Matrix Designs and Methods for Secure and Efficient Compressed Sensing

The idea of balancing the resources spent in the acquisition and encoding of natural signals strictly to their intrinsic information content has interested nearly a decade of research under the name of compressed sensing. In this doctoral dissertation we develop some extensions and improvements upon this technique's foundations, by modifying the random sensing matrices on which the signals of interest are projected to achieve different objectives. Firstly, we propose two methods for the adaptation of sensing matrix ensembles to the second-order moments of natural signals. These techniques leverage the maximisation of different proxies for the quantity of information acquired by compressed sensing, and are efficiently applied in the encoding of electrocardiographic tracks with minimum-complexity digital hardware. Secondly, we focus on the possibility of using compressed sensing as a method to provide a partial, yet cryptanalysis-resistant form of encryption; in this context, we show how a random matrix generation strategy with a controlled amount of perturbations can be used to distinguish between multiple user classes with different quality of access to the encrypted information content. Finally, we explore the application of compressed sensing in the design of a multispectral imager, by implementing an optical scheme that entails a coded aperture array and Fabry-Pérot spectral filters. The signal recoveries obtained by processing real-world measurements show promising results, that leave room for an improvement of the sensing matrix calibration problem in the devised imager.

Non-parametric estimation of the diffusion coefficient of a branching diffusion with immigration

Wir betrachten Systeme von endlich vielen Partikeln, wobei die Partikel sich unabhängig voneinander gemäß eindimensionaler Diffusionen [dX_t = b(X_t),dt + sigma(X_t),dW_t] bewegen. Die Partikel sterben mit positionsabhängigen Raten und hinterlassen eine zufällige Anzahl an Nachkommen, die sich gemäß eines Übergangskerns im Raum verteilen. Zudem immigrieren neue Partikel mit einer konstanten Rate. Ein Prozess mit diesen Eigenschaften wird Verzweigungsprozess mit Immigration genannt. Beobachten wir einen solchen Prozess zu diskreten Zeitpunkten, so ist zunächst nicht offensichtlich, welche diskret beobachteten Punkte zu welchem Pfad gehören. Daher entwickeln wir einen Algorithmus, um den zugrundeliegenden Pfad zu rekonstruieren. Mit Hilfe dieses Algorithmus konstruieren wir einen nichtparametrischen Schätzer für den quadrierten Diffusionskoeffizienten $sigma^2(cdot),$ wobei die Konstruktion im Wesentlichen auf dem Auffüllen eines klassischen Regressionsschemas beruht. Wir beweisen Konsistenz und einen zentralen Grenzwertsatz.

Influence of reported study design characteristics on intervention effect estimates from randomized, controlled trials

Published evidence suggests that aspects of trial design lead to biased intervention effect estimates, but findings from different studies are inconsistent. This study combined data from 7 meta-epidemiologic studies and removed overlaps to derive a final data set of 234 unique meta-analyses containing 1973 trials. Outcome measures were classified as "mortality," "other objective," "or subjective," and Bayesian hierarchical models were used to estimate associations of trial characteristics with average bias and between-trial heterogeneity. Intervention effect estimates seemed to be exaggerated in trials with inadequate or unclear (vs. adequate) random-sequence generation (ratio of odds ratios, 0.89 [95% credible interval {CrI}, 0.82 to 0.96]) and with inadequate or unclear (vs. adequate) allocation concealment (ratio of odds ratios, 0.93 [CrI, 0.87 to 0.99]). Lack of or unclear double-blinding (vs. double-blinding) was associated with an average of 13% exaggeration of intervention effects (ratio of odds ratios, 0.87 [CrI, 0.79 to 0.96]), and between-trial heterogeneity was increased for such studies (SD increase in heterogeneity, 0.14 [CrI, 0.02 to 0.30]). For each characteristic, average bias and increases in between-trial heterogeneity were driven primarily by trials with subjective outcomes, with little evidence of bias in trials with objective and mortality outcomes. This study is limited by incomplete trial reporting, and findings may be confounded by other study design characteristics. Bias associated with study design characteristics may lead to exaggeration of intervention effect estimates and increases in between-trial heterogeneity in trials reporting subjectively assessed outcomes.

Estimation with Interval Censored Data in Longitudinal Studies

In biostatistical applications interest often focuses on the estimation of the distribution of a time-until-event variable T. If one observes whether or not T exceeds an observed monitoring time at a random number of monitoring times, then the data structure is called interval censored data. We extend this data structure by allowing the presence of a possibly time-dependent covariate process that is observed until end of follow up. If one only assumes that the censoring mechanism satisfies coarsening at random, then, by the curve of dimensionality, typically no regular estimators will exist. To fight the curse of dimensionality we follow the approach of Robins and Rotnitzky (1992) by modeling parameters of the censoring mechanism. We model the right-censoring mechanism by modeling the hazard of the follow up time, conditional on T and the covariate process. For the monitoring mechanism we avoid modeling the joint distribution of the monitoring times by only modeling a univariate hazard of the pooled monitoring times, conditional on the follow up time, T, and the covariates process, which can be estimated by treating the pooled sample of monitoring times as i.i.d. In particular, it is assumed that the monitoring times and the right-censoring times only depend on T through the observed covariate process. We introduce inverse probability of censoring weighted (IPCW) estimator of the distribution of T and of smooth functionals thereof which are guaranteed to be consistent and asymptotically normal if we have available correctly specified semiparametric models for the two hazards of the censoring process. Furthermore, given such correctly specified models for these hazards of the censoring process, we propose a one-step estimator which will improve on the IPCW estimator if we correctly specify a lower-dimensional working model for the conditional distribution of T, given the covariate process, that remains consistent and asymptotically normal if this latter working model is misspecified. It is shown that the one-step estimator is efficient if each subject is at most monitored once and the working model contains the truth. In general, it is shown that the one-step estimator optimally uses the surrogate information if the working model contains the truth. It is not optimal in using the interval information provided by the current status indicators at the monitoring times, but simulations in Peterson, van der Laan (1997) show that the efficiency loss is small.

Beherrschung stark korrelierter Logistik- und Produktions-Prozesse

Bei der Simulation von Logistik- und Produktionssystem werden Zufallszahlengeneratoren verwendet, um stochastische Einflüsse zu modellieren. Ein wichtiges Qualitätsmerkmal dieser Generatoren ist die Er-zeugung möglichst unabhängiger Zufallszahlen. Werden jedoch reale Prozesse betrachtet, so sind die Daten im Allgemeinen nicht unabhängig. Diese Arbeit befasst sich mit der Analyse von Praxisdaten bezüglich des Auftretens von Abhängigkeiten. Dazu werden Korrelationsstrukturen gesucht. Außerdem wird gezeigt, dass unabhängige Zufallszahlen in der Regel ungeeignet sind, um stochastische Prozesse mit ausgeprägten Abhängigkeiten zu modellieren.

Effects of study precision and risk of bias in networks of interventions: a network meta-epidemiological study

BACKGROUND Empirical research has illustrated an association between study size and relative treatment effects, but conclusions have been inconsistent about the association of study size with the risk of bias items. Small studies give generally imprecisely estimated treatment effects, and study variance can serve as a surrogate for study size. METHODS We conducted a network meta-epidemiological study analyzing 32 networks including 613 randomized controlled trials, and used Bayesian network meta-analysis and meta-regression models to evaluate the impact of trial characteristics and study variance on the results of network meta-analysis. We examined changes in relative effects and between-studies variation in network meta-regression models as a function of the variance of the observed effect size and indicators for the adequacy of each risk of bias item. Adjustment was performed both within and across networks, allowing for between-networks variability. RESULTS Imprecise studies with large variances tended to exaggerate the effects of the active or new intervention in the majority of networks, with a ratio of odds ratios of 1.83 (95% CI: 1.09,3.32). Inappropriate or unclear conduct of random sequence generation and allocation concealment, as well as lack of blinding of patients and outcome assessors, did not materially impact on the summary results. Imprecise studies also appeared to be more prone to inadequate conduct. CONCLUSIONS Compared to more precise studies, studies with large variance may give substantially different answers that alter the results of network meta-analyses for dichotomous outcomes.

Synesthesia: when colors count

A tacitly held assumption in synesthesia research is the unidirectionality of digit-color associations. This notion is based on synesthetes' report that digits evoke a color percept, but colors do not elicit any numerical impression. In a random color generation task, we found evidence for an implicit co-activation of digits by colors, a finding that constrains neurological theories concerning cross-modal associations in general and synesthesia in particular.

Linear Bayes policy for learning in contextual-bandits

Machine and Statistical Learning techniques are used in almost all online advertisement systems. The problem of discovering which content is more demanded (e.g. receive more clicks) can be modeled as a multi-armed bandit problem. Contextual bandits (i.e., bandits with covariates, side information or associative reinforcement learning) associate, to each specific content, several features that define the “context” in which it appears (e.g. user, web page, time, region). This problem can be studied in the stochastic/statistical setting by means of the conditional probability paradigm using the Bayes’ theorem. However, for very large contextual information and/or real-time constraints, the exact calculation of the Bayes’ rule is computationally infeasible. In this article, we present a method that is able to handle large contextual information for learning in contextual-bandits problems. This method was tested in the Challenge on Yahoo! dataset at ICML2012’s Workshop “new Challenges for Exploration & Exploitation 3”, obtaining the second place. Its basic exploration policy is deterministic in the sense that for the same input data (as a time-series) the same results are obtained. We address the deterministic exploration vs. exploitation issue, explaining the way in which the proposed method deterministically finds an effective dynamic trade-off based solely in the input-data, in contrast to other methods that use a random number generator.

Photovoltaic LiNbO3particles: Applications to Biomedicine/Biophotonics

Recently, a novel method to trap and pattern ensembles of nanoparticles has been proposed and tested. It relies on the photovoltaic (PV) properties of certain ferroelectric crystals such as LiNbO3 [1,2]. These crystals, when suitably doped, develop very high electric fields in response to illumination with light of suitable wavelength. The PV effect lies in the asymmetrical excitation of electrons giving rise to PV currents and associated space-charge fields (photorefractive effect). The field generated in the bulk of the sample propagates to the surrounding medium as evanescent fields. When dielectric or metal nanoparticles are deposited on the surface of the sample the evanescent fields give rise to either electrophoretic or dielectrophoretic forces, depending on the charge state of the particles, that induce the trapping and patterning effects [3,4]. The purpose of this work has been to explore the effects of such PV fields in the biology and biomedical areas. A first work was able to show the necrotic effects induced by such fields on He-La tumour cells grown on the surface of an illuminated iron-doped LiNbO3 crystal [5]. In principle, it is conceived that LiNbO3 nanoparticles may be advantageously used for such biomedical purposes considering the possibility of such nanoparticles being incorporated into the cells. Previous experiments using microparticles have been performed [5] with similar results to those achieved with the substrate. Therefore, the purpose of this work has been to fabricate and characterize the LiNbO3 nanoparticles and assess their necrotic effects when they are incorporated on a culture of tumour cells. Two different preparation methods have been used: 1) mechanical grinding from crystals, and 2) bottom-up sol-gel chemical synthesis from metal-ethoxide precursors. This later method leads to a more uniform size distribution of smaller particles (down to around 50 nm). Fig. 1(a) and 1(b) shows SEM images of the nanoparticles obtained with both method. An ad hoc software taking into account the physical properties of the crystal, particullarly donor and aceptor concentrations has been developped in order to estimate the electric field generated in noparticles. In a first stage simulations of the electric current of nanoparticles, in a conductive media, due to the PV effect have been carried out by MonteCarlo simulations using the Kutharev 1-centre transport model equations [6] . Special attention has been paid to the dependence on particle size and [Fe2+]/[Fe3+]. First results on cubic particles shows large dispersion for small sizes due to the random number of donors and its effective concentration (Fig 2). The necrotic (toxicity) effect of nanoparticles incorporated into a tumour cell culture subjected to 30 min. illumination with a blue LED is shown in Fig.3. For each type of nanoparticle the percent of cell survival in dark and illumination conditions has been plot as a function of the particle dilution factor. Fig. 1a corresponds to mechanical grinding particles whereas 1b and 1c refer to chemically synthesized particles with two oxidation states. The light effect is larger with mechanical grinding nanoparticles, but dark toxicity is also higher. For chemically synthesized nanoparticles dark toxicity is low but only in oxidized samples, where the PV effect is known to be larger, the light effect is appreciable. These preliminary results demonstrate that Fe:LiNbO· nanoparticles have a biological damaging effect on cells, although there are many points that should be clarified and much space for PV nanoparticles optimization. In particular, it appears necessary to determine the fraction of nanoparticles that become incorporated into the cells and the possible existence of threshold size effects. This work has been supported by MINECO under grant MAT2011-28379-C03.

Mean-value identities as an opportunity for Monte Carlo error reduction

In the Monte Carlo simulation of both lattice field theories and of models of statistical mechanics, identities verified by exact mean values, such as Schwinger-Dyson equations, Guerra relations, Callen identities, etc., provide well-known and sensitive tests of thermalization bias as well as checks of pseudo-random-number generators. We point out that they can be further exploited as control variates to reduce statistical errors. The strategy is general, very simple, and almost costless in CPU time. The method is demonstrated in the twodimensional Ising model at criticality, where the CPU gain factor lies between 2 and 4.

Comparative analysis of the visual performance and aberrometric outcomes with a new hybrid and two silicone hydrogel multifocal contact lenses: a pilot study

Background: The aim was to evaluate the visual performance achieved with a new multifocal hybrid contact lens and to compare it with that obtained with two other currently available multifocal soft contact lenses. Methods: This pilot prospective comparative study comprised a total of 16 presbyopic eyes of eight patients ranging in age from 43 to 58 years. All patients were fitted with three different models of multifocal contact lens: Duette multifocal (SynergEyes), Air Optix AQUA multifocal (Alcon) and Biofinity multifocal (CooperVision). Fittings were performed randomly in each patient according to a random number sequence, with a wash-out period between fittings of seven days. At two weeks post-fitting, visual, photopic contrast sensitivity and ocular aberrometry were evaluated. Results: No statistically significant differences were found in distance and near visual acuity achieved with the three different types of multifocal contact lens (p ≥ 0.05). Likewise, no significant differences between lenses were found in the monocular and binocular defocus curve (p ≥ 0.10). Concerning contrast sensitivity, better monocular contrast sensitivities for 6, 12 and 18 cycles per degree were found with the Duette and Air Optix multifocal compared to Biofinity (p = 0.02). Binocularly, differences between lenses were not significant (p ≥ 0.27). Furthermore, trefoil aberration was significantly higher with Biofinity multifocal (p < 0.01) and Air Optix (p = 0.01) multifocal compared to Duette. Conclusions: The Duette multifocal hybrid contact lens seems to provide similar visual quality outcomes in presbyopic patients with low corneal astigmatism, when compared with other soft multifocal contact lenses. This preliminary result should be confirmed in studies with larger samples.

A randomised controlled trial investigating the effect of lutein and antioxidant dietary supplementation on visual function in healthy eyes

Background & aims It has been suggested that retinal lutein may improve visual acuity for images that are illuminated by white light. Our aim was to determine the effect of a lutein and antioxidant dietary supplement on visual function. Methods A prospective, 9- and 18-month, double-masked randomised controlled trial. For the 9-month trial, 46 healthy participants were randomised (using a random number generator) to placebo (n=25) or active (n=21) groups. Twenty-nine of these subjects went on to complete 18 months of supplementation, 15 from the placebo group, and 14 from the active group. The active group supplemented daily with 6mg lutein combined with vitamins and minerals. Outcome measures were distance and near visual acuity, contrast sensitivity, and photostress recovery time. The study had 80% power at the 5% significance level for each outcome measure. Data were collected at baseline, 9, and 18 months. Results There were no statistically significant differences between groups for any of the outcome measures over 9 or 18 months. Conclusion There was no evidence of effect of 9 or 18 months of daily supplementation with a lutein-based nutritional supplement on visual function in this group of people with healthy eyes. ISRCTN78467674.

Effect of lutein and antioxidant dietary supplementation on contrast sensitivity in age-related macular disease:A randomized controlled trial

Objective: The aim of the study is to determine the effect of lutein combined with vitamin and mineral supplementation on contrast sensitivity in people with age-related macular disease (ARMD). Design: A prospective, 9-month, double-masked randomized controlled trial. Setting: Aston University, Birmingham, UK and a UK optometric clinical practice. Subjects: Age-related maculopathy (ARM) and atrophic age-related macular degeneration (AMD) participants were randomized (using a random number generator) to either placebo (n = 10) or active (n=15) groups. Three of the placebo group and two of the active group dropped out. Interventions: The active group supplemented daily with 6 mg lutein combined with vitamins and minerals. The outcome measure was contrast sensitivity (CS) measured using the Pelli-Robson chart, for which the study had 80% power at the 5% significance level to detect a change of 0.3log units. Results: The CS score increased by 0.07 ± 0.07 and decreased by 0.02 ± 0.18 log units for the placebo and active groups, respectively. The difference between these values is not statistically significant (z = 0.903, P = 0.376). Conclusion: The results suggest that 6 mg of lutein supplementation in combination with other antioxidants is not beneficial for this group. Further work is required to establish optimum dosage levels.

A randomised controlled trial investigating the effect of nutritional supplementation on visual function in normal, and age-related macular disease affected eyes:design and methodology [ISRCTN78467674]

Background: Age-related macular disease is the leading cause of blind registration in the developed world. One aetiological hypothesis involves oxidation, and the intrinsic vulnerability of the retina to damage via this process. This has prompted interest in the role of antioxidants, particularly the carotenoids lutein and zeaxanthin, in the prevention and treatment of this eye disease. Methods: The aim of this randomised controlled trial is to determine the effect of a nutritional supplement containing lutein, vitamins A, C and E, zinc, and copper on measures of visual function in people with and without age-related macular disease. Outcome measures are distance and near visual acuity, contrast sensitivity, colour vision, macular visual field, glare recovery, and fundus photography. Randomisation is achieved via a random number generator, and masking achieved by third party coding of the active and placebo containers. Data collection will take place at nine and 18 months, and statistical analysis will employ Student's t test. Discussion: A paucity of treatment modalities for age-related macular disease has prompted research into the development of prevention strategies. A positive effect on normals may be indicative of a role of nutritional supplementation in preventing or delaying onset of the condition. An observed benefit in the age-related macular disease group may indicate a potential role of supplementation in prevention of progression, or even a degree reversal of the visual effects caused by this condition.

A Limit Theorem for Multi-Type Subcritical Age-Dependent Branching Processes with two Types of Immigration

Марусия Н. Славчова-Божкова - В настоящата работа се обобщава една гранична теорема за докритичен многомерен разклоняващ се процес, зависещ от възрастта на частиците с два типа имиграция. Целта е да се обобщи аналогичен резултат в едномерния случай като се прилагат “coupling” метода, теория на възстановяването и регенериращи процеси.