The level sets of the resolvent norm and convexity properties of Banach spaces

We construct a bounded linear operator on a separable, reflexive and strictly convex Banach space whose resolvent norm is constant in a neighbourhood of zero.

Calcification and ossification of the convexity of the falx cerebri and related subdural space in human cadavers

OBJECTIVE: The present work was planned to report the incidence of calcification and ossification of an isolated cranial dural fold. The form, degree of severity and range of extension of such changes will be described. Involvement of the neighboring brain tissue and blood vessels, whether meningeal or cerebral, will also be determined. The results of this study might highlight the occasional incidence of intracranial calcification and ossification in images of the head and their interpretation, by radiologists and neurologists, to be of dural or vascular origin.

METHODS: Two human formalin-fixed cadavers, one middle-aged female another older male, were investigated at the Anatomy Laboratory, College of Medicine, King Faisal University, Dammam, Kingdom of Saudi Arabia during the period from 2000 to 2003. In each cadaver, the skullcap was removed and the convexity of the cranial dura mater, as well as the individual dural folds, were carefully examined for any calcification or ossification. The meningeal and cerebral blood vessels together with the underlying brain were grossly inspected for such structural changes. Calcified or ossified tissues, when identified, were subjected to histological examination to confirm their construction.

RESULTS: The female cadaver showed a calcified parietal emissary vein piercing the skullcap and projecting into the scalp. The latter looked paler and deficient in hair on its right side. The base of the stump was surrounded by a granular patch of calcification. The upper convex border of the falx cerebri was hardened and it presented granules, plaques and a cauliflower mass, which all proved to be osseous in structure. The meningeal and right cerebral vessels were mottled with calcium granules. The underlying temporal and parietal lobes of the right cerebral hemisphere were degenerated. The male cadaver also revealed a calcified upper border of the falx cerebri and superior sagittal sinus. Osseous granules and plaques, similar to those of the first specimen, were also identified but without gross changes in the underlying brain.

CONCLUSION: Calcification or ossification of an isolated site of the cranial dura mater and the intracranial blood vessels might occur. These changes should be kept in mind while interpreting images of the skull and brain. Clinical assessment and laboratory investigations are required to determine whether these changes are idiopathic, traumatic, or as a manifestation of a generalized disease such as hyperparathyroidism, vitamin D-intoxication, or chronic renal failure.

The convex variable step-size (CVSS) algorithm

This letter introduces the convex variable step-size (CVSS) algorithm. The convexity of the resulting cost function is guaranteed. Simulations presented show that with the proposed algorithm, we obtain similar results, as with the VSS algorithm in initial convergence, while there are potential performance gains when abrupt changes occur.

Equidiscrimination contours around an achromatic colour are convex but not balanced

A model based on the postreceptor channels followed by a Minkowski norm (Minkowski model) is widely used to fit experimental data on colour discrimination. This model predicts that contours of equal discrimination in colour space are convex and balanced (symmetrical). We have tested these predictions in an experiment. Two new statistical tests have been developed to analyse convexity and balancedness of experimental curves. Using these tests we have found that while they are in line with the convexity prediction, our experimental contours strongly testify against balancedness. It follows that the Minkowski model is, generally, inappropriate to model colour discrimination data. © 2002 Elsevier Science (USA).

Short-Sale Constraints and the Pricing of Managerial Skills

We investigate the impact of the absence of short selling on the pricing of managerial skills in the mutual fund industry. In the presence of divergent opinions regarding managerial skills, fund managers can strategically use fees to attract only the most optimistic capital. The recognition of this fee strategy helps explain a set of stylized observations and puzzles in the mutual fund industry, including the underperformance of active funds, the existence of flow convexity, and the negative correlation between gross-of-fee α and fees.

Using Graph Components Derived from an Associative Concept Dictionary to Predict fMRI Neural Activation Patterns that Represent the Meaning of Nouns

In this study, we introduce an original distance definition for graphs, called the Markov-inverse-F measure (MiF). This measure enables the integration of classical graph theory indices with new knowledge pertaining to structural feature extraction from semantic networks. MiF improves the conventional Jaccard and/or Simpson indices, and reconciles both the geodesic information (random walk) and co-occurrence adjustment (degree balance and distribution). We measure the effectiveness of graph-based coefficients through the application of linguistic graph information for a neural activity recorded during conceptual processing in the human brain. Specifically, the MiF distance is computed between each of the nouns used in a previous neural experiment and each of the in-between words in a subgraph derived from the Edinburgh Word Association Thesaurus of English. From the MiF-based information matrix, a machine learning model can accurately obtain a scalar parameter that specifies the degree to which each voxel in (the MRI image of) the brain is activated by each word or each principal component of the intermediate semantic features. Furthermore, correlating the voxel information with the MiF-based principal components, a new computational neurolinguistics model with a network connectivity paradigm is created. This allows two dimensions of context space to be incorporated with both semantic and neural distributional representations.

Comparisons of anterior segment biometry between Chinese and Caucasians using anterior segment optical coherence tomography.

PURPOSE: To compare anterior segment parameters between eyes of Chinese and Caucasians using anterior segment optical coherence tomography and to evaluate the association between these parameters and anterior chamber angle width between the two ethnic groups. METHODS: 60 Chinese and 60 Caucasians, 30 with open angles and 30 with narrow angles (defined as Shaffer grade < or =2 in > or =3 quadrants during dark room gonioscopy) in each group, were consecutively enrolled. One eye of each subject was randomly selected for imaging in a completely darkened room. Measurements, including anterior chamber depth (ACD), scleral spur-to-scleral spur distance (anterior chamber width (ACW)), anterior chamber angle width, iris convexity and iris thickness, were compared between the groups. The associations between angle opening distance and biometric measurements were evaluated with univariate and multivariate regression analyses. RESULTS: There were no differences in age, axial length, anterior chamber angle measurements, pupil diameter and iris convexity between Chinese and Caucasians in both open-angle and narrow-angle groups. However, the ACD and ACW were smaller and the iris was thicker in Chinese. In the multivariate analysis, the ACD was the most influential biometric parameter for angle opening distance in both Chinese and Caucasians. After adjusting the effects of axial length, age and sex, ACD and ACW were significantly smaller in Chinese. CONCLUSIONS: Chinese eyes had smaller ACD, smaller ACW and greater iris thickness than Caucasians. ACD was the most influential parameter in determining the angle width in both ethnic groups.

Noise resilient discrete-time cross-relation sensor characterisation

In-situ characterisation of thermocouple sensors is a challenging problem. Recently the authors presented a blind characterisation technique based on the cross-relation method of blind identification. The method allows in-situ identification of two thermocouple probes, each with a different dynamic response, using only sampled sensor measurement data. While the technique offers certain advantages over alternative methods, including low estimation variance and the ability to compensate for noise induced bias, the robustness of the method is limited by the multimodal nature of the cost function. In this paper, a normalisation term is proposed which improves the convexity of
the cost function. Further, a normalisation and bias compensation hybrid approach is presented that exploits the advantages of both normalisation and bias compensation. It is found that the optimum of the hybrid cost function is less biased and more stable than when only normalisation is applied. All results were verified by simulation.