Heteroscedastic latent variable modelling with applications to multivariate statistical process control

We present an approach for conducting multivariate statistical process control (MSPC) in noisy environments, i.e., when the signal to noise ratio is low, and, furthermore, noise standard deviation (uncertainty) affecting each collected value can vary over time, and is assumingly known. This approach is based upon a latent variable model structure, HLV (standing for heteroscedastic latent variable model), that explicitly integrates information regarding data uncertainty. Moderate amounts of missing data can also be handled in a coherent and fully integrated way through HLV. Several examples show the added value achieved under noisy conditions by adopting such an approach and a case study illustrates its application to a real industrial context of pulp and paper product quality data analysis.http://www.sciencedirect.com/science/article/B6TFP-4GX1HVW-2/1/c5e6b0a181b2fb4ffd7803ff38c9dac

Multiscale statistical process control with multiresolution data

An approach is presented for conducting multiscale statistical process control that adequately integrates data at different resolutions (multiresolution data), called MR-MSSPC. Its general structure is based on Bakshi's MSSPC framework designed to handle data at a single resolution. Significant modifications were introduced in order to process multiresolution information. The main MR-MSSPC features are presented and illustrated through three examples. Issues related to real world implementations and with the interpretation of the multiscale covariance structure are addressed in a fourth example, where a CSTR system under feedback control is simulated. Our approach proved to be able to provide a clearer definition of the regions where significant events occur and a more sensitive response when the process is brought back to normal operation, when it is compared with previous approaches based on single resolution data. © 2006 American Institute of Chemical Engineers AIChE J, 200

The Clapping Book

A steady horizontal air stream flows across a book clamped at its downstream end. Pages lift off to form a growing bent stack whose shape is determined by the torques associated with aerodynamic forces, weight and elastic resistance to bending. As more pages lift off to join the bent stack, the increasing importance of bending rigidity to dynamic pressure eventually causes the book to clap shut. The process restarts, and self-sustained oscillations emerge. [Fluid dynamics video]Comment: 1 page, Video submission for the 26th Annual Gallery of Fluid Motion (American Physical Society). Videos available from http://ecommons.library.cornell.edu/bitstream/1813/11473/2/GFM_clapping_reis_mpeg1.mpg low (mpeg-1) and http://ecommons.library.cornell.edu/bitstream/1813/11473/3/GFM_clapping_reis_mpeg2.mpg high (mpeg-2) resolutio

Drivers to Equity Valuation: Perpetuities or Annuities Approach? An Application to the main European Stock Markets

Academics and practitioners have been applying equity valuation methods mainly based on discount cash flow models, residual income models or dividend discount models combined with balance sheet and income statement multiples of market comparables to analyse share price and to provide price targets for investors or even base for transactions such as mergers and acquisitions (M&A). Most of those methods rely on mathematical deductions of growing or constant perpetuities or near perpetuities (such as annuities) to attain market values. However, it is of the outmost relevance for valuation to verify how the theoretical models relate with real values and what is its relationship with companies’ firm past age. Beyond stating a non-linear relationship for valuation models and ascertain important valuation drivers, using a sample of more than 3400 European companies with cross section data, this paper contributes to the improvement of valuation model’s effectiveness by inducing non-explicit period valuation modifications to long term annuities and perpetuities considering class age intervals. This paper’s originality is supported by the study of the relation of past company age with predicted annuities, the proof of non-compliance of perpetuity-based valuation models and the contribution with new value drivers for valuation purposes. &nbsp

Twisting instabilities in elastic ribbons with inhomogeneous pre-stress: a macroscopic analog of thermodynamic phase transition

We study elastic ribbons subject to large, tensile pre-stress confined to a central region within the cross-section. These ribbons can buckle spontaneously to form helical shapes, featuring regions of alternating chirality (phases) that are separated by so-called perversions (phase boundaries). This instability cannot be described by classical rod theory, which incorporates pre-stress through effective natural curvature and twist; these are both zero due to the mirror symmetry of the pre-stress. Using dimension reduction, we derive a one-dimensional (1D) 'rod-like' model from a plate theory, which accounts for inhomogeneous pre-stress as well as finite rotations. The 1D model successfully captures the qualitative features of torsional buckling under a prescribed end-to-end displacement and rotation, including the co-existence of buckled phases possessing opposite twist, and is in good quantitative agreement with the results of numerical (finite-element) simulations and model experiments on elastomeric samples. Our model system provides a macroscopic analog of phase separation and pressure-volume-temperature state diagrams, as described by the classical thermodynamic theory of phase transitions.Comment: 29 pages; 11 figure

A geometrically exact model for thin magneto-elastic shells

We develop a reduced model for hard-magnetic, thin, linear-elastic shells that can be actuated through an external magnetic field, with geometrically exact strain measures. Assuming a reduced kinematics based on the Kirchhoff-Love assumption, we derive a reduced two-dimensional magneto-elastic energy that can be minimized through numerical analysis. In parallel, we simplify the reduced energy by expanding it up to the second-order in the displacement field and provide a physical interpretation. Our theoretical analysis allows us to identify and interpret the two primary mechanisms dictating the magneto-elastic response: a combination of equivalent magnetic pressure and forces at the first order, and distributed magnetic torques at the second order. We contrast our reduced framework against a three-dimensional nonlinear model by investigating three test cases involving the indentation and the pressure buckling of shells under magnetic loading. We find excellent agreement between the two approaches, thereby verifying our reduced model for shells undergoing nonlinear and non-axisymmetric deformations. We believe that our model for magneto-elastic shells will serve as a valuable tool for the rational design of magnetic structures, enriching the set of reduced magnetic models.Comment: 24 pages, 5 figure

Determinants Of Firm Terminal Value: The Perspective Of North American And European Financial Analysts

Company valuation models attempt to estimate the value of a company in two stages: (1) comprising of a period of explicit analysis and (2) based on unlimited production period of cash flows obtained through a mathematical approach of perpetuity, which is the terminal value. In general, these models, whether they belong to the Dividend Discount Model (DDM), the Discount Cash Flow (DCF), or RIM (Residual Income Models) group, discount one attribute (dividends, free cash flow, or results) to a given discount rate. This discount rate, obtained in most cases by the CAPM (Capital asset pricing model) or APT (Arbitrage pricing theory) allows including in the analysis the cost of invested capital based on the risk taking of the attributes. However, one cannot ignore that the second stage of valuation that is usually 53-80% of the company value (Berkman et al., 1998) and is loaded with uncertainties. In this context, particular attention is needed to estimate the value of this portion of the company, under penalty of the assessment producing a high level of error. Mindful of this concern, this study sought to collect the perception of European and North American financial analysts on the key features of the company that they believe contribute most to its value. For this feat, we used a survey with closed answers. From the analysis of 123 valid responses using factor analysis, the authors conclude that there is great importance attached (1) to the life expectancy of the company, (2) to liquidity and operating performance, (3) to innovation and ability to allocate resources to R&D, and (4) to management capacity and capital structure, in determining the value of a company or business in long term. These results contribute to our belief that we can formulate a model for valuating companies and businesses where the results to be obtained in the evaluations are as close as possible to those found in the stock market

Defect-Defect Interactions in the Buckling of Imperfect Spherical Shells

We perform finite element simulations to study the impact of defect-defect interactions on the pressure-induced buckling of thin, elastic, spherical shells containing two dimpled imperfections. Throughout, we quantify the critical buckling pressure of these shells using their knockdown factor. We examine cases featuring either identical or different geometric defects and systematically explore the parameter space, including the angular separation between the defects, their widths and amplitudes, and the radius-to-thickness ratio of the shell. As the angular separation between the defects is increased, the buckling strength initially decreases, then increases before reaching a plateau. Our primary finding is that the onset of defect-defect interactions, as quantified by a characteristic length scale associated with the onset of the plateau, is set by the critical buckling wavelength reported in the classic shell-buckling literature. Beyond this threshold, within the plateau regime, the buckling behavior of the shell is dictated by the largest defect