Geometry of discrete and continuous bounded surfaces

We work on reconstructing discrete and continuous surfaces with boundaries using length constraints. First, for a bounded discrete surface, we discuss the rigidity and number of embeddings in three-dimensional space, modulo rigid transformations, for given real edge lengths. Our work mainly considers the maximal number of embeddings of rigid graphs in three-dimensional space for specific geometries (annulus, strip). We modify a commonly used semi-algebraic, geometrical formulation using Bézout\u27s theorem, from Euclidean distances corresponding to edge lengths. We suggest a simple way to construct a rigid graph having a finite upper bound. We also implement a generalization of counting embeddings for graphs by segmenting multiple rigid graphs in d-dimensional space. Our computational methodology uses vector and matrix operations and can work best with a relatively small number of points

Independent domination versus packing in subcubic graphs

In 2011, Henning, L\"{o}wenstein, and Rautenbach observed that the domination number of a graph is bounded from above by the product of the packing number and the maximum degree of the graph. We prove a stronger statement in subcubic graphs: the independent domination number is bounded from above by three times the packing number.Comment: 9 pages, 3 figure

Peculiar Mammographic and Ultrasonographic Findings of a Retained Silastic Drain in the Breast

Foreign bodies, such as surgical sponges or drains, are sometimes retained after surgical procedures.1 Retention of a drain in the breast tissue postoperatively is an unusual complication. This report describes two cases of characteristic sonographic findings related to retained silastic drains following breast surgery

Restructuring of the chaebols and financial sector in Korea

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Direct and Indirect Detection of Neutralino Dark Matter and Collider Signatures in an SO(10)SO(10) Model with Two Intermediate Scales

We investigate the detectability of neutralino Dark Matter via direct and indirect searches as well as collider signatures of an $SO(10)$ model with two intermediate scales. We compare the direct Dark Matter detection cross section and the muon flux due to neutralino annihilation in the Sun that we obtain in this model with mSUGRA predictions and with the sensitivity of current and future experiments. In both cases, we find that the detectability improves as the model deviates more from mSUGRA. In order to study collider signatures, we choose two benchmark points that represent the main phenomenological features of the model: a lower value of $|\mu|$ and reduced third generation sfermion masses due to extra Yukawa coupling contributions in the Renormalization Group Equations, and increased first and second generation slepton masses due to new gaugino loop contributions. We show that measurements at the LHC can distinguish this model from mSUGRA in both cases, by counting events containing leptonically decaying $Z^0$ bosons, heavy neutral Higgs bosons, or like--sign lepton pairs.Comment: 21 pages, 16 figure

Paratracheal Air Cysts: Sonographic Findings in Two Cases

We report two cases of paratracheal air cyst discovered incidentally at neck ultrasonography and confirmed at CT. The cysts were located at the inferoposterior aspect of the right lobe of the thyroid. Ultrasonography revealed an ill-defined hypoechoic mass containing hyperechoic foci which mimicked calcifications. Neck CT confirmed the presence of an ill-defined air pocket which communicated with the trachea through a slit

Sonographic Detection of Intrathyroidal Branchial Cleft Cyst: A Case Report

We report here on an extremely rare case of an intrathyroidal branchial cleft cyst. Intrathyroidal branchial cleft cyst is rare disease entity and it has nonspecific findings on sonography, so the diagnosis of the lesion is very difficult. However, during aspiration, if pus-like materials are aspirated from a thyroid cyst, we should consider the possibility of intrathyroidal branchial cleft cyst in the differential diagnosis