Data methods in optometry. Part 6: fitting a regression line to data

1. Fitting a linear regression to data provides much more information about the relationship between two variables than a simple correlation test. A goodness of fit test of the line should always be carried out. Hence, r squared estimates the strength of the relationship between Y and X, ANOVA whether a statistically significant line is present, and the ‘t’ test whether the slope of the line is significantly different from zero. 2. Always check whether the data collected fit the assumptions for regression analysis and, if not, whether a transformation of the Y and/or X variables is necessary. 3. If the regression line is to be used for prediction, it is important to determine whether the prediction involves an individual y value or a mean. Care should be taken if predictions are made close to the extremities of the data and are subject to considerable error if x falls beyond the range of the data. Multiple predictions require correction of the P values. 3. If several individual regression lines have been calculated from a number of similar sets of data, consider whether they should be combined to form a single regression line. 4. If the data exhibit a degree of curvature, then fitting a higher-order polynomial curve may provide a better fit than a straight line. In this case, a test of whether the data depart significantly from a linear regression should be carried out.

Optical data transmission using periodic in-line all-optical format conversion

We introduce a novel transmission technique of periodic in-line all-optical format conversion between return-to-zero and non-return-to-zero-like aimed at delaying the accumulation of format-specific impairments. A particular realization of this approach using in-line normal dispersion fibre-enhanced nonlinear optical loop mirrors at 40Gbit/s data rate is presented. © 2004 Optical Society of America.

Study of the operating regime for all-optical passive 2R regeneration of dispersion-managed RZ data at 40 Gb/s using in-line NOLMs

In this letter, we numerically demonstrate that the use of inline nonlinear optical loop mirrors in strongly dispersion-managed transmission systems dominated by pulse distortion and amplitude noise can achieve all-optical passive 2R regeneration of a 40-Gb/s return-to-zero data stream. We define the tolerance limits of this result to the parameters of the input pulses.

Optical data transmission using periodic in-line all-optical format conversion

We introduce a novel transmission technique of periodic in-line all-optical format conversion between return-to-zero and non-return-to-zero-like aimed at delaying the accumulation of format-specific impairments. A particular realization of this approach using in-line normal dispersion fibre-enhanced nonlinear optical loop mirrors at 40Gbit/s data rate is presented.

Improving envelopment in Data Envelopment Analysis under variable returns to scale

In a Data Envelopment Analysis model, some of the weights used to compute the efficiency of a unit can have zero or negligible value despite of the importance of the corresponding input or output. This paper offers an approach to preventing inputs and outputs from being ignored in the DEA assessment under the multiple input and output VRS environment, building on an approach introduced in Allen and Thanassoulis (2004) for single input multiple output CRS cases. The proposed method is based on the idea of introducing unobserved DMUs created by adjusting input and output levels of certain observed relatively efficient DMUs, in a manner which reflects a combination of technical information and the decision maker's value judgements. In contrast to many alternative techniques used to constrain weights and/or improve envelopment in DEA, this approach allows one to impose local information on production trade-offs, which are in line with the general VRS technology. The suggested procedure is illustrated using real data. © 2011 Elsevier B.V. All rights reserved.

Information capacity of optical fiber channels with zero average dispersion

We study the statistics of optical data transmission in a noisy nonlinear fiber channel with a weak dispersion management and zero average dispersion. Applying analytical expressions for the output probability density functions both for a nonlinear channel and for a linear channel with additive and multiplicative noise we calculate in a closed form a lower bound estimate on the Shannon capacity for an arbitrary signal-to-noise ratio.

Handling varying amounts of missing data when classifying mental-health risk levels

One of the main challenges of classifying clinical data is determining how to handle missing features. Most research favours imputing of missing values or neglecting records that include missing data, both of which can degrade accuracy when missing values exceed a certain level. In this research we propose a methodology to handle data sets with a large percentage of missing values and with high variability in which particular data are missing. Feature selection is effected by picking variables sequentially in order of maximum correlation with the dependent variable and minimum correlation with variables already selected. Classification models are generated individually for each test case based on its particular feature set and the matching data values available in the training population. The method was applied to real patients' anonymous mental-health data where the task was to predict the suicide risk judgement clinicians would give for each patient's data, with eleven possible outcome classes: zero to ten, representing no risk to maximum risk. The results compare favourably with alternative methods and have the advantage of ensuring explanations of risk are based only on the data given, not imputed data. This is important for clinical decision support systems using human expertise for modelling and explaining predictions.

Algorithmic Minimization of Non-zero Entries in 0,1-Matrices

In this paper we present algorithms which work on pairs of 0,1- matrices which multiply again a matrix of zero and one entries. When applied over a pair, the algorithms change the number of non-zero entries present in the matrices, meanwhile their product remains unchanged. We establish the conditions under which the number of 1s decreases. We recursively define as well pairs of matrices which product is a specific matrix and such that by applying on them these algorithms, we minimize the total number of non-zero entries present in both matrices. These matrices may be interpreted as solutions for a well known information retrieval problem, and in this case the number of 1 entries represent the complexity of the retrieve and information update operations.

Exergoeconomic analysis of solar organic rankine cycle for geothermal air conditioned net zero energy buildings

This study is an attempt at achieving Net Zero Energy Building (NZEB) using a solar Organic Rankine Cycle (ORC) based on exergetic and economic measures. The working fluid, working conditions of the cycle, cycle configuration, and solar collector type are considered the optimization parameters for the solar ORC system. In the first section, a procedure is developed to compare ORC working fluids based on their molecular components, temperature-entropy diagram and fluid effects on the thermal efficiency, net power generated, vapor expansion ratio, and exergy efficiency of the Rankine cycle. Fluids with the best cycle performance are recognized in two different temperature levels within two different categories of fluids: refrigerants and non-refrigerants. Important factors that could lead to irreversibility reduction of the solar ORC are also investigated in this study. In the next section, the system requirements needed to maintain the electricity demand of a geothermal air-conditioned commercial building located in Pensacola of Florida is considered as the criteria to select the optimal components and optimal working condition of the system. The solar collector loop, building, and geothermal air conditioning system are modeled using TRNSYS. Available electricity bills of the building and the 3-week monitoring data on the performance of the geothermal system are employed to calibrate the simulation. The simulation is repeated for Miami and Houston in order to evaluate the effect of the different solar radiations on the system requirements. The final section discusses the exergoeconomic analysis of the ORC system with the optimum performance. Exergoeconomics rests on the philosophy that exergy is the only rational basis for assigning monetary costs to a system’s interactions with its surroundings and to the sources of thermodynamic inefficiencies within it. Exergoeconomic analysis of the optimal ORC system shows that the ratio Rex of the annual exergy loss to the capital cost can be considered a key parameter in optimizing a solar ORC system from the thermodynamic and economic point of view. It also shows that there is a systematic correlation between the exergy loss and capital cost for the investigated solar ORC system.

Data compilation on the biological response to ocean acidification: environmental and experimental context of data sets and related literature

The exponential growth of studies on the biological response to ocean acidification over the last few decades has generated a large amount of data. To facilitate data comparison, a data compilation hosted at the data publisher PANGAEA was initiated in 2008 and is updated on a regular basis (doi:10.1594/PANGAEA.149999). By January 2015, a total of 581 data sets (over 4 000 000 data points) from 539 papers had been archived. Here we present the developments of this data compilation five years since its first description by Nisumaa et al. (2010). Most of study sites from which data archived are still in the Northern Hemisphere and the number of archived data from studies from the Southern Hemisphere and polar oceans are still relatively low. Data from 60 studies that investigated the response of a mix of organisms or natural communities were all added after 2010, indicating a welcomed shift from the study of individual organisms to communities and ecosystems. The initial imbalance of considerably more data archived on calcification and primary production than on other processes has improved. There is also a clear tendency towards more data archived from multifactorial studies after 2010. For easier and more effective access to ocean acidification data, the ocean acidification community is strongly encouraged to contribute to the data archiving effort, and help develop standard vocabularies describing the variables and define best practices for archiving ocean acidification data.

Benthic and substrate cover data derived from photo-transect surveys in Lizard Island Reef conducted on December 10-15, 2011

Underwater georeferenced photo-transect surveys were conducted on December 10-15, 2011 at various sections of the reef at Lizard Island, Great Barrier Reef. For this survey a snorkeler or diver swam over the bottom while taking photos of the benthos at a set height using a standard digital camera and towing a GPS in a surface float which logged the track every five seconds. A standard digital compact camera was placed in an underwater housing and fitted with a 16 mm lens which provided a 1.0 m x 1.0 m footprint, at 0.5 m height above the benthos. Horizontal distance between photos was estimated by three fin kicks of the survey diver/snorkeler, which corresponded to a surface distance of approximately 2.0 - 4.0 m. The GPS was placed in a dry-bag and logged the position as it floated at the surface while being towed by the photographer. A total of 5,735 benthic photos were taken. A floating GPS setup connected to the swimmer/diver by a line enabled recording of coordinates of each benthic photo (Roelfsema 2009). Approximation of coordinates of each benthic photo was conducted based on the photo timestamp and GPS coordinate time stamp, using GPS Photo Link Software (www.geospatialexperts.com). Coordinates of each photo were interpolated by finding the GPS coordinates that were logged at a set time before and after the photo was captured. Benthic or substrate cover data was derived from each photo by randomly placing 24 points over each image using the Coral Point Count for Microsoft Excel program (Kohler and Gill, 2006). Each point was then assigned to 1 of 78 cover types, which represented the benthic feature beneath it. Benthic cover composition summary of each photo scores was generated automatically using CPCE program. The resulting benthic cover data of each photo was linked to GPS coordinates, saved as an ArcMap point shapefile, and projected to Universal Transverse Mercator WGS84 Zone 55 South.

Benthic and substrate cover data derived from photo-transect surveys in Lizard Island, Great Barrier Reef conducted on October 3-7, 2012

Underwater georeferenced photo-transect surveys were conducted on October 3-7, 2012 at various sections of the reef and lagoon at Lizard Island, Great Barrier Reef. For this survey a snorkeler swam while taking photos of the benthos at a set distance from the benthos using a standard digital camera and towing a GPS in a surface float which logged the track every five seconds. A Canon G12 digital camera was placed in a Canon underwater housing and photos were taken at 1 m height above the benthos. Horizontal distance between photos was estimated by three fin kicks of the survey snorkeler, which corresponded to a surface distance of approximately 2.0 - 4.0 m. The GPS was placed in a dry bag and logged the position at the surface while being towed by the photographer (Roelfsema, 2009). A total of 1,265 benthic photos were taken. Approximation of coordinates of each benthic photo was conducted based on the photo timestamp and GPS coordinate time stamp, using GPS Photo Link Software (www.geospatialexperts.com). Coordinates of each photo were interpolated by finding the GPS coordinates that were logged at a set time before and after the photo was captured. Benthic or substrate cover data was derived from each photo by randomly placing 24 points over each image using the Coral Point Count for Microsoft Excel program (Kohler and Gill, 2006). Each point was then assigned to 1 of 79 cover types, which represented the benthic feature beneath it. Benthic cover composition summary of each photo scores was generated automatically using CPCE program. The resulting benthic cover data of each photo was linked to GPS coordinates, saved as an ArcMap point shapefile, and projected to Universal Transverse Mercator WGS84 Zone 55 South.

Habitat Map for Lizard Island reef, Australia derived from a photo-transect survey field data collected in December 2011 and September/October 2012

An object based image analysis approach (OBIA) was used to create a habitat map of the Lizard Reef. Briefly, georeferenced dive and snorkel photo-transect surveys were conducted at different locations surrounding Lizard Island, Australia. For the surveys, a snorkeler or diver swam over the bottom at a depth of 1-2m in the lagoon, One Tree Beach and Research Station areas, and 7m depth in Watson's Bay, while taking photos of the benthos at a set height using a standard digital camera and towing a surface float GPS which was logging its track every five seconds. The camera lens provided a 1.0 m x 1.0 m footprint, at 0.5 m height above the benthos. Horizontal distance between photos was estimated by fin kicks, and corresponded to a surface distance of approximately 2.0 - 4.0 m. Approximation of coordinates of each benthic photo was done based on the photo timestamp and GPS coordinate time stamp, using GPS Photo Link Software (www.geospatialexperts.com). Coordinates of each photo were interpolated by finding the gps coordinates that were logged at a set time before and after the photo was captured. Dominant benthic or substrate cover type was assigned to each photo by placing 24 points random over each image using the Coral Point Count excel program (Kohler and Gill, 2006). Each point was then assigned a dominant cover type using a benthic cover type classification scheme containing nine first-level categories - seagrass high (>=70%), seagrass moderate (40-70%), seagrass low (<= 30%), coral, reef matrix, algae, rubble, rock and sand. Benthic cover composition summaries of each photo were generated automatically in CPCe. The resulting benthic cover data for each photo was linked to GPS coordinates, saved as an ArcMap point shapefile, and projected to Universal Transverse Mercator WGS84 Zone 56 South. The OBIA class assignment followed a hierarchical assignment based on membership rules with levels for "reef", "geomorphic zone" and "benthic community" (above).

(Table 2) Zinc complexation data from POLARSTERN cruise ANT-XXIV/3

The speciation of dissolved zinc (Zn) was investigated by voltammetry in the Atlantic sector of the Southern Ocean along two transects across the major frontal systems: along the Zero Meridian and across the Drake Passage. In the Southern Ocean south of the APF we found detectable labile inorganic Zn throughout the surface waters in contrast to studies from lower latitudes. Using a combination of ASV titrations and pseudopolarography revealed the presence of significant concentration of electrochemically inert Zn ligands throughout the Southern Ocean. These ligands however were nearly always saturated due to the presence of excess concentrations of dissolved Zn that were associated with the high nutrient waters south of the Antarctic Polar Front (APF). Only in surface waters did the concentration of Zn complexing ligands exceed the dissolved Zn concentrations suggesting a biological source for these ligands. Our findings have clear implications for the biogeochemical cycling of Zn and for the interpretation of paleo records utilizing Zn in opal as a tracer of Zn speciation in the water column.