Self-Organizing Maps and the US Urban Spatial Structure

This article considers urban spatial structure in US cities using a multi- dimensional approach. We select six key variables (commuting costs, den- sity, employment dispersion/concentration, land-use mix, polycentricity and size) from the urban literature and define measures to quantify them. We then apply these measures to 359 metropolitan areas from the 2000 US Census. The adopted methodological strategy combines two novel techniques for the social sciences to explore the existence of relevant pat- terns in such multi-dimensional datasets. Geodesic self-organizing maps (SOM) are used to visualize the whole set of information in a meaningful way, while the recently developed clustering algorithm of the max-p is applied to draw boundaries within the SOM and analyze which cities fall into each of them. JEL C45, R0, R12, R14. Keywords Urban spatial structure, self-organizing maps, US metropolitan areas

On the Cost of Essentially Fair Clusterings

Clustering is a fundamental tool in data mining. It partitions points into groups (clusters) and may be used to make decisions for each point based on its group. However, this process may harm protected (minority) classes if the clustering algorithm does not adequately represent them in desirable clusters -- especially if the data is already biased. At NIPS 2017, Chierichetti et al. proposed a model for fair clustering requiring the representation in each cluster to (approximately) preserve the global fraction of each protected class. Restricting to two protected classes, they developed both a 4-approximation for the fair $k$-center problem and a $O(t)$-approximation for the fair $k$-median problem, where $t$ is a parameter for the fairness model. For multiple protected classes, the best known result is a 14-approximation for fair $k$-center. We extend and improve the known results. Firstly, we give a 5-approximation for the fair $k$-center problem with multiple protected classes. Secondly, we propose a relaxed fairness notion under which we can give bicriteria constant-factor approximations for all of the classical clustering objectives $k$-center, $k$-supplier, $k$-median, $k$-means and facility location. The latter approximations are achieved by a framework that takes an arbitrary existing unfair (integral) solution and a fair (fractional) LP solution and combines them into an essentially fair clustering with a weakly supervised rounding scheme. In this way, a fair clustering can be established belatedly, in a situation where the centers are already fixed

A Combinatorial Solution to Non-Rigid 3D Shape-to-Image Matching

We propose a combinatorial solution for the problem of non-rigidly matching a 3D shape to 3D image data. To this end, we model the shape as a triangular mesh and allow each triangle of this mesh to be rigidly transformed to achieve a suitable matching to the image. By penalising the distance and the relative rotation between neighbouring triangles our matching compromises between image and shape information. In this paper, we resolve two major challenges: Firstly, we address the resulting large and NP-hard combinatorial problem with a suitable graph-theoretic approach. Secondly, we propose an efficient discretisation of the unbounded 6-dimensional Lie group SE(3). To our knowledge this is the first combinatorial formulation for non-rigid 3D shape-to-image matching. In contrast to existing local (gradient descent) optimisation methods, we obtain solutions that do not require a good initialisation and that are within a bound of the optimal solution. We evaluate the proposed method on the two problems of non-rigid 3D shape-to-shape and non-rigid 3D shape-to-image registration and demonstrate that it provides promising results.Comment: 10 pages, 7 figure

Helical modes in carbon nanotubes generated by strong electric fields

Helical modes, conducting opposite spins in opposite directions, are shown to exist in metallic armchair nanotubes in an all-electric setup. This is a consequence of the interplay between spin-orbit interaction and strong electric fields. The helical regime can also be obtained in chiral metallic nanotubes by applying an additional magnetic field. In particular, it is possible to obtain helical modes at one of the two Dirac points only, while the other one remains gapped. Starting from a tight-binding model we derive the effective low-energy Hamiltonian and the resulting spectrum

Frequency Of Development Of Connective Tissue Disease In Statin-Users Versus Nonusers

Statins have pleiotropic properties that may affect the development of connective tissue diseases (CTD). The objective of this study was to compare the risk of CTD diagnoses in statin users and nonusers. This study was a propensity score-matched analysis of adult patients (30 to 85 years old) in the San Antonio military medical community. The study was divided into baseline (October 1, 2003 to September 30, 2005), and follow-up (October 1, 2005 to March 5, 2010) periods. Statin users received a statin prescription during fiscal year 2005. Nonusers did not receive a statin at any time during the study. The outcome measure was the occurrence of 3 diagnosis codes of the International Classification of Diseases, 9th Revision, Clinical Modification consistent with CTD. We described co-morbidities during the baseline period using the Charlson Comorbidity Index. We created a propensity score based on 41 variables. We then matched statin users and nonusers 1:1, using a caliper of 0.001. Of 46,488 patients who met study criteria (13,640 statin users and 32,848 nonusers), we matched 6,956 pairs of statin users and nonusers. Matched groups were similar in terms of patient age, gender, incidence of co-morbidities, total Charlson Comorbidity Index, health care use, and medication use. The odds ratio for CTD was lower in statin users than nonusers (odds ratio: 0.80; 95% confidence interval: 0.64 to 0.99; p = 0.05). Secondary analysis and sensitivity analysis confirmed these results. In conclusion, statin use was associated with a lower risk of CTD. Published by Elsevier Inc.Pharmac

An Exact Algorithm for the Steiner Forest Problem

The Steiner forest problem asks for a minimum weight forest that spans a given number of terminal sets. The problem has famous linear programming based 2-approximations [Agrawal et al., 1995; Goemans and Williamson, 1995; Jain, 2001] whose bottleneck is the fact that the most natural formulation of the problem as an integer linear program (ILP) has an integrality gap of 2. We propose new cut-based ILP formulations for the problem along with exact branch-and-bound based algorithms. While our new formulations cannot improve the integrality gap, we can prove that one of them yields stronger linear programming bounds than the two previous strongest formulations: The directed cut formulation [Balakrishnan et al., 1989; Chopra and Rao, 1994] and the advanced flow-based formulation by Magnanti and Raghavan [Magnanti and Raghavan, 2005]. In an experimental evaluation, we show that the linear programming bounds of the new formulations are indeed strong on practical instances and that our new branch-and-bound algorithms outperform branch-and-bound algorithms based on the previous formulations. Our formulations can be seen as a cut-based analogon to [Magnanti and Raghavan, 2005], whose existence was an open problem

Spinal epidural lipomatosis: a review of its causes and recommendations for treatment

Journal ArticleSpinal epidural lipomatosis is most commonly observed in patients receiving long-term exogenous steroid therapy, but can also be seen in patients with endogenous steroid overproduction, obesity, or idiopathic disease. With this condition, there is hypertrophy of the epidural adipose tissue, causing a narrowing of the spinal canal and compression of neural structures. A majority of patients will present with progressive myelopathy, but radicular symptoms are also common. Conservative treatment-weaning from steroids or weight loss-can reverse the hypertrophy of the adipose tissue and relieve the neural compression. If conservative management fails, surgery with decompressive laminectomy is also very successful at improving the patient's neurological symptoms

Cervical spine deformity associated with resection of spinal cord tumors

Journal ArticlePostoperative sagittal-plane cervical spine deformities are a concern when laminectomy is performed for tumor resection in the spinal cord. These deformities appear to occur more commonly after resection of intramedullary spinal cord lesions, compared with laminectomy for stenosis caused by degenerative spinal conditions. Postlaminectomy deformities are most common in pediatric patients with an immature skeletal system, but are also more common in young adults (, 25 years of age) in comparison with older adults. The extent of laminectomy and facetectomy, number of laminae removed, location of laminectomy, preoperative loss of lordosis, and postoperative radiation therapy in the spine have all been reported to influence the risk of postlaminectomy spinal deformities. When these occur, patients should be monitored closely with serial imaging studies, because a significant percentage will have progressive deformities. These can range from focal kyphosis to more complicated swan-neck deformities. General indications for surgical intervention include progressive deformity, axial pain in the area, and neurological symptoms attributable to the deformity. Surgical options include anterior, posterior, and combined anterior-posterior procedures. The authors have reviewed the literature on postlaminectomy kyphosis as it relates to resection of cervical spinal cord tumors, and they summarize some general factors to consider when treating these patients

An Exact Algorithm for the Steiner Forest Problem

The Steiner forest problem asks for a minimum weight forest that spans a given number of terminal sets. The problem has famous linear programming based 2-approximations [Agrawal et al., 1995; Goemans and Williamson, 1995; Jain, 2001] whose bottleneck is the fact that the most natural formulation of the problem as an integer linear program (ILP) has an integrality gap of 2. We propose new cut-based ILP formulations for the problem along with exact branch-and-bound based algorithms. While our new formulations cannot improve the integrality gap, we can prove that one of them yields stronger linear programming bounds than the two previous strongest formulations: The directed cut formulation [Balakrishnan et al., 1989; Chopra and Rao, 1994] and the advanced flow-based formulation by Magnanti and Raghavan [Magnanti and Raghavan, 2005]. In an experimental evaluation, we show that the linear programming bounds of the new formulations are indeed strong on practical instances and that our new branch-and-bound algorithms outperform branch-and-bound algorithms based on the previous formulations. Our formulations can be seen as a cut-based analogon to [Magnanti and Raghavan, 2005], whose existence was an open problem