Some error estimates for the finite volume element method for a parabolic problem

We study spatially semidiscrete and fully discrete finite volume element methods for the homogeneous heat equation with homogeneous Dirichlet boundary conditions and derive error estimates for smooth and nonsmooth initial data. We show that the results of our earlier work \cite{clt11} for the lumped mass method carry over to the present situation. In particular, in order for error estimates for initial data only in $L_2$ to be of optimal second order for positive time, a special condition is required, which is satisfied for symmetric triangulations. Without any such condition, only first order convergence can be shown, which is illustrated by a counterexample. Improvements hold for triangulations that are almost symmetric and piecewise almost symmetric

The lifecycle of geotagged data

The world is a big place. At any given instant something is happening somewhere, but even when nothing in particular is going on people still find ways to generate data, such as posting on s

Optimal control of number squeezing in trapped Bose-Einstein condensates

We theoretically analyze atom interferometry based on trapped ultracold atoms, and employ optimal control theory in order to optimize number squeezing and condensate trapping. In our simulations, we consider a setup where the confinement potential is transformed from a single to a double well, which allows to split the condensate. To avoid in the ensuing phase-accumulation stage of the interferometer dephasing due to the nonlinear atom-atom interactions, the atom number fluctuations between the two wells should be sufficiently low. We show that low number fluctuations (high number squeezing) can be obtained by optimized splitting protocols. Two types of solutions are found: in the Josephson regime we find an oscillatory tunnel control and a parametric amplification of number squeezing, while in the Fock regime squeezing is obtained solely due to the nonlinear coupling, which is transformed to number squeezing by peaked tunnel pulses. We study splitting and squeezing within the frameworks of a generic two-mode model, which allows us to study the basic physical mechanisms, and the multi-configurational time dependent Hartree for bosons method, which allows for a microscopic modeling of the splitting dynamics in realistic experiments. Both models give similar results, thus highlighting the general nature of these two solution schemes. We finally analyze our results in the context of atom interferometry.Comment: 17 pages, 21 figures, minor correction

The network structure of visited locations according to geotagged social media photos

Businesses, tourism attractions, public transportation hubs and other points of interest are not isolated but part of a collaborative system. Making such collaborative network surface is not always an easy task. The existence of data-rich environments can assist in the reconstruction of collaborative networks. They shed light into how their members operate and reveal a potential for value creation via collaborative approaches. Social media data are an example of a means to accomplish this task. In this paper, we reconstruct a network of tourist locations using fine-grained data from Flickr, an online community for photo sharing. We have used a publicly available set of Flickr data provided by Yahoo! Labs. To analyse the complex structure of tourism systems, we have reconstructed a network of visited locations in Europe, resulting in around 180,000 vertices and over 32 million edges. An analysis of the resulting network properties reveals its complex structure.Comment: 8 pages, 3 figure

Re-ranking Permutation-Based Candidate Sets with the n-Simplex Projection

In the realm of metric search, the permutation-based approaches have shown very good performance in indexing and supporting approximate search on large databases. These methods embed the metric objects into a permutation space where candidate results to a given query can be efficiently identified. Typically, to achieve high effectiveness, the permutation-based result set is refined by directly comparing each candidate object to the query one. Therefore, one drawback of these approaches is that the original dataset needs to be stored and then accessed during the refining step. We propose a refining approach based on a metric embedding, called n-Simplex projection, that can be used on metric spaces meeting the n-point property. The n-Simplex projection provides upper- and lower-bounds of the actual distance, derived using the distances between the data objects and a finite set of pivots. We propose to reuse the distances computed for building the data permutations to derive these bounds and we show how to use them to improve the permutation-based results. Our approach is particularly advantageous for all the cases in which the traditional refining step is too costly, e.g. very large dataset or very expensive metric function

Shonan Rotation Averaging: Global Optimality by Surfing SO(p)nSO(p)^n

Shonan Rotation Averaging is a fast, simple, and elegant rotation averaging algorithm that is guaranteed to recover globally optimal solutions under mild assumptions on the measurement noise. Our method employs semidefinite relaxation in order to recover provably globally optimal solutions of the rotation averaging problem. In contrast to prior work, we show how to solve large-scale instances of these relaxations using manifold minimization on (only slightly) higher-dimensional rotation manifolds, re-using existing high-performance (but local) structure-from-motion pipelines. Our method thus preserves the speed and scalability of current SFM methods, while recovering globally optimal solutions.Comment: 30 pages (paper + supplementary material). To appear at the European Conference on Computer Vision (ECCV) 202

Rethinking summarization and storytelling for modern social multimedia

Traditional summarization initiatives have been focused on specific types of documents such as articles, reviews, videos, image feeds, or tweets, a practice which may result in pigeonholing the summarization task in the context of modern, content-rich multimedia collections. Consequently, much of the research to date has revolved around mostly toy problems in narrow domains and working on single-source media types. We argue that summarization and story generation systems need to re-focus the problem space in order to meet the information needs in the age of user-generated content in different formats and languages. Here we create a framework for flexible multimedia storytelling. Narratives, stories, and summaries carry a set of challenges in big data and dynamic multi-source media that give rise to new research in spatial-temporal representation, viewpoint generation, and explanatio

Feasibility of neuromuscular training in patients with severe hip or knee OA: The individualized goal-based NEMEX-TJR training program

<p>Abstract</p> <p>Background</p> <p>Although improvements are achieved by general exercise, training to improve sensorimotor control may be needed for people with osteoarthritis (OA). The aim was to apply the principles of neuromuscular training, which have been successfully used in younger and middle-aged patients with knee injuries, to older patients with severe hip or knee OA. We hypothesized that the training program was feasible, determined as: 1) at most acceptable self-reported pain following training; 2) decreased or unchanged pain during the training period; 3) few joint specific adverse events related to training, and 4) achieved progression of training level during the training period.</p> <p>Methods</p> <p>Seventy-six patients, between 60 and 77 years, with severe hip (n = 38, 55% women) or knee OA (n = 38, 61% women) underwent an individualized, goal-based neuromuscular training program (NEMEX-TJR) in groups for a median of 11 weeks (quartiles 7 to 15) prior to total joint replacement (TJR). Pain was self-reported immediately after each training session on a 0 to 10 cm, no pain to pain as bad as it could be, scale, where 0-2 indicates safe, > 2 to 5 acceptable and > 5 high risk pain. Joint specific adverse events were: not attending or ceasing training because of increased pain/problems in the index joint related to training, and self-reported pain > 5 after training. The level of difficulty of training was registered.</p> <p>Results</p> <p>Patients with severe OA of the hip or knee reported safe pain (median 2 cm) after training. Self-reported pain was lower at training sessions 10 and 20 (p = 0.04) and unchanged at training sessions 5 and 15 (p = 0.170, p = 0.161) compared with training session 1. There were no joint specific adverse events in terms of not attending or ceasing training. Few patients (n = 17, 22%) reported adverse events in terms of self-reported pain > 5 after one or more training sessions. Progression of training level was achieved over time (p < 0.001).</p> <p>Conclusions</p> <p>The NEMEX-TJR training program is feasible in patients with severe hip or knee OA, in terms of safe self-reported pain following training, decreased or unchanged pain during the training period, few joint specific adverse events, and achieved progression of training level during the training period.</p

Patellofemoral pain syndrome (PFPS): a systematic review of anatomy and potential risk factors

Patellofemoral Pain Syndrome (PFPS), a common cause of anterior knee pain, is successfully treated in over 2/3 of patients through rehabilitation protocols designed to reduce pain and return function to the individual. Applying preventive medicine strategies, the majority of cases of PFPS may be avoided if a pre-diagnosis can be made by clinician or certified athletic trainer testing the current researched potential risk factors during a Preparticipation Screening Evaluation (PPSE). We provide a detailed and comprehensive review of the soft tissue, arterial system, and innervation to the patellofemoral joint in order to supply the clinician with the knowledge required to assess the anatomy and make recommendations to patients identified as potentially at risk. The purpose of this article is to review knee anatomy and the literature regarding potential risk factors associated with patellofemoral pain syndrome and prehabilitation strategies. A comprehensive review of knee anatomy will present the relationships of arterial collateralization, innervations, and soft tissue alignment to the possible multifactoral mechanism involved in PFPS, while attempting to advocate future use of different treatments aimed at non-soft tissue causes of PFPS

The effects of thermal capsulorrhaphy of medial parapatellar capsule on patellar lateral displacement

<p>Abstract</p> <p>Background</p> <p>The effectiveness of thermal shrinkage on the medial parapatellar capsule for treating recurrent patellar dislocation is controversial. One of reasons why it is still controversial is that the effectiveness is still qualitatively measured. The purpose of this study was to quantitatively determine the immediate effectiveness of the medial parapatellar capsule shrinkage as in clinical setting.</p> <p>Methods</p> <p>Nine cadaveric knees were used to collect lateral displacement data before and after medial shrinkage or open surgery. The force and displacement were recorded while a physician pressed the patella from the medial side to mimic the physical exam used in clinic. Ten healthy subjects were used to test the feasibility of the technique on patients and establish normal range of lateral displacement of the patella under a medial force. The force applied, the resulting displacement and the ratio of force over displacement were compared among four data groups (normal knees, cadaveric knees before medial shrinkage, after shrinkage and after open surgery).</p> <p>Results</p> <p>Displacements of the cadaveric knees both before and after thermal modification were similar to normal subjects, and the applied forces were significantly higher. No significant differences were found between before and after thermal modification groups. After open surgery, displacements were reduced significantly while applied forces were significantly higher.</p> <p>Conclusion</p> <p>No immediate difference was found after thermal shrinkage of the medial parapatellar capsule. Open surgery immediately improved of the lateral stiffness of the knee capsule.</p