Testing for financial crashes using the Log Periodic Power Law model

Many papers claim that a Log Periodic Power Law (LPPL) model fitted to financial market bubbles that precede large market falls or 'crashes', contains parameters that are confined within certain ranges. Further, it is claimed that the underlying model is based on influence percolation and a martingale condition. This paper examines these claims and their validity for capturing large price falls in the Hang Seng stock market index over the period 1970 to 2008. The fitted LPPLs have parameter values within the ranges specified post hoc by Johansen and Sornette (2001) for only seven of these 11 crashes. Interestingly, the LPPL fit could have predicted the substantial fall in the Hang Seng index during the recent global downturn. Overall, the mechanism posited as underlying the LPPL model does not do so, and the data used to support the fit of the LPPL model to bubbles does so only partially. © 2013.

Binocular interaction:Contrast matching and contrast discrimination are predicted by the same model

How do signals from the 2 eyes combine and interact? Our recent work has challenged earlier schemes in which monocular contrast signals are subject to square-law transduction followed by summation across eyes and binocular gain control. Much more successful was a new 'two-stage' model in which the initial transducer was almost linear and contrast gain control occurred both pre- and post-binocular summation. Here we extend that work by: (i) exploring the two-dimensional stimulus space (defined by left- and right-eye contrasts) more thoroughly, and (ii) performing contrast discrimination and contrast matching tasks for the same stimuli. Twenty-five base-stimuli made from 1 c/deg patches of horizontal grating, were defined by the factorial combination of 5 contrasts for the left eye (0.3-32%) with five contrasts for the right eye (0.3-32%). Other than in contrast, the gratings in the two eyes were identical. In a 2IFC discrimination task, the base-stimuli were masks (pedestals), where the contrast increment was presented to one eye only. In a matching task, the base-stimuli were standards to which observers matched the contrast of either a monocular or binocular test grating. In the model, discrimination depends on the local gradient of the observer's internal contrast-response function, while matching equates the magnitude (rather than gradient) of response to the test and standard. With all model parameters fixed by previous work, the two-stage model successfully predicted both the discrimination and the matching data and was much more successful than linear or quadratic binocular summation models. These results show that performance measures and perception (contrast discrimination and contrast matching) can be understood in the same theoretical framework for binocular contrast vision. © 2007 VSP.

The transition from severe to mild wear in law alloy steel

The wear rates of sliding surfaces are significantly reduced if mild oxidational wear can be encouraged. It is hence of prime importance in the interest of component life and material conservation to understand the factors necessary to promote mild, oxidational wear, The present work investigates the fundamental mechanism of the running-in wear of BS EN 31!EN 8 steel couples. under various conditions of load. speed and test duration. Unidirectional sliding experiments were carried out on a pin-on~disc wear machine where frictional force, wear rate, temperature and contact resistance were continuously monitored during each test. Physical methods of analysis (x-ray, scanning electron microscopy etc.) were used to examine the wear debris and worn samples. The wear rate versus load curves revealed mild wear transitions, which under long duration of running, categorized mild wear into four distinct regions.α-Fe20s. Fe304, FeO and an oxide mixture were the predominant oxides in four regions of oxidational wear which were identified above the Welsh T2 transition. The wear curves were strongly effected by the speed and test duration. A surface model was used to calculate the surface parameters, and the results were found to be comparable with the experimentally observed parameters. Oxidation was responsible for the transition from severe to mild wear at a load corresponding to the Welsh T2 transition. In the running-in period sufficient energy input and surface hardness enabled oxide growth rate to increase and eventually exceeded the rate of removal, where mild wear ensued. A model was developed to predict the wear volume up to the transition. Remarkable agreement was found between the theoretical prediction and the experimentally-measured values. The oxidational mechanjsm responsible for transitjon to mild wear under equilibrium conditions was related to the formation of thick homogenous oxide plateaux on subsurface hardened layers, FeO was the oxide formed initially at the onset of mild wear but oxide type changed.during the total running period to give an equilibrium oxide whose nature depended on the loads applied.

Contrast integration over area is extensive: a three-stage model of spatial summation

Classical studies of area summation measure contrast detection thresholds as a function of grating diameter. Unfortunately, (i) this approach is compromised by retinal inhomogeneity and (ii) it potentially confounds summation of signal with summation of internal noise. The Swiss cheese stimulus of T. S. Meese and R. J. Summers (2007) and the closely related Battenberg stimulus of T. S. Meese (2010) were designed to avoid these problems by keeping target diameter constant and modulating interdigitated checks of first-order carrier contrast within the stimulus region. This approach has revealed a contrast integration process with greater potency than the classical model of spatial probability summation. Here, we used Swiss cheese stimuli to investigate the spatial limits of contrast integration over a range of carrier frequencies (1–16 c/deg) and raised plaid modulator frequencies (0.25–32 cycles/check). Subthreshold summation for interdigitated carrier pairs remained strong (~4 to 6 dB) up to 4 to 8 cycles/check. Our computational analysis of these results implied linear signal combination (following square-law transduction) over either (i) 12 carrier cycles or more or (ii) 1.27 deg or more. Our model has three stages of summation: short-range summation within linear receptive fields, medium-range integration to compute contrast energy for multiple patches of the image, and long-range pooling of the contrast integrators by probability summation. Our analysis legitimizes the inclusion of widespread integration of signal (and noise) within hierarchical image processing models. It also confirms the individual differences in the spatial extent of integration that emerge from our approach.

Breakage model development and application with CFD for predicting breakage of whey protein precipitate particles

Particle breakage due to fluid flow through various geometries can have a major influence on the performance of particle/fluid processes and on the product quality characteristics of particle/fluid products. In this study, whey protein precipitate dispersions were used as a case study to investigate the effect of flow intensity and exposure time on the breakage of these precipitate particles. Computational fluid dynamic (CFD) simulations were performed to evaluate the turbulent eddy dissipation rate (TED) and associated exposure time along various flow geometries. The focus of this work is on the predictive modelling of particle breakage in particle/fluid systems. A number of breakage models were developed to relate TED and exposure time to particle breakage. The suitability of these breakage models was evaluated for their ability to predict the experimentally determined breakage of the whey protein precipitate particles. A "power-law threshold" breakage model was found to provide a satisfactory capability for predicting the breakage of the whey protein precipitate particles. The whey protein precipitate dispersions were propelled through a number of different geometries such as bends, tees and elbows, and the model accurately predicted the mean particle size attained after flow through these geometries. © 2005 Elsevier Ltd. All rights reserved.

Fluctuation-driven traffic congestion in a scale-free model of the Internet

In studies of complex heterogeneous networks, particularly of the Internet, significant attention was paid to analysing network failures caused by hardware faults or overload. There network reaction was modelled as rerouting of traffic away from failed or congested elements. Here we model network reaction to congestion on much shorter time scales when the input traffic rate through congested routes is reduced. As an example we consider the Internet where local mismatch between demand and capacity results in traffic losses. We describe the onset of congestion as a phase transition characterised by strong, albeit relatively short-lived, fluctuations of losses caused by noise in input traffic and exacerbated by the heterogeneous nature of the network manifested in a power-law load distribution. The fluctuations may result in the network strongly overreacting to the first signs of congestion by significantly reducing input traffic along the communication paths where congestion is utterly negligible. © 2013 IEEE.