Cohort 1 comprised biopsies of 197 patients graded according to the standard Gleason system (SGS) in the period 1997/2004, and cohort 2, 176 biopsies graded according to the modified system in the period 2005/2011. Time to BR was analyzed with the Kaplan-Meier product-limit analysis and prediction of shorter time to recurrence using univariate and multivariate Cox proportional hazards model. Patients in cohort 2 reflected time-related changes: striking increase in clinical stage T1c, systematic use of extended biopsies, and lower percentage of total length of cancer in millimeter in all cores. The MGS used in cohort 2 showed fewer biopsies with Gleason score ≤ 6 and more biopsies of the intermediate Gleason score 7. Time to BR using the Kaplan-Meier curves showed statistical significance using the MGS in cohort 2, but not the SGS in cohort 1. Only the MGS predicted shorter time to BR on univariate analysis and on multivariate analysis was an independent predictor. The results favor that the 2005 International Society of Urological Pathology modified system is a refinement of the Gleason grading and valuable for contemporary clinical practice.

Prognostic Value Of Dna And Mrna E6/e7 Of Human Papillomavirus In The Evolution Of Cervical Intraepithelial Neoplasia Grade 2.

This study aimed at evaluating whether human papillomavirus (HPV) groups and E6/E7 mRNA of HPV 16, 18, 31, 33, and 45 are prognostic of cervical intraepithelial neoplasia (CIN) 2 outcome in women with a cervical smear showing a low-grade squamous intraepithelial lesion (LSIL). This cohort study included women with biopsy-confirmed CIN 2 who were followed up for 12 months, with cervical smear and colposcopy performed every three months. Women with a negative or low-risk HPV status showed 100% CIN 2 regression. The CIN 2 regression rates at the 12-month follow-up were 69.4% for women with alpha-9 HPV versus 91.7% for other HPV species or HPV-negative status (P < 0.05). For women with HPV 16, the CIN 2 regression rate at the 12-month follow-up was 61.4% versus 89.5% for other HPV types or HPV-negative status (P < 0.05). The CIN 2 regression rate was 68.3% for women who tested positive for HPV E6/E7 mRNA versus 82.0% for the negative results, but this difference was not statistically significant. The expectant management for women with biopsy-confirmed CIN 2 and previous cytological tests showing LSIL exhibited a very high rate of spontaneous regression. HPV 16 is associated with a higher CIN 2 progression rate than other HPV infections. HPV E6/E7 mRNA is not a prognostic marker of the CIN 2 clinical outcome, although this analysis cannot be considered conclusive. Given the small sample size, this study could be considered a pilot for future larger studies on the role of predictive markers of CIN 2 evolution.

Predictive Value Of Phase I Trials For Safety In Later Trials And Final Approved Dose: Analysis Of 61 Approved Cancer Drugs.

Phase I trials use a small number of patients to define a maximum tolerated dose (MTD) and the safety of new agents. We compared data from phase I and registration trials to determine whether early trials predicted later safety and final dose. We searched the U.S. Food and Drug Administration (FDA) website for drugs approved in nonpediatric cancers (January 1990-October 2012). The recommended phase II dose (R2PD) and toxicities from phase I were compared with doses and safety in later trials. In 62 of 85 (73%) matched trials, the dose from the later trial was within 20% of the RP2D. In a multivariable analysis, phase I trials of targeted agents were less predictive of the final approved dose (OR, 0.2 for adopting ± 20% of the RP2D for targeted vs. other classes; P = 0.025). Of the 530 clinically relevant toxicities in later trials, 70% (n = 374) were described in phase I. A significant relationship (P = 0.0032) between increasing the number of patients in phase I (up to 60) and the ability to describe future clinically relevant toxicities was observed. Among 28,505 patients in later trials, the death rate that was related to drug was 1.41%. In conclusion, dosing based on phase I trials was associated with a low toxicity-related death rate in later trials. The ability to predict relevant toxicities correlates with the number of patients on the initial phase I trial. The final dose approved was within 20% of the RP2D in 73% of assessed trials.

Value Of Sentinel Lymph Node Biopsy In Papillary Thyroid Cancer: Initial Results Of A Prospective Trial.

The objectives of the study were to evaluate the performance of sentinel lymph node biopsy (SLNB) in detecting occult metastases in papillary thyroid carcinoma (PTC) and to correlate their presence to tumor and patient characteristics. Twenty-three clinically node-negative PTC patients (21 females, mean age 48.4 years) were prospectively enrolled. Patients were submitted to sentinel lymph node (SLN) lymphoscintigraphy prior to total thyroidectomy. Ultrasound-guided peritumoral injections of (99m)Tc-phytate (7.4 MBq) were performed. Cervical single-photon emission computed tomography and computed tomography (SPECT/CT) images were acquired 15 min after radiotracer injection and 2 h prior to surgery. Intra-operatively, SLNs were located with a gamma probe and removed along with non-SLNs located in the same neck compartment. Papillary thyroid carcinoma, SLNs and non-SLNs were submitted to histopathology analysis. Sentinel lymph nodes were located in levels: II in 34.7 % of patients; III in 26 %; IV in 30.4 %; V in 4.3 %; VI in 82.6 % and VII in 4.3 %. Metastases in the SLN were noted in seven patients (30.4 %), in non-SLN in three patients (13.1 %), and in the lateral compartments in 20 % of patients. There were significant associations between lymph node (LN) metastases and the presence of angio-lymphatic invasion (p = 0.04), extra-thyroid extension (p = 0.03) and tumor size (p = 0.003). No correlations were noted among LN metastases and patient age, gender, stimulated thyroglobulin levels, positive surgical margins, aggressive histology and multifocal lesions. Sentinel lymph node biopsy can detect occult metastases in PTC. The risk of a metastatic SLN was associated with extra-thyroid extension, larger tumors and angio-lymphatic invasion. This may help guide future neck dissection, patient surveillance and radioiodine therapy doses.

The Value Of Audiovisual Archives.

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