Statnote 19: non-linear regression: fitting an exponential curve to data

Non-linear relationships are common in microbiological research and often necessitate the use of the statistical techniques of non-linear regression or curve fitting. In some circumstances, the investigator may wish to fit an exponential model to the data, i.e., to test the hypothesis that a quantity Y either increases or decays exponentially with increasing X. This type of model is straight forward to fit as taking logarithms of the Y variable linearises the relationship which can then be treated by the methods of linear regression.

Statnote 20: non-linear regression: fitting a general polynomial curve

In some circumstances, there may be no scientific model of the relationship between X and Y that can be specified in advance and indeed the objective of the investigation may be to provide a ‘curve of best fit’ for predictive purposes. In such an example, the fitting of successive polynomials may be the best approach. There are various strategies to decide on the polynomial of best fit depending on the objectives of the investigation.

Strong localization of whispering gallery modes in an optical fiber via asymmetric perturbation of the translation symmetry

Recently introduced Surface Nanoscale Axial Photonics (SNAP) is based on whispering gallery modes circulating around the optical FIber surface and undergoing slow axial propagation. In this paper we develop the theory of propagation of whispering gallery modes in a SNAP microresonator, which is formed by nanoscale asymmetric perturbation of the FIber translation symmetry and called here a nanobump microresonator. The considered modes are localized near a closed stable geodesic situated at the FIber surface. A simple condition for the stability of this geodesic corresponding to the appearance of a high Q-factor nanobump microresonator is found. The results obtained are important for engineering of SNAP devices and structures.

Asymmetric advertising impact

Companies under pressure from stakeholders to meet profit expectations are often tempted to cut advertising expenses, particularly in times of economic difficulties. However, firms may not fully grasp the actual impact of such drastic cuts. Indeed, the general assumption is that advertising effects are symmetric: the numerical sales impact of budget increase or decrease would be the same in absolute value. Our paper addresses this gap by developing a new model based on multivariate time-series analysis (VAR models) to capture these asymmetric dynamic relationships. Our results show that advertising models are improved by allowing the capture of these asymmetric patterns.

Performance impact of asymmetric filtered 40Gb/s RZ DPSK system:tight optical filtering considerations

We present the impact of Asymmetric filtering of strong (e.g. 35 GHz) optical filters on the performance of 42.7 Gb/s 50% RZ-DPSK systems. The performance is evaluated when offsetting the filter by substantial amounts and it is found that with an offset of almost half the bit rate there is a significant improvement in the calculated Q.

Evaluating the environmental Kuznets curve

We examine the empirical evidence for an environmental Kuznets curve using a semiparametric smooth coefficient regression model that allows us to incorporate flexibility in the parameter estimates, while maintaining the basic econometric structure that is typically used to estimate the pollution-income relationship. This allows us to assess the sensitivity to parameter heterogeneity of typical parametric models used to estimate the relationship between pollution and income, as well as identify why the results from such models are seldom found to be robust. Our results confirm that the resulting relationship between pollution and income is fragile; we show that the estimated pollution-income relationship depends substantially on the heterogeneity of the slope coefficients and the parameter values at which the relationship is evaluated. Different sets of parameters obtained from the semiparametric model give rise to many different shapes for the pollution-income relationship that are commonly found in the literature.

Characterization of asymmetric filtered 40 Gb/s RZ-DPSK system-strong filtering considerations

We present the impact of frequency offsetting of strong (e.g. 35 GHz) optical filters on the performance of 42.7 Gb/s 50% RZ-DPSK systems. The performance is evaluated when offsetting the filter by substantial amounts and it is found that with an offset of almost half the bit rate there is a significant improvement in the calculated 'Q' (> 1 dB). We deployed balanced, constructive single ended and destructive single ended detection, so that we could investigate the physical origins of the penalty reduction of asymmetric filtering of 42.7 Gb/s 50% RZ-DPSK system.

Laminar distribution of the pathological changes in sporadic frontotemporal lobar degeneration with transactive response (TAR) DNA-binding protein of 43kDa (TDP-43) proteinopathy:a quantitative study using polynomial curve fitting

Aims: Previous data suggest heterogeneity in laminar distribution of the pathology in the molecular disorder frontotemporal lobar degeneration (FTLD) with transactive response (TAR) DNA-binding protein of 43kDa (TDP-43) proteinopathy (FTLD-TDP). To study this heterogeneity, we quantified the changes in density across the cortical laminae of neuronal cytoplasmic inclusions, glial inclusions, neuronal intranuclear inclusions, dystrophic neurites, surviving neurones, abnormally enlarged neurones, and vacuoles in regions of the frontal and temporal lobe. Methods: Changes in density of histological features across cortical gyri were studied in 10 sporadic cases of FTLD-TDP using quantitative methods and polynomial curve fitting. Results: Our data suggest that laminar neuropathology in sporadic FTLD-TDP is highly variable. Most commonly, neuronal cytoplasmic inclusions, dystrophic neurites and vacuolation were abundant in the upper laminae and glial inclusions, neuronal intranuclear inclusions, abnormally enlarged neurones, and glial cell nuclei in the lower laminae. TDP-43-immunoreactive inclusions affected more of the cortical profile in longer duration cases; their distribution varied with disease subtype, but was unrelated to Braak tangle score. Different TDP-43-immunoreactive inclusions were not spatially correlated. Conclusions: Laminar distribution of pathological features in 10 sporadic cases of FTLD-TDP is heterogeneous and may be accounted for, in part, by disease subtype and disease duration. In addition, the feedforward and feedback cortico-cortical connections may be compromised in FTLD-TDP. © 2012 The Authors. Neuropathology and Applied Neurobiology © 2012 British Neuropathological Society.

Long period grating directional bend sensor based on asymmetric index modification of cladding

A long period grating (LPG) written in a standard optical fibre was modified by using a femtosecond laser to induce an asymmetric change in the cladding's refractive index. This device produced blue and red wavelength shifts depending on the orientation of applied curvature, with maximum sensitivities of -1.6 nm m and +3.8 nm m, suggesting that this type of LPG may be useful as a shape sensor.

Characterization of asymmetric filtered 40 Gb/s RZ-DPSK system-strong filtering considerations

We present the impact of frequency offsetting of strong (e.g. 35 GHz) optical filters on the performance of 42.7 Gb/s 50% RZ-DPSK systems. The performance is evaluated when offsetting the filter by substantial amounts and it is found that with an offset of almost half the bit rate there is a significant improvement in the calculated 'Q' (> 1 dB). We deployed balanced, constructive single ended and destructive single ended detection, so that we could investigate the physical origins of the penalty reduction of asymmetric filtering of 42.7 Gb/s 50% RZ-DPSK system.

Directional bend sensor based on an asymmetric modification of the fiber cladding by femtosecond laser

A femtosecond laser was used to modify a part of the cladding of a standard LPG bend sensor. The device produced wavelength shifts depending upon the direction of bend, thus making a shape sensor. © 2005 Optical Society of America.