Definition and quantification of assets

The word ‘asset’ was originally taken into the English language, from the Latin ‘ad satis’ and French ‘asez’, as a term used at law meaning sufficient estate or effects to discharge debts. It later came to be used in the sense of property available for the payment of debts. Assets were understood to be property (objects owned and rights of ownership) that could be exchanged for cash. The importance of factual knowledge of the money equivalents of property and debts, in managing mercantile affairs, was emphasised in accounting manuals during the eighteenth and nineteenth centuries. The rights of investors and creditors to factual up-to-date information about the financial state of affairs of companies, given the advent of limited liability, underscored the early company legislation that required the preparation and auditing of statements of property and debts. During the latter part of the nineteenth century the emphasis in accounting moved away from assets as exchangeable property to assets as deferred costs. Expectations took the place of observables. The abstract (expectational) notion of assets as ‘future economic benefits’ was embraced by accountants in the absence of rigorous definitions of the elements and functions of dated statements of financial position and performance. Assets are quantified financially by a heterogeneous mass of potentially inconsistent rules that, by and large, have no regard for the empirical nature of measurement. Consequently, accountants have failed to provide the community with up-to-date factual information about the financial state of affairs and performance of business entities - and, hence, with an informative basis for financial action.

Sequential fixed-width confidence bands for kernel regression estimation

We consider a random design model based on independent and identically distributed (iid) pairs of observations (Xi, Yi), where the regression function m(x) is given by m(x) = E(Yi|Xi = x) with one independent variable. In a nonparametric setting the aim is to produce a reasonable approximation to the unknown function m(x) when we have no precise information about the form of the true density, f(x) of X. We describe an estimation procedure of non-parametric regression model at a given point by some appropriately constructed fixed-width (2d) confidence interval with the confidence coefficient of at least 1−. Here, d(> 0) and 2 (0, 1) are two preassigned values. Fixed-width confidence intervals are developed using both Nadaraya-Watson and local linear kernel estimators of nonparametric regression with data-driven bandwidths.

The sample size was optimized using the purely and two-stage sequential procedure together with asymptotic properties of the Nadaraya-Watson and local linear estimators. A large scale simulation study was performed to compare their coverage accuracy. The numerical results indicate that the confidence bands based on the local linear estimator have the best performance than those constructed by using Nadaraya-Watson estimator. However both estimators are shown to have asymptotically correct coverage properties.

Sample size determination for kernel regression estimation using sequential fixed-width confidence bands

We consider a random design model based on independent and identically distributed pairs of observations (Xi, Yi), where the regression function m(x) is given by m(x) = E(Yi|Xi = x) with one independent variable. In a nonparametric setting the aim is to produce a reasonable approximation to the unknown function m(x) when we have no precise information about the form of the true density, f(x) of X. We describe an estimation procedure of non-parametric regression model at a given point by some appropriately constructed fixed-width (2d) confidence interval with the confidence coefficient of at least 1−. Here, d(> 0) and 2 (0, 1) are two preassigned values. Fixed-width confidence intervals are developed using both Nadaraya-Watson and local linear kernel estimators of nonparametric regression with data-driven bandwidths. The sample size was optimized using the purely and two-stage sequential procedures together with asymptotic properties of the Nadaraya-Watson and local linear estimators. A large scale simulation study was performed to compare their coverage accuracy. The numerical results indicate that the confi dence bands based on the local linear estimator have the better performance than those constructed by using Nadaraya-Watson estimator. However both estimators are shown to have asymptotically correct coverage properties.

A novel monotonic fixed-point algorithm for l1-regularized least square vector and matrix problem

Least square problem with l₁ regularization has been proposed as a promising method for sparse signal reconstruction (e.g., basis pursuit de-noising and compressed sensing) and feature selection (e.g., the Lasso algorithm) in signal processing, statistics, and related fields. These problems can be cast as l₁-regularized least-square program (LSP). In this paper, we propose a novel monotonic fixed point method to solve large-scale l₁-regularized LSP. And we also prove the stability and convergence of the proposed method. Furthermore we generalize this method to least square matrix problem and apply it in nonnegative matrix factorization (NMF). The method is illustrated on sparse signal reconstruction, partner recognition and blind source separation problems, and the method tends to convergent faster and sparser than other l₁-regularized algorithms.

Fixed-angle locking proximal humerus plate: an evaluation of functional results and implant-related outcomes

Background
Displaced and unstable proximal humeral fractures are challenging injuries to treat. Proximal humeral locking plates are a recent development for the treatment of these complex fractures.

Methods
Retrospective analysis of 23 patients with 23 proximal humeral fractures treated with the Synthes locking proximal humerus plate. These were Neer two-, three- and four-part fractures. Follow-up was at a mean of 22 months and included clinical assessment using the Constant score (CS) and the Short Form-12 health questionnaire. Radiographic assessment was performed to assess implant-related complication in relation to the initial fracture pattern and the presence of adequate medial support.

Results
The mean CS for all patients was 60.4 (range, 29–85). The mean adjusted CS was 82% (range, 30–117), active forward flexion 127 degrees and the active abduction 115 degrees. Initial fracture pattern, the presence or absence of adequate medial support and age did not significantly influence the clinical scores. Complications included one infection, two cases of avascular necrosis, two cases of varus collapse with screw penetration and one non-union. The overall reoperation rate was 26%. There was an increased rate of complications in those with inadequate medial support (P = 0.0183) and a trend to higher complication rates in four-part fractures.

Conclusion
Using the locking proximal humerus plate for the treatment of proximal humeral fractures is an acceptable procedure with comparable outcomes with historical controls, but with a complication rate of 30%. More important than implant selection, however, is the ability to achieve a stable reduction with calcar support.