Interdependence between Greece and other European stock markets: A comparison of wavelet and VMD copula, and the portfolio implications

The interdependence of Greece and other European stock markets and the subsequent portfolio implications are examined in wavelet and variational mode decomposition domain. In applying the decomposition techniques, we analyze the structural properties of data and distinguish between short and long term dynamics of stock market returns. First, the GARCH-type models are fitted to obtain the standardized residuals. Next, different copula functions are evaluated, and based on the conventional information criteria and time varying parameter, Joe-Clayton copula is chosen to model the tail dependence between the stock markets. The short-run lower tail dependence time paths show a sudden increase in comovement during the global financial crises. The results of the long-run dependence suggest that European stock markets have higher interdependence with Greece stock market. Individual country’s Value at Risk (VaR) separates the countries into two distinct groups. Finally, the two-asset portfolio VaR measures provide potential markets for Greece stock market investment diversification.

Design of experiments for bivariate binary responses modelled by Copula functions

Optimal design for generalized linear models has primarily focused on univariate data. Often experiments are performed that have multiple dependent responses described by regression type models, and it is of interest and of value to design the experiment for all these responses. This requires a multivariate distribution underlying a pre-chosen model for the data. Here, we consider the design of experiments for bivariate binary data which are dependent. We explore Copula functions which provide a rich and flexible class of structures to derive joint distributions for bivariate binary data. We present methods for deriving optimal experimental designs for dependent bivariate binary data using Copulas, and demonstrate that, by including the dependence between responses in the design process, more efficient parameter estimates are obtained than by the usual practice of simply designing for a single variable only. Further, we investigate the robustness of designs with respect to initial parameter estimates and Copula function, and also show the performance of compound criteria within this bivariate binary setting.

Copula-based spatial modelling of geometallurgical variables

The most important aspect of modelling a geological variable, such as metal grade, is the spatial correlation. Spatial correlation describes the relationship between realisations of a geological variable sampled at different locations. Any method for spatially modelling such a variable should be capable of accurately estimating the true spatial correlation. Conventional kriged models are the most commonly used in mining for estimating grade or other variables at unsampled locations, and these models use the variogram or covariance function to model the spatial correlations in the process of estimation. However, this usage assumes the relationships of the observations of the variable of interest at nearby locations are only influenced by the vector distance between the locations. This means that these models assume linear spatial correlation of grade. In reality, the relationship with an observation of grade at a nearby location may be influenced by both distance between the locations and the value of the observations (ie non-linear spatial correlation, such as may exist for variables of interest in geometallurgy). Hence this may lead to inaccurate estimation of the ore reserve if a kriged model is used for estimating grade of unsampled locations when nonlinear spatial correlation is present. Copula-based methods, which are widely used in financial and actuarial modelling to quantify the non-linear dependence structures, may offer a solution. This method was introduced by Bárdossy and Li (2008) to geostatistical modelling to quantify the non-linear spatial dependence structure in a groundwater quality measurement network. Their copula-based spatial modelling is applied in this research paper to estimate the grade of 3D blocks. Furthermore, real-world mining data is used to validate this model. These copula-based grade estimates are compared with the results of conventional ordinary and lognormal kriging to present the reliability of this method.

Radiographic outcomes over time after endoscopic anterior scoliosis correction

A prospective, consecutive series of 106 patients receiving endoscopic anterior scoliosis correction. The aim was to analyse changes in radiographic parameters and rib hump in the two years following surgery. Endoscopic anterior scoliosis correction is a level sparing approach, therefore it is important to assess the amount of decompensation which occurs after surgery. All patients received a single anterior rod and vertebral body screws using a standard compression technique. Cleared disc spaces were packed with either mulched femoral head allograft or rib head/iliac crest autograft. Radiographic parameters (major, instrumented, minor Cobb, T5-T12 kyphosis) and rib hump were measured at 2,6,12 and 24 months after surgery. Paired t-tests and Wilcoxon signed ranks tests were used to assess the statistical significant of changes between adjacent time intervals.----- Results: Mean loss of major curve correction from 2 to 24 months after surgery was 4 degrees. Mean loss of rib hump correction was 1.4 degrees. Mean sagittal kyphosis increased from 27 degrees at 2 months to 30.6 degrees at 24 months. Rod fractures and screw-related complications resulted in several degrees less correction than patients without complications, but overall there was no clinically significant decompensation following complications. The study concluded that there are small changes in deformity measures after endoscopic anterior scoliosis surgery, which are statistically significant but not clinically significant.

Percutaneous insertion of Dual Growth Rods using a new mobile bearing implant

Growth rods are commonly used for the treatment of scoliosis in the immature spine. Many variations have been proposed but breakage of implants is a common problem. Growth rod insertion commonly involves large exposures at initial insertion followed by multiple smaller procedures for lengthening. We present our early experiences using a percutaneous technique of insertion of a new titanium mobile bearing implant (Medtronic Inc). The implant allows some rotatory motion in the middle of the construct thus reducing construct stresses and thus possibly reducing rod breakage risk. Based on this small initial series with 12 months follow-up, percutaneous insertion of growth rods using the new implant is a safe and reliable technique although the infection rate in our sample was of note. This may be related to the titanium wear and inflammation seen in the soft tissues at time of operation and visualised on histology. No implants have required removal due to infection, and all infections were treated with debridement at next lengthening and suppressive antibiotics. Propionibacterium is one of the commonest infections seen with spinal implants and sometimes does not respond to simple antibiotic suppression. The technique allows preservation of the soft tissues until definitive fusion is needed and may lead to a decrease in hospital stay. The implant is low profile and seems to offer advantages over other systems on the market. Further follow up is needed to look at longer term outcomes with this new implant type.

A new measure to quantify chest wall deformity in scoliosis patients : does rib hump measurement correlate with anterior chest wall deformity post surgery?

The primary aims of scoliosis surgery are to halt the progression of the deformity, and to reduce its severity (cosmesis). Currently, deformity correction is measured in terms of posterior parameters (Cobb angles and rib hump), even though the cosmetic concern for most patients is anterior chest wall deformity. In this study, we propose a new measure for assessing anterior chest wall deformity and examine the correlation between rib hump and the new measure. 22 sets of CT scans were retrieved from the QUT/Mater Paediatric Spinal Research Database. The Image J software (NIH) was used to manipulate formatted CT scans into 3-dimensional anterior chest wall reconstructions. A ‘chest wall angle’ was then measured in relation to the first sacral vertebral body. The chest wall angle was found to be a reliable tool in the analysis of chest wall deformity. No correlation was found between the new measure and rib hump angle. Since rib hump has been shown to correlate with vertebral rotation on CT, this suggests that there maybe no correlation between anterior and posterior deformity measures. While most surgical procedures will adequately address the coronal imbalance & posterior rib hump elements of scoliosis, they do not reliably alter the anterior chest wall shape. This implies that anterior chest wall deformity is to a large degree an intrinsic deformity, not directly related to vertebral rotation.

The anatomical and biomechanical consequences of anterior vertebral stapling for the fusionless correction of scoliosis

Fusionless scoliosis surgery is an emerging treatment for idiopathic scoliosis as it offers theoretical advantages over current forms of treatment. Anterior vertebral stapling using a nitinol staple is one such treatment. Despite increasing interest in this technique, little is known about the effects on the spine following insertion, or the mechanism of action of the staple. The aims of this study were threefold; (1) to measure changes in the bending stiffness of a single motion segment following staple insertion, (2) to describe the forces that occur within the staple during spinal movement, and (3) to describe the anatomical changes that occur following staple insertion. Results suggest that staple insertion consistently decreased stiffness in all directions of motion. An explanation for the finding may be found in the outcomes of the strain gauge testing and micro-CT scan. The strain gauge testing showed that once inserted, the staple tips applied a baseline compressive force to the surrounding trabecular bone and vertebral end-plate. This finding would be consistent with the current belief that the clinical effect of the staples is via unilateral compression of the physis. Interestingly however, as each specimen progressed through the five cycles of each test, the baseline load on the staple tips gradually decreased, implying that the force at the staple tip-bone interface was decreasing. We believe that this was likely occurring as a result of structural damage to the trabecular bone and vertebral end-plate by the staple effectively causing ‘loosening’ of the staple. This hypothesis is further supported by the findings of the micro-CT scan. The pictures depict significant trabecular bone and physeal injury around the staple blades. These results suggest that the current hypothesis that stapling modulates growth through physeal compression may be incorrect, but rather the effect occurs through mechanical disruption of the vertebral growth plate.

i-Cobb - An innovative technique in spinal radiographic measurement

The measurement of Cobb angles from radiographs is routine practice in spinal clinics. The technique relies on the use and availability of specialist equipment such as a goniometer, cobbometer or protractor. The aim of this study was to validate the use of i-Phone (Apple Inc) combined with Tilt Meter Pro software as compared to a protractor in the measurement of Cobb angles. Between November 2008 and December 2008 20 patients were selected at random from the Paediatric Spine Research Groups Database. A power calculation was performed which indicated if n=240 measurements the study had a 96% chance of detecting a 5 degree difference between groups. All patients had idiopathic scoliosis with a range of curve types and severities. The study found the i-Phone combined with Tilt Meter Pro software offers a faster alternative to the traditional method of Cobb angle measurement. The use of i-Phone offers a more convenient way of measuring Cobb angles in the outpatient setting. The intra-observer repeatability of the iPhone is equivalent to the protractor in the measurement of Cobb angles.

Lateral bone density variations in the scoliotic spine

Adolescent Idiopathic Scoliosis (AIS) is the most common deformity of the spine, affecting 2-4% of the population. Previous studies have shown that the vertebrae in scoliotic spines undergo abnormal shape changes, however there has been little exploration of how AIS affects bone density distribution within the vertebrae. Existing pre-operative CT scans of 53 female idiopathic scoliosis patients with right-sided main thoracic curves were used to measure the lateral (right to left) bone density profile at mid-height through each vertebral body. This study demonstrated that AIS patients have a marked convex/concave asymmetry in bone density for vertebral levels at or near the apex of the scoliotic curve. To the best of our knowledge, the only previous studies of bone density distribution in AIS are those of Périé et al [1,2], who reported a coronal plane ‘mechanical migration’ of 0.54mm toward the concavity of the scoliotic curve in the lumbar apical vertebrae of 11 scoliosis patients. This is comparable to the value of 0.8mm (4%) in our study, especially since our patients had more severe scoliotic curves. From a bone adaptation perspective, these results suggest that the axial loading on the scoliotic spine is strongly asymmetric.

Effect of bone graft type on fusion rates following endoscopic anterior scoliosis correction

Bone graft is generally considered fundamental in achieving solid fusion in scoliosis correction and pseudarthrosis following instrumentation may predispose to implant failure. In endoscopic anterior-instrumented scoliosis surgery, autologous rib or iliac crest graft has been utilised traditionally but both techniques increase operative duration and cause donor site morbidity. Allograft bone and bone- morphogenetic-protein alternatives may improve fusion rates but this remains controversial. This study's objective was to compare two-year postoperative fusion rates in a series of patients who underwent endoscopic anterior instrumentation for thoracic scoliosis utilising various bone graft types. Significantly better rates of fusion occurred in endoscopic anterior instrumented scoliosis correction using femoral allograft compared to autologous rib-heads and iliac crest graft. This may be partly explained by the difficulty obtaining sufficient quantities of autologous graft. Lower fusion rates in the autologous graft group appeared to predispose to rod fracture although the clinical consequence of implant failure is uncertain.

Computed tomography evaluation of axial vertebral derotation in endoscopic anterior instrumentation for adolescent idiopathic scoliosis

Thoracoscopic instrumented anterior spinal fusion for adolescent idiopathic scoliosis (AIS) has clinical benefits that include reduced pulmonary morbidity, postoperative pain, and improved cosmesis. However, quantitative data on radiological improvement of vertebral rotation using this method is lacking. This study’s objectives were to measure preoperative and postoperative axial vertebral rotational deformity at the curve apex in endoscopically-treated anterior-instrumented scoliosis patients using CT, and assess the relevance of these findings to clinically measured chest wall rib hump deformity correction. This is the first quantitative CT study to confirm that endoscopic anterior instrumented fusion for AIS substantially improves axial vertebral body rotational deformity at the apex of the curve. The margin of correction of 43% compares favourably with historically published figures of 24% for patients with posterior all-hook-rod constructs. CT measurements correlated significantly to the clinical outcome of rib hump deformity correction.