Deformations of surfaces associated with integrable Gauss–Mainardi–Codazzi equations

Cataloged from PDF version of article.Using the formulation of the immersion of a two-dimensional surface into the three-dimensional Euclidean space proposed recently, a mapping from each symmetry of integrable equations to surfaces in ℝ3 can be established. We show that among these surfaces the sphere plays a unique role. Indeed, under the rigid SU(2) rotations all integrable equations are mapped to a sphere. Furthermore we prove that all compact surfaces generated by the infinitely many generalized symmetries of the sine-Gordon equation are homeomorphic to a sphere. We also find some new Weingarten surfaces arising from the deformations of the modified Kurteweg-de Vries and of the nonlinear Schrödinger equations. Surfaces can also be associated with the motion of curves. We study curve motions on a sphere and we identify a new integrable equation characterizing such a motion for a particular choice of the curve velocity. © 2000 American Institute of Physics

Censoring Distances Based on Labeled Cortical Distance Maps in Cortical Morphometry

Shape differences are manifested in cortical structures due to neuropsychiatric disorders. Such differences can be measured by labeled cortical distance mapping (LCDM) which characterizes the morphometry of the laminar cortical mantle of cortical structures. LCDM data consist of signed distances of gray matter (GM) voxels with respect to GM/white matter (WM) surface. Volumes and descriptive measures (such as means and variances) for each subject and the pooled distances provide the morphometric differences between diagnostic groups, but they do not reveal all the morphometric information contained in LCDM distances. To extract more information from LCDM data, censoring of the distances is introduced. For censoring of LCDM distances, the range of LCDM distances is partitioned at a fixed increment size; and at each censoring step, and distances not exceeding the censoring distance are kept. Censored LCDM distances inherit the advantages of the pooled distances. Furthermore, the analysis of censored distances provides information about the location of morphometric differences which cannot be obtained from the pooled distances. However, at each step, the censored distances aggregate, which might confound the results. The influence of data aggregation is investigated with an extensive Monte Carlo simulation analysis and it is demonstrated that this influence is negligible. As an illustrative example, GM of ventral medial prefrontal cortices (VMPFCs) of subjects with major depressive disorder (MDD), subjects at high risk (HR) of MDD, and healthy control (Ctrl) subjects are used. A significant reduction in laminar thickness of the VMPFC and perhaps shrinkage in MDD and HR subjects is observed when compared to Ctrl subjects. The methodology is also applicable to LCDM-based morphometric measures of other cortical structures affected by disease.Comment: 25 pages, 10 figure

Combined surgical treatment for missed rupture of triceps tendon associated with avulsion of the ulnar collateral ligament and flexor-pronator muscle mass

Triceps tendon ruptures are rare injuries. Coexistence of ipsilateral ulnar collateral ligament injury is even rarer. Here, we describe an unusual combination injury to elbow of a 39-year-old male construction worker consisting of triceps tendon rupture, avulsion of elbow ulnar collateral ligament and flexor pronator muscle origin ipsilaterally. A simultaneous repair and reconstruction of all damaged structures was proposed with individualized postoperative rehabilitation. Return to pre-injury level of activities obtained with this treatment protocol. High degree of suspicion and careful examination were needed to prevent missed diagnosis and prolonged instability which may be inevitable after inappropriate treatment of such injury

Open string theory and planar algebras

In this note we show that abstract planar algebras are algebras over the topological operad of moduli spaces of stable maps with Lagrangian boundary conditions, which in the case of the projective line are described in terms of real rational functions. These moduli spaces appear naturally in the formulation of open string theory on the projective line. We also show two geometric ways to obtain planar algebras from real algebraic geometry, one based on string topology and one on Gromov-Witten theory. In particular, through the well known relation between planar algebras and subfactors, these results establish a connection between open string theory, real algebraic geometry, and subfactors of von Neumann algebras.Comment: 13 pages, LaTeX, 7 eps figure

Relationship between Neural Alteration and Perineural Invasion in Pancreatic Cancer Patients with Hyperglycemia

Background: Patients with higher levels of fasting serum glucose have higher death rates from pancreatic cancer compared to patients with lower levels of fasting serum glucose. However, the reasons have not been studied. The goal of the current study was to examine the neural alterations in pancreatic cancer patients with hyperglycemia and to identify the relationship between the neural alterations and perineural invasion. Methodology/Principal Findings: The clinical and pathological features of 61 formalin-fixed pancreatic cancer specimens and 10 normal pancreases as controls were analyzed. Furthermore, the expression of Protein Gene Product 9.5 (PGP9.5), Myelin P0 protein (MPP), NGF, TrkA, and p75 were examined by immunohistochemistry. The median number of nerves, the median area of neural tissue, and the median nerve diameter per 10 mm 2 were larger in the hyperglycemia group than those in the euglycemia group (p = 0.007, p = 0.009, and p = 0.004, respectively). The integrated optical density (IOD) of MPP staining was lower in the hyperglycemia group than those in the euglycemia group (p = 0.019), while the expression levels of NGF and p75 were higher in the hyperglycemia group than those in the euglycemia group (p = 0.002, and p = 0.026, respectively). The nerve bundle invasion of pancreatic cancer was more frequent in the hyperglycemia group than in the euglycemia group (p = 0.000). Conclusions/Significance: Nerve damage and regeneration occur simultaneously in the tumor microenvironment o