A new modularity measure for Fuzzy Community detection problems based on overlap and grouping functions

One of the main challenges of fuzzy community detection problems is to be able to measure the quality of a fuzzy partition. In this paper, we present an alternative way of measuring the quality of a fuzzy community detection output based on n-dimensional grouping and overlap functions. Moreover, the proposed modularity measure generalizes the classical Girvan–Newman (GN) modularity for crisp community detection problems and also for crisp overlapping community detection problems. Therefore, it can be used to compare partitions of different nature (i.e. those composed of classical, overlapping and fuzzy communities). Particularly, as is usually done with the GN modularity, the proposed measure may be used to identify the optimal number of communities to be obtained by any network clustering algorithm in a given network. We illustrate this usage by adapting in this way a well-known algorithm for fuzzy community detection problems, extending it to also deal with overlapping community detection problems and produce a ranking of the overlapping nodes. Some computational experiments show the feasibility of the proposed approach to modularity measures through n-dimensional overlap and grouping functions.

Effect of pharmacological pupil dilation on measurements and iol power calculation made using the new swept-source optical coherence tomography-based optical biometer

Purpose: to determine whether pupil dilation affects biometric measurements and intraocular lens (IOL) power calculation made using the new swept-source optical coherence tomography-based optical biometer (IOLMaster 700©; Carl Zeiss Meditec, Jena, Germany). Procedures: eighty-one eyes of 81 patients evaluated for cataract surgery were prospectively examined using the IOLMaster 700© before and after pupil dilation with tropicamide 1%. The measurements made were: axial length (AL), central corneal thickness (CCT), aqueous chamber depth (ACD), lens thickness (LT), mean keratometry (MK), white-to-white distance (WTW) and pupil diameter (PD). Holladay II and SRK/T formulas were used to calculate IOL power. Agreement between measurement modes (with and without dilation) was assessed through intraclass correlation coefficients (ICC) and Bland-Altman plots. Results: mean patient age was 75.17 ± 7.54 years (range: 57–92). Of the variables determined, CCT, ACD, LT and WTW varied significantly according to pupil dilation. Excellent intraobserver correlation was observed between measurements made before and after pupil dilation. Mean IOL power calculation using the Holladay 2 and SRK/T formulas were unmodified by pupil dilation. Conclusions: the use of pupil dilation produces statistical yet not clinically significant differences in some IOLMaster 700© measurements. However, it does not affect mean IOL power calculation.

Agreement and clinical comparison between a new swept-source optical coherence tomography-based optical biometer and an optical low-coherence reflectometry biometer

Purpose To compare measurements taken using a swept-source optical coherence tomography-based optical biometer (IOLmaster 700) and an optical low-coherence reflectometry biometer (Lenstar 900), and to determine the clinical impacts of differences in their measurements on intraocular lens (IOL) power predictions. Methods Eighty eyes of 80 patients scheduled to undergo cataract surgery were examined with both biometers. The measurements made using each device were axial length (AL), central corneal thickness (CCT), aqueous depth (AQD), lens thickness (LT), mean keratometry (MK), white-to-white distance (WTW), and pupil diameter (PD). Holladay 2 and SRK/T formulas were used to calculate IOL power. Differences in measurement between the two biometers were determined using the paired t-test. Agreement was assessed through intraclass correlation coefficients (ICC) and Bland–Altman plots. Results Mean patient age was 76.3±6.8 years (range 59–89). Using the Lenstar, AL and PD could not be measured in 12.5 and 5.25% of eyes, respectively, while IOLMaster 700 took all measurements in all eyes. The variables CCT, AQD, LT, and MK varied significantly between the two biometers. According to ICCs, correlation between measurements made with both devices was excellent except for WTW and PD. Using the SRK/T formula, IOL power prediction based on the data from the two devices were statistically different, but differences were not clinically significant. Conclusions No clinically relevant differences were detected between the biometers in terms of their measurements and IOL power predictions. Using the IOLMaster 700, it was easier to obtain biometric measurements in eyes with less transparent ocular media or longer AL.

Euclidean Distance Between Haar Orthogonal and Gaussian Matrices

In this work, we study a version of the general question of how well a Haar-distributed orthogonal matrix can be approximated by a random Gaussian matrix. Here, we consider a Gaussian random matrix (Formula presented.) of order n and apply to it the Gram–Schmidt orthonormalization procedure by columns to obtain a Haar-distributed orthogonal matrix (Formula presented.). If (Formula presented.) denotes the vector formed by the first m-coordinates of the ith row of (Formula presented.) and (Formula presented.), our main result shows that the Euclidean norm of (Formula presented.) converges exponentially fast to (Formula presented.), up to negligible terms. To show the extent of this result, we use it to study the convergence of the supremum norm (Formula presented.) and we find a coupling that improves by a factor (Formula presented.) the recently proved best known upper bound on (Formula presented.). Our main result also has applications in Quantum Information Theory.

Properties of polycrystalline gas sensors based on d.c. and a.c. electrical measurements

Electrical properties of polycrystalline gas sensors are analyzed by d.c. and a.c. measurements. d.c. electrical conductivity values compared with those obtained by admittance spectroscopy methods help to obtain a detailed 'on line' analysis of conductivity-modulated gas sensors. The electrical behaviour of grain boundaries is obtained and a new design of sensors can be achieved by enhancing the activity of surface states in the detecting operation. A Schottky barrier model is used to explain the grain boundary action under the presence of surrounding gases. The height of this barrier is a function of gas concentration due to the trapping of excess charge generated by gas adsorption at the interface. A comparison between this dependence, and a plot of the real and imaginary components of the admittance versus frequency at different gas concentrations, provides information on the different parameters that play a role in the conduction mechanisms. These methods have been applied to the design of a CO sensor based on tin oxide films for domestic purposes, the characteristics of which are presented.