An anatomical analysis of the mini-modified orbitozygomatic and supra-orbital approaches

Seven sides of cadaver heads were used to compare the surgical exposures provided by the mini-modified orbitozygomatic (MOz) and supra-orbital (SO) approaches. The Optotrak 3020 computerized tracking system (Northern Digital, Waterloo, ON, Canada) was utilized to evaluate the area of anatomical exposure defined by six points: (1) ipsilateral sphenoid ridge; (2) most distal point of the ipsilateral middle cerebral artery (MCA); (3) most distal point of the ipsilateral posterior cerebral artery (PCA); (4) most distal point of the contralateral PCA; (5) most distal point of the contralateral MCA; and (6) contralateral sphenoid ridge. Additionally, angles of approach for the ipsilateral MCA bifurcation, ipsilateral ICA bifurcation, basilar artery tip, contralateral MCA and ICA bifurcation and anterior communicating artery (AcomA) were evaluated, first for SO and then for MOz. An image guidance system was used to evaluate the limits of surgical exposure. No differences in the area of surgical exposure were noted (p > 0.05). Vertical angles were significantly wider for the ipsilateral and contralateral ICA bifurcation, AcomA, contralateral MCA and basilar tip (p < 0.05) for MOz. No differences in horizontal angles were observed between the approaches for the six targets (p > 0.05). There were no differences in the limits of exposure. MOz affords no additional surgical working space. However, our results demonstrate systematically that vertical exposure is improved. The MOz should be performed while planning an approach to these regions and a wider exposure in the vertical axis is needed. (C) 2012 Elsevier Ltd. All rights reserved.

Bayesian Analysis of Linear Inverse Problems with Applications in Economics and Finance

In my PhD thesis I propose a Bayesian nonparametric estimation method for structural econometric models where the functional parameter of interest describes the economic agent's behavior. The structural parameter is characterized as the solution of a functional equation, or by using more technical words, as the solution of an inverse problem that can be either ill-posed or well-posed. From a Bayesian point of view, the parameter of interest is a random function and the solution to the inference problem is the posterior distribution of this parameter. A regular version of the posterior distribution in functional spaces is characterized. However, the infinite dimension of the considered spaces causes a problem of non continuity of the solution and then a problem of inconsistency, from a frequentist point of view, of the posterior distribution (i.e. problem of ill-posedness). The contribution of this essay is to propose new methods to deal with this problem of ill-posedness. The first one consists in adopting a Tikhonov regularization scheme in the construction of the posterior distribution so that I end up with a new object that I call regularized posterior distribution and that I guess it is solution of the inverse problem. The second approach consists in specifying a prior distribution on the parameter of interest of the g-prior type. Then, I detect a class of models for which the prior distribution is able to correct for the ill-posedness also in infinite dimensional problems. I study asymptotic properties of these proposed solutions and I prove that, under some regularity condition satisfied by the true value of the parameter of interest, they are consistent in a "frequentist" sense. Once I have set the general theory, I apply my bayesian nonparametric methodology to different estimation problems. First, I apply this estimator to deconvolution and to hazard rate, density and regression estimation. Then, I consider the estimation of an Instrumental Regression that is useful in micro-econometrics when we have to deal with problems of endogeneity. Finally, I develop an application in finance: I get the bayesian estimator for the equilibrium asset pricing functional by using the Euler equation defined in the Lucas'(1978) tree-type models.

Comparative analysis of midline guidance and axon pathfinding in the chelicerates Achaearanea tepidariorum and Cupiennius salei

Die Neurogenese und axonale Wegfindung sind in den vergangenen Jahrzehnten Thema einer Vielzahl wissenschaftlicher Untersuchungen in den verschiedensten Organismen gewesen. Die zusammengetragenen Daten in Insekten und Crustaceen geben eine gute Übersicht darüber, wie das Nervensystem in Arthropoden aufgebaut wird. Die entwicklungsbiologischen Prozesse, die daran beteiligt sind, sind in den beiden genannten Gruppen sehr gut verstanden. In den Gruppen der Cheliceraten und Myriapoden jedoch wurden ähnliche Analysen bisher kaum durchgeführt. Das Hauptanliegen dieser Arbeit war es daher, Mechanismen in den Spinnen Achaearanea tepidariorum und Cupiennius salei, zwei Vertretern der Cheliceraten, zu untersuchen, die eine Rolle im Leitsystem der ventralen Mittellinie und bei der axonalen Wegfindung spielen. Eine Vorraussetzung hierfür sind Kenntnisse über die Architektur des Zentralnervensystems. In einem ersten Schritt beschrieb ich daher grundlegend die Morphologie des Nervensystems im Verlauf der gesamten Embryoalentwicklung. Ich konnte zeigen, dass in Spinnen ein für Arthropoden typisches Strickleiternervensystem gebildet wird. Dieses wird von segmental angelegten Neuronen geformt, wobei sowohl Gruppen von Zellen als auch einzelne Neurone daran beteiligt sind, die primären axonalen Trakte zu etablieren. Im Besonderen konnte ich eine Zelle identifizieren, die in Position, Projektionsmuster und der Expression des Markergens even-skipped vergleichbar zum PR2 Neuron in Drosophila ist, welches die posteriore Wurzel des Segmentalnervs anlegt.rnrnIn einem zweiten Ansatz untersuchte ich die ventrale Mittellinie in Spinnen im Bezug auf ihre mögliche Funktion in der axonalen Wegfindung. Es konnte gezeigt werden, dass es sich beim Epithel der Mittellinie, das die Lücke zwischen beiden Keimstreifhälften während des gesamten Prozesses der Inversion überspannt, um eine transiente Struktur handelt, die keine neuralen Zellen hervorbringt. Es ist daher vergleichbar mit der so genannten Floor plate in Vertebraten, die ebenfalls nur vorübergehend existiert. Die Untersuchung von single minded (sim) zeigte, dass es, anders als in Drosophila, wo sim ein wichtiges regulatorisches Gen für die korrekte Spezifizierung von Mittellinienzellen ist, nicht in den Zellen der Mittellinie, sondern in diesen benachbarten Zellen, exprimiert wird. Das ist vergleichbar mit Vertebraten. Zusätzlich konnte ich Expression von sim an den Basen der Gliedmassen und im Kopf nachweisen. Wie in Vertebraten könnte sim an der Musterbildung dieser Gewebe beteiligt sein. Dennoch spielt die Mittellinie in Spinnen eine wichtige Rolle als Organisator für auswachsende, kommissurale Axone. Diese Funktion teilt sie mit anderen Invertebraten und Vertebraten.rnrnDie Signaltransduktionskaskade, die an der axonalen Wegfindung an der Mittellinie beteiligt ist, ist in den verschiedensten Organismen hoch konserviert. In der vorliegenden Arbeit konnte ich sowohl in Achaearanea als auch in Cupiennius ein netrin Homolog identifizieren und eine konservierte Funktion des Wegfindungsmoleküls während der Bildung der Kommissuren aufzeigen. RNAi Experimente belegen, dass, wird die Funktion von netrin herunterreguliert, das Strickleiternervensystem nicht korrekt gebildet wird, ins Besondere die kommissuralen Faszikel. Des Weiteren konnte ich eine neue Funktion von netrin, die bisher in anderen Organsimen noch nicht beschrieben wurde, identifizieren. Neben seiner Rolle in der axonalen Wegfindung, scheint netrin auch an der epithelialen Morphogenese im zentralen Nervensystem beteiligt zu sein. In dieser Funktion scheint netrin in Gliazellen, die die epithelialen Vesikel der Invaginationsgruppen umhüllen, wichtig zu sein, um neurale Vorläuferzellen in einem undifferenzierten Zustand zu halten. Der Abbau von netrin Transkript durch RNA Interferenz führt zu einer verfrühten Segregation neuraler Vorläuferzellen aus dem epithelialen Verband der Invaginationsgruppen und zu einer Zunahme an Zellen, die den frühen Differenzierungsmarker islet exprimieren.

A Bayesian changepoint analysis on spatio-temporal point processes

Changepoint analysis is a well established area of statistical research, but in the context of spatio-temporal point processes it is as yet relatively unexplored. Some substantial differences with regard to standard changepoint analysis have to be taken into account: firstly, at every time point the datum is an irregular pattern of points; secondly, in real situations issues of spatial dependence between points and temporal dependence within time segments raise. Our motivating example consists of data concerning the monitoring and recovery of radioactive particles from Sandside beach, North of Scotland; there have been two major changes in the equipment used to detect the particles, representing known potential changepoints in the number of retrieved particles. In addition, offshore particle retrieval campaigns are believed may reduce the particle intensity onshore with an unknown temporal lag; in this latter case, the problem concerns multiple unknown changepoints. We therefore propose a Bayesian approach for detecting multiple changepoints in the intensity function of a spatio-temporal point process, allowing for spatial and temporal dependence within segments. We use Log-Gaussian Cox Processes, a very flexible class of models suitable for environmental applications that can be implemented using integrated nested Laplace approximation (INLA), a computationally efficient alternative to Monte Carlo Markov Chain methods for approximating the posterior distribution of the parameters. Once the posterior curve is obtained, we propose a few methods for detecting significant change points. We present a simulation study, which consists in generating spatio-temporal point pattern series under several scenarios; the performance of the methods is assessed in terms of type I and II errors, detected changepoint locations and accuracy of the segment intensity estimates. We finally apply the above methods to the motivating dataset and find good and sensible results about the presence and quality of changes in the process.

An angiographic analysis of atherosclerosis progression in below-the-knee arteries after femoropopliteal angioplasty in claudicants

Purpose: To report an angiographic investigation of midterm atherosclerotic disease progression in below-the-knee (BTK) arteries of claudicants. Methods: Angiograms were performed in 58 consecutive claudicants (35 men; mean age 68.3±8.7 years) with endovascular treatment of femoropopliteal arteries in 58 limbs after a mean follow-up of 3.6±1.2 years. Angiograms were reviewed in consensus by 2 experienced readers blinded to clinical data. Progression of atherosclerosis in 4 BTK arterial segments (tibioperoneal trunk, anterior and posterior tibial arteries, and peroneal artery) was assessed according to the Bollinger score. The composite per calf Bollinger score represented the average of the 4 BTK arterial segment scores. The association of the Bollinger score with cardiovascular risk factors and gender was scrutinized. Results: A statistically significant increase in atherosclerotic burden was observed for the mean composite per calf Bollinger score (5.7±8.3 increase, 95% CI 3.5 to 7.9, p<0.0001), as well as for each single arterial segment analyzed. In multivariate linear regression analysis, diabetes mellitus was associated with a more pronounced progression of atherosclerotic burden in crural arteries (β: 5.6, p=0.035, 95% CI 0.398 to 10.806). Conclusion: Progression of infrapopliteal atherosclerotic lesions is common in claudicants during midterm follow-up. Presence of diabetes mellitus was confirmed as a major risk factor for more pronounced atherosclerotic BTK disease progression.

Investigating interocclusal perception in tactile teeth sensibility using symmetric and asymmetric analysis

The purpose of this clinical trial was to determine the active tactile sensibility of natural teeth and to obtain a statistical analysis method fitting a psychometric function through the observed data points. On 68 complete dentulous test persons (34 males, 34 females, mean age 45.9 ± 16.1 years), one pair of healthy natural teeth each was tested: n = 24 anterior teeth and n = 44 posterior teeth. The computer-assisted, randomized measurement was done by having the subjects bite on thin copper foils of different thickness (5-200 µm) inserted between the teeth. The threshold of active tactile sensibility was defined by the 50% value of correct answers. Additionally, the gradient of the sensibility curve and the support area (90-10% value) as a description of the shape of the sensibility curve were calculated. For modeling the sensibility curve, symmetric and asymmetric functions were used. The mean sensibility threshold was 14.2 ± 12.1 µm. The older the subject, the higher the tactile threshold (r = 0.42, p = 0.0006). The support area was 41.8 ± 43.3 µm. The higher the 50% threshold, the smaller the gradient of the curve and the larger the support area. The curves showing the active tactile sensibility of natural teeth demonstrate a tendency towards asymmetry, so that the active tactile sensibility of natural teeth can mathematically best be described by using the asymmetric Weibull function.

Core networks for visual-concrete and abstract thought content: a brain electric microstate analysis

Commonality of activation of spontaneously forming and stimulus-induced mental representations is an often made but rarely tested assumption in neuroscience. In a conjunction analysis of two earlier studies, brain electric activity during visual-concrete and abstract thoughts was studied. The conditions were: in study 1, spontaneous stimulus-independent thinking (post-hoc, visual imagery or abstract thought were identified); in study 2, reading of single nouns ranking high or low on a visual imagery scale. In both studies, subjects' tasks were similar: when prompted, they had to recall the last thought (study 1) or the last word (study 2). In both studies, subjects had no instruction to classify or to visually imagine their thoughts, and accordingly were not aware of the studies' aim. Brain electric data were analyzed into functional topographic brain images (using LORETA) of the last microstate before the prompt (study 1) and of the word-type discriminating event-related microstate after word onset (study 2). Conjunction analysis across the two studies yielded commonality of activation of core networks for abstract thought content in left anterior superior regions, and for visual-concrete thought content in right temporal-posterior inferior regions. The results suggest that two different core networks are automatedly activated when abstract or visual-concrete information, respectively, enters working memory, without a subject task or instruction about the two classes of information, and regardless of internal or external origin, and of input modality. These core machineries of working memory thus are invariant to source or modality of input when treating the two types of information.

Evaluative comparison of physician-based vs. patient-based outcomes in posterior lumbar fusion

Posterior lumbar fusion is a frequently performed procedure in spinal surgery. High percentages of good and excellent results are indicated by physicians. On the other hand patient-based outcomes are reported. Little is known about the correlations of these two assessment types. We aimed at their comparison. The analysis included 1013 patients with degenerative spinal disease or spondylolisthesis from an international spine registry, treated with posterior lumbar fusion. All patients were pre/postop assessed by physician-based McNab criteria (‘excellent’, ‘good’, ‘fair’, ‘poor’). Of these patients, 210 (mean age 61 years; 57% females) were in addition assessed by patient-based Oswestry Disability Index (ODI). The remaining 803 patients (mean age 59 years; 56% females) were assessed by patient-based Core Outcome Measure Index (COMI), including Visual Analogue Scale (VAS) for back and leg pain as well as verbal self-rating (‘helped a lot’, ‘helped’, ‘helped only little’, ‘didn’t help’, ‘made things worse’). McNab criteria were compared to the Minimal Clinically Important Difference (MCID) in ODI (12.8), in VAS back (1.2) and leg pain (1.6). We investigated the correlations between McNab criteria and these patient-based outcomes. In the ‘excellent’ group as rated by physicians, the proposed MCID was reached in 83% of patients for ODI, in 69% for VAS back and in 83% for VAS leg pain. All patients said the treatment had ‘helped’ or ‘helped a lot’. In the ‘good’ group 56% (ODI), 66% (back pain) and 86% (leg pain) reached the MCID. 96% of patients perceived the treatment as positive. In the ‘fair’ group 37% (ODI), 55% (back pain) and 63% (leg pain) reached the MCID. 49% had positive treatment considerations. The ‘poor’ group revealed 30% (ODI), 35% (back pain) and 44% (leg pain) of patients with reached MCID. Only 15% rated the treatment as positive. The Spearman correlation coefficients between McNab criteria on the one hand and ODI, back and leg pain as well as patients’ verbal self-rating on the other hand were 0.57, 0.37, 0.36 and 0.46 respectively. The comparison of physician and patient-based outcomes showed the highest correlations between McNab criteria and ODI, somewhat weaker correlations with patients’ self-rating and the weakest correlations with back and leg pain. Based on these findings, physicians’ evaluation of patient outcomes can be considered a valuable part of patient assessment, corresponding very well with patients’ perceptions of success or failure of spinal surgery.

Growth hormone receptor polymorphism and growth hormone therapy response in children: a bayesian meta-analysis

Recombinant human growth hormone (rhGH) therapy is used in the long-term treatment of children with growth disorders, but there is considerable treatment response variability. The exon 3-deleted growth hormone receptor polymorphism (GHR(d3)) may account for some of this variability. The authors performed a systematic review (to April 2011), including investigator-only data, to quantify the effects of the GHR(fl-d3) and GHR(d3-d3) genotypes on rhGH therapy response and used a recently established Bayesian inheritance model-free approach to meta-analyze the data. The primary outcome was the 1-year change-in-height standard-deviation score for the 2 genotypes. Eighteen data sets from 12 studies (1,527 children) were included. After several prior assumptions were tested, the most appropriate inheritance model was codominant (posterior probability = 0.93). Compared with noncarriers, carriers had median differences in 1-year change-in-height standard-deviation score of 0.09 (95% credible interval (CrI): 0.01, 0.17) for GHR(fl-d3) and of 0.14 (95% CrI: 0.02, 0.26) for GHR(d3-d3). However, the between-study standard deviation of 0.18 (95% CrI: 0.10, 0.33) was considerable. The authors tested by meta-regression for potential modifiers and found no substantial influence. They conclude that 1) the GHR(d3) polymorphism inheritance is codominant, contrasting with previous reports; 2) GHR(d3) genotypes account for modest increases in rhGH effects in children; and 3) considerable unexplained variability in responsiveness remains.

EEG microstate analysis in drug-naive patients with panic disorder

Patients with panic disorder (PD) have a bias to respond to normal stimuli in a fearful way. This may be due to the preactivation of fear-associated networks prior to stimulus perception. Based on EEG, we investigated the difference between patients with PD and normal controls in resting state activity using features of transiently stable brain states (microstates). EEGs from 18 drug-naive patients and 18 healthy controls were analyzed. Microstate analysis showed that one class of microstates (with a right-anterior to left-posterior orientation of the mapped field) displayed longer durations and covered more of the total time in the patients than controls. Another microstate class (with a symmetric, anterior-posterior orientation) was observed less frequently in the patients compared to controls. The observation that selected microstate classes differ between patients with PD and controls suggests that specific brain functions are altered already during resting condition. The altered resting state may be the starting point of the observed dysfunctional processing of phobic stimuli.

Investigating human audio-visual object perception with a combination of hypothesis-generating and hypothesis-testing fMRI analysis tools

Primate multisensory object perception involves distributed brain regions. To investigate the network character of these regions of the human brain, we applied data-driven group spatial independent component analysis (ICA) to a functional magnetic resonance imaging (fMRI) data set acquired during a passive audio-visual (AV) experiment with common object stimuli. We labeled three group-level independent component (IC) maps as auditory (A), visual (V), and AV, based on their spatial layouts and activation time courses. The overlap between these IC maps served as definition of a distributed network of multisensory candidate regions including superior temporal, ventral occipito-temporal, posterior parietal and prefrontal regions. During an independent second fMRI experiment, we explicitly tested their involvement in AV integration. Activations in nine out of these twelve regions met the max-criterion (A < AV > V) for multisensory integration. Comparison of this approach with a general linear model-based region-of-interest definition revealed its complementary value for multisensory neuroimaging. In conclusion, we estimated functional networks of uni- and multisensory functional connectivity from one dataset and validated their functional roles in an independent dataset. These findings demonstrate the particular value of ICA for multisensory neuroimaging research and using independent datasets to test hypotheses generated from a data-driven analysis.

Posterior Simulation in the Generalized Linear Model with Semiparmetric Random Effects

Generalized linear mixed models with semiparametric random effects are useful in a wide variety of Bayesian applications. When the random effects arise from a mixture of Dirichlet process (MDP) model, normal base measures and Gibbs sampling procedures based on the Pólya urn scheme are often used to simulate posterior draws. These algorithms are applicable in the conjugate case when (for a normal base measure) the likelihood is normal. In the non-conjugate case, the algorithms proposed by MacEachern and Müller (1998) and Neal (2000) are often applied to generate posterior samples. Some common problems associated with simulation algorithms for non-conjugate MDP models include convergence and mixing difficulties. This paper proposes an algorithm based on the Pólya urn scheme that extends the Gibbs sampling algorithms to non-conjugate models with normal base measures and exponential family likelihoods. The algorithm proceeds by making Laplace approximations to the likelihood function, thereby reducing the procedure to that of conjugate normal MDP models. To ensure the validity of the stationary distribution in the non-conjugate case, the proposals are accepted or rejected by a Metropolis-Hastings step. In the special case where the data are normally distributed, the algorithm is identical to the Gibbs sampler.

Ozone and Mortality: A Meta-Analysis of Time-Series Studies and Comparison to a Multi-City Study (The National Morbidity, Mortality, and Air Pollution Study)

While many time-series studies of ozone and daily mortality identified positive associations,others yielded null or inconclusive results. We performed a meta-analysis of 144 effect estimates from 39 time-series studies, and estimated pooled effects by lags, age groups,cause-specific mortality, and concentration metrics. We compared results to estimates from the National Morbidity, Mortality, and Air Pollution Study (NMMAPS), a time-series study of 95 large U.S. cities from 1987 to 2000. Both meta-analysis and NMMAPS results provided strong evidence of a short-term association between ozone and mortality, with larger effects for cardiovascular and respiratory mortality, the elderly, and current day ozone exposure as compared to other single day lags. In both analyses, results were not sensitive to adjustment for particulate matter and model specifications. In the meta-analysis we found that a 10 ppb increase in daily ozone is associated with a 0.83 (95% confidence interval: 0.53, 1.12%) increase in total mortality, whereas the corresponding NMMAPS estimate is 0.25%(0.12, 0.39%). Meta-analysis results were consistently larger than those from NMMAPS,indicating publication bias. Additional publication bias is evident regarding the choice of lags in time-series studies, and the larger heterogeneity in posterior city-specific estimates in the meta-analysis, as compared with NMAMPS.

Visual and quantitative electroencephalographic analysis of healthy young and adult cats under medetomidine sedation

A study was designed to investigate the effect of medetomidine sedation on quantitative electroencephalography (q-EEG) in healthy young and adult cats to determine objective guidelines for diagnostic EEG recordings and interpretation. Preliminary visual examination of EEG recordings revealed high-voltage low-frequency background activity. Spindles, k-complexes and vertex sharp transients characteristic of sleep or sedation were superimposed on a low background activity. Neither paroxysmal activity nor EEG burst-suppression were observed. The spectral analysis of q-EEG included four parameters, namely, relative power (%), and mean, median and peak frequency (Hz) of all four frequency bands (delta, theta, alpha and beta). The findings showed a prevalence of slow delta and theta rhythms as opposed to fast alpha and beta rhythms in both young (group A) and adult (group B) cats. A posterior gradient was reported for the theta band and an anterior gradient for the alpha and beta bands in both groups, respectively. The relative power value in group B compared to group A was significantly higher for theta, alpha and beta bands, and lower for the delta band. The mean and median frequency values in group B was significantly higher for delta, theta and beta bands and lower for the alpha band. The study has shown that a medetomidine sedation protocol for feline EEG may offer a method for investigating bio-electrical cortical activity. The use of q-EEG analysis showed a decrease in high frequency bands and increased activity of the low frequency band in healthy cats under medetomidine sedation.

Immediate and early non-occlusal loading of Straumann implants with a chemically modified surface (SLActive) in the posterior mandible and maxilla: interim results from a prospective multicenter randomized-controlled study

OBJECTIVE: Immediate and early loading of dental implants can simplify treatment and increase overall patient satisfaction. The purpose of this 3-year prospective randomized-controlled multicenter study was to assess the differences in survival rates and bone level changes between immediately and early-loaded implants with a new chemically modified surface (SLActive). This investigation shows interim results obtained after 5 months. MATERIAL AND METHODS: Patients > or =18 years of age missing at least one tooth in the posterior maxilla or mandible were enrolled in the study. Following implant placement, patients received a temporary restoration either on the day of surgery (immediate loading) or 28-34 days after surgery (early loading); restorations consisted of single crowns or two to four unit fixed dental prostheses. Permanent restorations were placed 20-23 weeks following surgery. The primary efficacy variable was change in bone level (assessed by standardized radiographs) from baseline to 5 months; secondary variables included implant survival and success rates. RESULTS: A total of 266 patients were enrolled (118 males and 148 females), and a total of 383 implants were placed (197 and 186 in the immediate and early loading groups, respectively). Mean patient age was 46.3+/-12.8 years. After 5 months, implant survival rates were 98% in the immediate group and 97% in the early group. Mean bone level change from baseline was 0.81+/-0.89 mm in the immediate group and 0.56+/-0.73 mm in the early group (P<0.05). Statistical analysis revealed a significant center effect (P<0.0001) and a significant treatment x center interaction (P=0.008). CONCLUSIONS: The results suggested that Straumann implants with an SLActive can be used predictably in time-critical (early or immediate) loading treatment protocols when appropriate patient selection criteria are observed. The mean bone level changes observed from baseline to 5 months (0.56 and 0.81 mm) corresponded to physiological observations from other studies, i.e., were not clinically significant. The presence of a significant center effect and treatment x center interaction indicated that the differences in bone level changes between the two groups were center dependent.