Paradox in deviation measure and trap in method improvement—take international comparison as an example

<abstract> <p>Due to the problem of "true value agnostic" in the measurement of the real world, people believe that the existing methods can be closer to the true value by improving them. Therefore, they are willing to excessively affirm the more advanced method and deny the relatively "traditional" method. Taking the exchange rate method and purchasing power parity method commonly used in international economic comparison as examples, this paper generalizes the problems revealed by the exchange-rate-deviation index and concludes that there are at least three paradoxes in the deviation measurement of different methods. These paradoxes are the paradox of behavior significance, the paradox of comparative object, and the paradox of measurement result. The reason is that there is a cautionary trap in the improvement or innovation of measurement methods in reality. Sometimes the improved method is not necessarily better than the unimproved method. People tend to prefer advanced technology and methodology, but the problem of statistical input and related statistical benefits need to be considered in practical measurement. In fact, these basic problems still exist in some of the methods of economic statistics that we regard as common sense. When learning or introducing new methods, scholars do not absolutize the existing methods and conclusions. They should pay attention to critical experience, avoid the trap of improvement methods, and seek real improvement or innovation.</p> </abstract>

Defining the effective deformation of the vertebral column

SummaryThe Cobb angle is calculated in the coronal plane, irrespective of vertebral rotation, lordokyphosis and local wedge properties of individual verte-brae other than the end plates used for the measurement. Rigorous three-dimensional generalizations of the Cobb angle are complicated for at least two reasons. Firstly, the vertebral column is segmented, not continuous, making the choice of rigorous model ambiguous. Secondly, there exists an inherent curvature (in terms of thoracic kyphosis and lumbar lordosis) that may be considered physiologically healthy or ’normal’. When attempting to find a three-dimensional deviation measure, such normal sagittal curvature must be compensated for.In this paper we introduce a three-dimensional local deformation parameter (which we call the local effective deformation) motivated by both biomechanics and the basic theory of spatial curves, and simultaneously introduce a technical procedure to estimate the parameter from CT scans using MPR (multi-phase reconstruction) in PACS (IDS-7). A detailed description of the proposed modelling of vertebral column deformation is given, together with a stepwise procedure to estimate the three-dimensional deformation (in terms of local effective deformation). As a deformation measure it requires knowledge about the natural healthy kypholordosis. A method is described by which such knowledge may be incorporated in future work.

Docking of peptides to GPCRs using a combination of CABS-dock with FlexPepDock refinement

The structural description of peptide ligands bound to G protein-coupled receptors (GPCRs) is important for the discovery of new drugs and deeper understanding of the molecular mechanisms of life. Here we describe a three-stage protocol for the molecular docking of peptides to GPCRs using a set of different programs: (1) CABS-dock for docking fully flexible peptides; (2) PD2 method for the reconstruction of atomistic structures from C-alpha traces provided by CABS-dock and (3) Rosetta FlexPepDock for the refinement of protein–peptide complex structures and model scoring. We evaluated the proposed protocol on the set of seven different GPCR–peptide complexes (including one containing a cyclic peptide), for which crystallographic structures are available. We show that CABS-dock produces high resolution models in the sets of top-scored models. These sets of models, after reconstruction to all-atom representation, can be further improved by Rosetta high-resolution refinement and/or minimization, leading in most of the cases to sub-Angstrom accuracy in terms of interface root-mean-square-deviation measure.

Two results on dynamic extensions of deviation measures

We give a dynamic extension result of the (static) notion of a deviation measure. We also study distribution-invariant deviation measures and show that the only dynamic deviation measure which is law invariant and recursive is the variance.

Generalized Batch Normalization: Towards Accelerating Deep Neural Networks

Utilizing recently introduced concepts from statistics and quantitative risk management, we present a general variant of Batch Normalization (BN) that offers accelerated convergence of Neural Network training compared to conventional BN. In general, we show that mean and standard deviation are not always the most appropriate choice for the centering and scaling procedure within the BN transformation, particularly if ReLU follows the normalization step. We present a Generalized Batch Normalization (GBN) transformation, which can utilize a variety of alternative deviation measures for scaling and statistics for centering, choices which naturally arise from the theory of generalized deviation measures and risk theory in general. When used in conjunction with the ReLU non-linearity, the underlying risk theory suggests natural, arguably optimal choices for the deviation measure and statistic. Utilizing the suggested deviation measure and statistic, we show experimentally that training is accelerated more so than with conventional BN, often with improved error rate as well. Overall, we propose a more flexible BN transformation supported by a complimentary theoretical framework that can potentially guide design choices.

Application of semi-deviation as a proxy for the expected return estimation in the Croatian equity market

In the field of portfolio management the focus has been on the out-of-sample estimation of the covariance matrix mainly because the estimation of expected return is much more challenging. However, recent research efforts have not only tried to improve the estimation of risk parameters by expanding the analysis beyond the mean-variance setting but also by testing whether risk measures can be used as proxies for the expected return in the stock market. In this research, we test the standard deviation (measure of total volatility) and the semi-deviation (measure of downside risk) as proxies for the expected market return in the illiquid and undeveloped Croatian stock market in the period from January 2005 until November 2017. In such an environment, the application of the proposed methodology yielded poor results, which helps explain the failure of the out-of-sample estimation of the maximum Sharpe ratio portfolio in earlier research in the Croatian equity market.