A Bayesian Approach to Manifold Topology Reconstruction

In this paper, we investigate the problem of statistical reconstruction of piecewise linear manifold topology. Given a noisy, probably undersampled point cloud from a one- or two-manifold, the algorithm reconstructs an approximated most likely mesh in a Bayesian sense from which the sample might have been taken. We incorporate statistical priors on the object geometry to improve the reconstruction quality if additional knowledge about the class of original shapes is available. The priors can be formulated analytically or learned from example geometry with known manifold tessellation. The statistical objective function is approximated by a linear programming / integer programming problem, for which a globally optimal solution is found. We apply the algorithm to a set of 2D and 3D reconstruction examples, demon-strating that a statistics-based manifold reconstruction is feasible, and still yields plausible results in situations where sampling conditions are violated

Predicting outcome in acute low back pain using different models of patient profiling

Study Design: Prospective observational study of prognostic indicators, utilising data from a randomised, controlled trial of physiotherapy care of acute low back pain (ALBP) with follow up at 6 weeks, 3 months and 6 months. Objective: To evaluate which patient profile offers the most useful guide to long-term outcome in ALBP. Summary of Background Data: The evidence used to inform prognostic decision-making is derived largely from studies where baseline data is used to predict future status. Clinicians often see patients on multiple occasions so may profile patients in a variety of ways. It is worth considering if better prognostic decisions can be made from alternative profiles. Methods: Clinical, psychological and demographic data were collected from a sample of 54 ALBP patients. Three clinical profiles were developed from information collected at baseline, information collected at 6 weeks, and the change in status between these two time points. A series of regression models were used to determine the independent and relative contributions of these profiles to the prediction of chronic pain and disability. Results: The baseline profile predicted long-term pain only. The 6-week profile predicted both long-term pain and disability. The change profile only predicted long-term disability (p \u3c 0.01). When predicting long-term pain, after the baseline profile had been added to the model, the 6-week profile did not add significantly when forced in at the second step (p \u3e 0.05). A similar result was obtained when the order of entry was reversed. When predicting long-term disability, after the 6-week profile was entered at the first step, the change profile was not significant when forced in at the second step. However, when the change profile was entered at the first step and the 6-week clinical profile was forced in at the second step, a significant contribution of the 6-week profile was found. Conclusions: The profile derived from information collected at 6 weeks provided the best guide to long-term pain and disability. The baseline profile and change in status offered less predictive value

International low back pain guidelines: A comparison of two research based models of care for the management of acute low back pain.

Evidence based guidelines for the management of acute low back pain (ALBP) have been formulated by numerous countries. There are discrepancies between guidelines regarding physiotherapy treatment. The aim of this study was to compare two research based models derived from international LBP guidelines. A single-blind randomised controlled trial was undertaken in a physiotherapy outpatients department. Subjects with ALBP were randomly allocated to an ‘assess/advise/treat’ group (n = 50) or an ‘assess/advise/wait’ group (n = 52). The primary outcome measure was the Roland and Morris Disability Questionnaire (RMDQ). Secondary outcome measures of pain (VAS, usual pain intensity) depressive symptoms (MZSRDS) somatic distress (MSPQ) anxiety (STAIS) quality of life (SF36) and general health (EuroQol) were also obtained. Outcomes were assessed at 6-weeks, 3-months and 6-months. At 6-weeks subjects in the assess/advise/treat group demonstrated less LBP related disability (p = 0.02) and depressive symptoms (p = 0.01), as well as better general health (p = 0.006, p = 0.05), vitality (p \u3c 0.001), social functioning (p = 0.004) and mental health (p = 0.002). At long-term assessment (3 and 6 months) subjects in the assess/advise/treat group were less distressed (p = 0.004), anxious (p = 0.01) and had fewer depressive symptoms (p = 0.001), as well as reporting better general health (p = 0.009, p = 0.05), emotional role (p = 0.03) and mental health (p = 0.04). Active physiotherapy produces better short-term outcomes than advice. Delaying treatment has no long-term consequences on pain or disability, but affects the development of psychosocial features

Evaluation de la capacité de complexation des eaux naturelles de la rivière Saguenay, Canada

La rivière Saguenay est un affluent majeur du fleuve Saint-Laurent, Québec, Canada. La rivière Saguenay draine une région très industrialisée et se divise en deux sections : la section supérieure est peu profonde et constituée d'eau douce, tandis que la section en aval renferme un fjord profond caractérisé par une thermohalocline à environ 25 m. Nous avons caractérisé la capacité de complexation (CC) et la constante de stabilité critique (CSC) de ses eaux douces, dans la section supérieure de la rivière. Cinq différentes stations ont été échantillonnées le même jour; ces échantillons ont été fractionnés en fonction de la masse moléculaire nominale (NMM) des ligands dissous à l'aide de quatre colonnes de chromatographie par perméation de gel (GPC) Séphadex G-10, G-15, G-25 et G-50 utilisées en série. Pour les échantillons globaux, la CC diminue d'amont en aval passant de 0,32 à 0,14 µM. Nous n'avons pu identifier la cause de cette diminution qui pourrait être un simple effet de dilution ou une augmentation d'ions métalliques en solution. Une fois fractionnés, nous trouvons que la CC augmente avec NMM; par contre, la CC normalisée par unité de carbone est plus grande pour les ligands de plus faible NMM. Les CSC obtenues sont toutes similaires, environ 5 x 107 L mol-1, sauf pour les ligands ayant une NMM entre 700 et 1 800 g mol-1 avec une CSC de 27 x 107 L mol-1.The Saguenay River is a major affluent of the St. Lawrence River, Quebec, Canada. The Saguenay River which drains a heavily industrialized region can be subdivided into two sections: the upper section is rather shallow and contains freshwater as the lower one is a deep fjord characterized by a thermohalocline at about 25 m. This work aimed at identifying the possible modifications brought up by anthropogenic sources upon the complexation capacity of the freshwater of this River. Five different stations were sampled for surface water the same day on the upper section of the River. The samples were filtered on 0,4 µm membrane (pre-cleaned with HNO3). A portion was analyzed and other ones were fractionnated as a function of the nominal molecular mass (NMM) of dissolved ligands by using in series four gel permeation chromatographic (GPC) columns filled with Sephadex G-10, G-15, G-25 and G-50 respectively, the elution being dope by purified 18MOhms water. The complexation capacity (CC) and critical stability constant (CSC) of the different fractions have been characterized using a method based on free Cu2+ back-titration by Differential Pulsed Anodic Stripping Voltammetry (DPASV) and a 1:1 complexation scheme. Because copper was giving two unresolved peaks on the tailing of the oxygen peak, all polarograms have been deconvolved by a PASCAL computer program based on a least-sqares nonlinear fit using the Taylor differential correction technique. All results compiled were from the peak centered at - 60 mV against an Ag/AgCl reference. By manipulating the usual equations to determine CC and CSC with the free Cu2+ back-titration, we were able to calculate CC by three different routes and CSC by two different routes ; when enough reliable data were available for each route, all values obtained were concordant. So we observed that, going downstream, the CC decreased from 0,32 to 0,14 µM for whole samples. At this point, we cannot identity the cause of this decrease wether it is due to simple dilution or by addition of new dissolved metallic ions into the stream. Once fractionnated, CC measured was seen increasing with NMM but normalized CC per unit of carbon has been found to be greater for ligands with small NMM (normalized CC decreased with increasing NMM). The CSC obtained were all similar, about 5 x 107 L mol-1, excepted for ligands with NMM between 700 and 1 800 g mol-1, the CSC being 27 x 107 L mol-1 from the inverse linearized method

A Bayesian Approach to Manifold Topology Reconstruction

In this paper, we investigate the problem of statistical reconstruction of piecewise linear manifold topology. Given a noisy, probably undersampled point cloud from a one- or two-manifold, the algorithm reconstructs an approximated most likely mesh in a Bayesian sense from which the sample might have been taken. We incorporate statistical priors on the object geometry to improve the reconstruction quality if additional knowledge about the class of original shapes is available. The priors can be formulated analytically or learned from example geometry with known manifold tessellation. The statistical objective function is approximated by a linear programming / integer programming problem, for which a globally optimal solution is found. We apply the algorithm to a set of 2D and 3D reconstruction examples, demon-strating that a statistics-based manifold reconstruction is feasible, and still yields plausible results in situations where sampling conditions are violated

Spreads in Effective Learning Rates: The Perils of Batch Normalization During Early Training

Excursions in gradient magnitude pose a persistent challenge when training deep networks. In this paper, we study the early training phases of deep normalized ReLU networks, accounting for the induced scale invariance by examining effective learning rates (LRs). Starting with the well-known fact that batch normalization (BN) leads to exponentially exploding gradients at initialization, we develop an ODE-based model to describe early training dynamics. Our model predicts that in the gradient flow, effective LRs will eventually equalize, aligning with empirical findings on warm-up training. Using large LRs is analogous to applying an explicit solver to a stiff non-linear ODE, causing overshooting and vanishing gradients in lower layers after the first step. Achieving overall balance demands careful tuning of LRs, depth, and (optionally) momentum. Our model predicts the formation of spreads in effective LRs, consistent with empirical measurements. Moreover, we observe that large spreads in effective LRs result in training issues concerning accuracy, indicating the importance of controlling these dynamics. To further support a causal relationship, we implement a simple scheduling scheme prescribing uniform effective LRs across layers and confirm accuracy benefits

Symmetry Detection in Large Scale City Scans

In this report we present a novel method for detecting partial symmetries in very large point clouds of 3D city scans. Unlike previous work, which was limited to data sets of a few hundred megabytes maximum, our method scales to very large scenes. We map the detection problem to a nearestneighbor search in a low-dimensional feature space, followed by a cascade of tests for geometric clustering of potential matches. Our algorithm robustly handles noisy real-world scanner data, obtaining a recognition performance comparable to state-of-the-art methods. In practice, it scales linearly with the scene size and achieves a high absolute throughput, processing half a terabyte of raw scanner data over night on a dual socket commodity PC

The translation, validity and reliability of the German version of the Fremantle Back Awareness Questionnaire

Background: The Fremantle Back Awareness Questionnaire (FreBAQ) claims to assess disrupted self-perception of the back. The aim of this study was to develop a German version of the Fre-BAQ (FreBAQ-G) and assess its test-retest reliability, its known-groups validity and its convergent validity with another purported measure of back perception. Methods: The FreBaQ-G was translated following international guidelines for the transcultural adaptation of questionnaires. Thirty-five patients with non-specific CLBP and 48 healthy participants were recruited. Assessor one administered the FreBAQ-G to each patient with CLBP on two separate days to quantify intra-observer reliability. Assessor two administered the FreBaQ-G to each patient on day 1. The scores were compared to those obtained by assessor one on day 1 to assess inter-observer reliability. Known-groups validity was quantified by comparing the FreBAQ-G score between patients and healthy controls. To assess convergent validity, patient\u27s FreBAQ-G scores were correlated to their two-point discrimination (TPD) scores. Results: Intra- and Inter-observer reliability were both moderate with ICC3.1 = 0.88 (95%CI: 0.77 to 0.94) and 0.89 (95%CI: 0.79 to 0.94), respectively. Intra- and inter-observer limits of agreement (LoA) were 6.2 (95%CI: 5.0±8.1) and 6.0 (4.8±7.8), respectively. The adjusted mean difference between patients and controls was 5.4 (95%CI: 3.0 to 7.8, p\u3c0.01). Patient\u27s FreBAQ-G scores were not associated with TPD thresholds (Pearson\u27s r = -0.05, p = 0.79). Conclusions: The FreBAQ-G demonstrated a degree of reliability and known-groups validity. Interpretation of patient level data should be performed with caution because the LoA were substantial. It did not demonstrate convergent validity against TPD. Floor effects of some items of the FreBAQ-G may have influenced the validity and reliability results. The clinimetric properties of the FreBAQ-G require further investigation as a simple measure of disrupted self-perception of the back before firm recommendations on its use can be made

Sequential Data-Adaptive Bandwidth Selection by Cross-Validation for Nonparametric Prediction

We consider the problem of bandwidth selection by cross-validation from a sequential point of view in a nonparametric regression model. Having in mind that in applications one often aims at estimation, prediction and change detection simultaneously, we investigate that approach for sequential kernel smoothers in order to base these tasks on a single statistic. We provide uniform weak laws of large numbers and weak consistency results for the cross-validated bandwidth. Extensions to weakly dependent error terms are discussed as well. The errors may be {\alpha}-mixing or L2-near epoch dependent, which guarantees that the uniform convergence of the cross validation sum and the consistency of the cross-validated bandwidth hold true for a large class of time series. The method is illustrated by analyzing photovoltaic data.Comment: 26 page