Unbelievable O(L1.5)O(L^{1.5}) worst case computational complexity achieved by spdspdsspdspds algorithm for linear programming problem

The Symmetric Primal-Dual Simplex Pivot Decision Strategy (spdspds) is a novel iterative algorithm to solve linear programming problems. Here, a simplex pivoting operation is considered simply as an exchange between a basic (dependent) variable and a non-basic (independent) variable, in the Tucker's Compact Symmetric Tableau (CST) which is a unique symmetric representation common to both the primal as well as the dual of a linear programming problem in its standard canonical form. From this viewpoint, the classical simplex pivoting operation of Dantzig may be considered as a restricted special case. The infeasibility index associated with a simplex tableau is defined as the sum of the number of primal variables and the number of dual variables, which are infeasible. A measure of goodness as a global effectiveness measure of a pivot selection is defined/determined as/by the decrease in the infeasibility index associated with such a pivot selection. At each iteration the selection of the simplex pivot element is governed by the anticipated decrease in the infeasibility index - seeking the best possible decrease in the infeasibility index - from among a wide range of candidate choices with non-zero values - limited only by considerations of potential numerical instability. Significant enhancement in computational efficiency can also be achieved by the utilization of the proposed concept of binding constraints. The algorithm terminates when further reduction in the infeasibility index is not possible; then the tableau is checked for the terminal tableau type to facilitate the problem classification - a termination with an infeasibility index of zero indicates optimum solution. The worst case computational complexity of spdspds is shown to be $O(L^{1.5})$.Comment: 20 pages, 7 figure

Renal Granulomatosis Post Intravesical Bacillus Calmette-Guerin Therapy for Non-Muscle-Invasive Bladder Cancer

Intravesical Bacillus Calmette–Guerin (BCG) immunotherapy is a proven, effective treatment for intermediate- and high-risk non-muscle-invasive bladder cancer. Minor side effects are common and expected but systemic effects can occur in \u3c 5% of treated patients. We present a rare case of a 49-year-old male that presented with fever and chills after 3 weeks of intravesical BCG therapy post transurethral resection of bladder tumor. New renal lesions were present on contrast-enhanced computed tomography scan which was histologically proven to be necrotizing renal granulomatosis

Case 213: Primary Spenic Angiosarcoma

A 75-year-old woman with a medical history of gastroesophageal reflux disease and type II diabetes presented to the hospital with a 3-month history of gradually worsening headaches, vague upper abdominal pain, and lower back pain. The patient denied fevers, night sweats, contact with sick individuals, occupational exposure to infection, bleeding, immunodeficiency, intravenous drug use, alcohol or tobacco abuse, history of malignancy, family history of genetic disorders, and international travel. Physical examination revealed a skin-colored mass protruding from the right side of her forehead, but there were no other notable abnormalities. Her diabetes was managed with diet, and the only prescription medication she was taking was esomeprazole. She was not taking anticoagulants. Initial laboratory work-up revealed anemia and profound thrombocytopenia (hemoglobin level, 9.4 g/dL; platelet count, 16 × 109/L); these were refractory to aggressive treatment, including plasmapheresis, immunosuppression with prednisolone, and numerous transfusions. Contrast material–enhanced magnetic resonance (MR) imaging of the head was performed at admission to further evaluate the patient’s headache and the mass on the patient’s forehead. Ultrasonography (US) of the abdomen was performed to evaluate the cause of abdominal pain. The discovery of liver lesions at US led us to perform contrast-enhanced computed tomography (CT) of the chest, abdomen, and pelvis. Contrast-enhanced MR imaging of the abdomen was performed to narrow the diagnostic considerations for the lesions identified at CT. Bone marrow biopsy revealed no evidence of infectious or neoplastic processes. Endoscopy and colonoscopy were performed; however, they revealed no abnormalities. Further laboratory work-up included extensive testing for parasites, fungi, bacteria, and viruses, including the human immunodeficiency virus (HIV). All of the results were negative. On the 17th day of admission, the patient became acutely unresponsive, her condition deteriorated rapidly, and she died. Unenhanced head CT was performed at the time of the patient’s acute decompensation

Global Properties of fp-Shell Interactions in Many-nucleon Systems

Spectral distribution theory, which can be used to compare microscopic interactions over a broad range of nuclei, is applied in an analysis of two modern effective interactions based on the realistic CD-Bonn potential for $0\hbar\Omega$ no-core shell model calculations in the fp shell, as well as in a comparison of these with the realistic shell-model GXPF1 interaction. In particular, we explore the ability of these interaction to account for the development of isovector pairing correlations and collective rotational motion in the fp shell. Our findings expose the similarities of these two-body interactions, especially as this relates to their pairing and rotational characteristics. Further, the GXPF1 interaction is used to determine the strength parameter of a quadrupole term that can be used to augment an isovector-pairing model interaction with Sp(4) dynamical symmetry, which in turn is shown to yield reasonable agreement with the low-lying energy spectra of $^{58}$Ni and $^{58}$Cu.Comment: 21 pages, 3 figures, accepted in Nuclear Physics

The Role of the Δ(1920)\Delta(1920) Resonance for Kaon Production in Heavy Ion Collisions

The long mean free path of $K^+$ mesons in nuclear matter makes this particle a suitable messenger for the dynamics of nucleus-nucleus reactions at intermediate energies (100 MeV to 3 GeV per nucleon). A prerequisite for this is the knowledge of the elementary production cross sections $\pi N \rightarrow \Sigma K$. Here these cross sections are studied for the first time with the explicite inclusion of the relevant baryon resonances up to 2 GeV as intermediate states. The baryon resonances -- $N(1710)\, I(J^P) = \frac{1}{2} (\frac{1}{2}^+),\, N(1720)\, \frac{1}{2} (\frac{3}{2}^+)$ and $\Delta(1920)\, \frac{3}{2} (\frac{3}{2}^+)\,$ -- are taken into account coherently in the calculations of the $\pi N \rightarrow \Sigma K$ process. (We refer to this model as the `resonance model'.) Also $K^*(892)\frac{1}{2} (1^-)$ vector meson exchange is included. It is shown that the total cross sections for different channels of the $\pi N \rightarrow \Sigma k$ reactions, i.e. $\pi^+ p \rightarrow \Sigma^+ K^+$, $\pi^- p \rightarrow \Sigma^- K^+$, $\pi^+ n \rightarrow \Sigma^0 K^+$ ($\pi^- p \rightarrow \Sigma^- K^+$) and $\pi^0 p \rightarrow \Sigma^0 K^+$ differ not only by absolute values but also by their energy dependence. This shape differences are due to the mixture of the isospin $I = 3/2$ $\Delta(1920)$ with isospin $I = 1/2$ nucleon resonances. However, this $I = 3/2$ resonance does not give a contribution to the $\pi N \rightarrow \Lambda K$ reactions. So the shapes of the total cross sections $\pi N \rightarrow \Lambda K$ for different isospin projections are the same. In spite of this, such cross sections averaged over different isospin projections in the same multipletComment: ( Replaced with corrections of printing errors in the Table. ) 18 pages, Latex file with 6 figures, 2 figures are included in the text. A compressed uuencode file for 4 figures is appended. Also available upon reques