Using Bayesian neural networks to classify segmented images

We present results that compare the performance of neural networks trained with two Bayesian methods, (i) the Evidence Framework of MacKay (1992) and (ii) a Markov Chain Monte Carlo method due to Neal (1996) on a task of classifying segmented outdoor images. We also investigate the use of the Automatic Relevance Determination method for input feature selection.

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.

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.

Polynomial function intervals for floating-point software verification

The focus of our work is the verification of tight functional properties of numerical programs, such as showing that a floating-point implementation of Riemann integration computes a close approximation of the exact integral. Programmers and engineers writing such programs will benefit from verification tools that support an expressive specification language and that are highly automated. Our work provides a new method for verification of numerical software, supporting a substantially more expressive language for specifications than other publicly available automated tools. The additional expressivity in the specification language is provided by two constructs. First, the specification can feature inclusions between interval arithmetic expressions. Second, the integral operator from classical analysis can be used in the specifications, where the integration bounds can be arbitrary expressions over real variables. To support our claim of expressivity, we outline the verification of four example programs, including the integration example mentioned earlier. A key component of our method is an algorithm for proving numerical theorems. This algorithm is based on automatic polynomial approximation of non-linear real and real-interval functions defined by expressions. The PolyPaver tool is our implementation of the algorithm and its source code is publicly available. In this paper we report on experiments using PolyPaver that indicate that the additional expressivity does not come at a performance cost when comparing with other publicly available state-of-the-art provers. We also include a scalability study that explores the limits of PolyPaver in proving tight functional specifications of progressively larger randomly generated programs. © 2014 Springer International Publishing Switzerland.

Visual performance of a new bi-aspheric, segmented, asymmetric multifocal IOL

PURPOSE: To assess the visual performance and subjective experience of eyes implanted with a new bi-aspheric, segmented, multifocal intraocular lens: the Mplus X (Topcon Europe Medical, Capelle aan den IJssel, Netherlands). METHODS: Seventeen patients (mean age: 64.0 ± 12.8 years) had binocular implantation (34 eyes) with the Mplus X. Three months after the implantation, assessment was made of: manifest refraction; uncorrected and corrected distance visual acuity; uncorrected and distance corrected near visual acuity; defocus curves in photopic conditions; contrast sensitivity; halometry as an objective measure of glare; and patient satisfaction with unaided near vision using the Near Acuity Visual Questionnaire. RESULTS: Mean residual manifest refraction was -0.13 ± 0.51 diopters (D). Twenty-five eyes (74%) were within a mean spherical equivalent of ±0.50 D. Mean uncorrected distance visual acuity was +0.10 ± 0.12 logMAR monocularly and 0.02 ± 0.09 logMAR binocularly. Thirty-two eyes (94%) could read 0.3 or better without any reading correction and all patients could read 0.3 or better with a reading correction. Mean monocular uncorrected near visual acuity was 0.18 ± 0.16 logMAR, improving to 0.15 ± 0.15 logMAR with distance correction. Mean binocular uncorrected near visual acuity was 0.11 ± 0.11 logMAR, improving to 0.09 ± 0.12 logMAR with distance correction. Mean binocular contrast sensitivity was 1.75 ± 0.14 log units at 3 cycles per degree, 1.88 ± 0.20 log units at 6 cycles per degree, 1.66 ± 0.19 log units at 12 cycles per degree, and 1.11 ± 0.20 log units at 18 cycles per degree. Mean binocular and monocular halometry showed a glare profile of less than 1° of debilitating light scatter. Mean Near Acuity Visual Questionnaire Rasch score (0 = no difficulty, 100 = extreme difficulty) for satisfaction for near vision was 20.43 ± 14.64 log-odd units. CONCLUSIONS: The Mplus X provides a good visual outcome at distance and near with minimal dysphotopsia. Patients were very satisfied with their uncorrected near vision. © SLACK Incorporated.