Discrete facility location with nonlinear diseconomies in fixed costs

A discrete facility location problem is formulated where the total fixed cost for establishing the facilities includes a component that is a nonlinear function of the number of facilities being established. Some theoretical properties of the solution are derived when this fixed cost is a convex nondecreasing function of the number of facilities. Based on these properties an efficient bisection heuristic is developed where at each iteration, the classical uncapacitated facility location and/or m-median subproblems are solved using available efficient heuristics.     

On a nonstandard two-parametric quantum algebra and its connections withU p,q (gl(2)) andU p,q(gl(1/1))

A quantum algebraU _{p, q} (,H,X _±) associated with a nonstandardR-matrix with two deformation parameters (p, q) is studied and, in particular, its universal -matrix is derived using Reshetikhin's method. Explicit construction of the (p, q)-dependent nonstandardR-matrix is obtained through a coloured generalized boson realization of the universal -matrix of the standardU _{p, q}(gl(2)) corresponding to a nongeneric case. General finite dimensional coloured representation of the universal -matrix ofU _{p, q}(gl(2)) is also derived. This representation, in nongeneric cases, becomes a source for various (p, q)-dependent nonstandardR-matrices. Superization ofU _{p, q}(,H,X _±) leads to the super-Hopf algebraU _{p, q}(gl(1/1)). A contraction procedure then yields a (p, q)-deformed super-Heisenberg algebraU _{p, q}(sh(1)) and its universal -matrix.     

In vivo (31)P MRS study of skeletal muscle metabolism in patients with postpolio residual paralysis

The muscle metabolism of at-rest patients with varying degrees of postpolio residual paralysis (PPRP) was studied and compared with that of controls using in vivo phosphorus magnetic resonance spectroscopy. The phosphocreatine (PCr)/inorganic phosphate (Pi) and PCr/adenosine triphosphate ratios were lower in patients than in controls. Reduction in PCr/Pi suggests abnormalities in oxidative phosphorylation. A significant increase was observed in the phosphomonoester/PCr ratio in patients, indicating the accumulation of intermediary compounds of the glycolytic pathway. Furthermore, the phosphodiester/PCr ratio was also significantly increased in patients. In general, the observed changes in metabolite ratios were found to be related to the degree of residual paralysis, suggesting that metabolic changes are secondary to chronic neurogenic processes. These metabolic alterations appear to be the possible cause of energy deficit and underlying muscle fatigue in PPRP patients. The present results provide an insight into the metabolic impairment and degree of muscle damage in patients with PPRP.     

Mössbauer study of a ferromagnetic metallic glass: Fe74Co10B16

Amorphous Fe₇₄Co₁₀B₁₆ (METGLAS 2605CO) has been studied in the temperature range of 77 K – 700 K by Mössbauer spectroscopy. Its crystallization temperature is found to be 665 ± 5 K and Curie temperature is estimated to be 760±10 K. The observed rapid decrease in reduced hyperfine fields can be explained well by Handrich's model for amorphous ferromagnets if one assumes a temperature dependent δ, a measure of fluctuations in the exchange interactions in such solids.     

On the estimation of second moment for organic compounds in wide-line pmr: analysis of group geometry

Neutron diffraction data available in the literature have been analyzed statistically to arrive at the ideal geometry for the commonly occurring groups, NH ₄ ⁺ , NH ₃ ⁺ , CH₃, CH₂, and CH; this has yielded optimum experimental values for the bond length and bond angle parameters. They are: N-H distance of 1.030 Å in both NH ₄ ⁺ and NH ₃ ⁺ groups, H-N-H angle of 109.47° and 108.1° respectively in NH ₄ ⁺ and NH ₃ ⁺ and 110.8° for the corresponding X-N-H angle in –NH ₃ ⁺ . For CH₃, CH₂, and CH groups the bond length C-H is 1.090 Å, while the H-C-H and X-C-H angles are respectively 108.2° and 110.5° in CH₃ and 107.2° and 109.3° in CH₂. The importance of using precise values of both bond lengths and bond angles for the ideal geometry when estimating theoretical second moments is emphasized.Contribution No. 564 from the Department of Crystallography and Biophysics, University of Madras, Guindy Campus, Madras-600025, India.     

Potential of magnetic resonance spectroscopy to detect metastasis in axillary lymph nodes in breast cancer

Focused pathological evaluation of axillary lymph nodes in breast cancer is gaining importance. Nuclear magnetic resonance (NMR) spectroscopy that assesses the whole of the specimen has the potential in evaluating micrometastases. The biochemical changes associated with breast cancer metastases in axillary nodes by in vitro NMR and its use in the detection of axillary metastases in a clinical setting in comparison with conventional histopathology is presented in this study. Eighty-eight lymph nodes obtained from 30 patients with breast cancer were investigated. Histopathology revealed metastases in 20 nodes from 11 patients, while in vitro NMR spectroscopy revealed metastases in 22 nodes. Out of these 22 nodes, 16 were the same, which showed metastases on histopathology, while 6 nodes have shown metastases only on in vitro magnetic resonance spectroscopy (MRS). These 6 nodes with suspicion of metastases on MRS were subjected to reevaluation with serial sectioning and immunohistochemistry, but no additional metastases were revealed. Forty metabolites could be identified from the MR spectrum of lymph nodes. The levels of the glycerophosphocholine-phosphocholine (GPC-PC), choline, lactate, alanine and uridine diphosphoglucose were elevated significantly in nodes with metastases. In addition, the intensity ratio of GPC-PC/threonine (Thr) was higher in nodes with metastases, and using this as marker, MRS detected the axillary metastases with a sensitivity, specificity and accuracy of 80%, 91% and 88%, respectively. Neoadjuvant chemotherapy (NACT) lowered the concentrations of GPC-PC and GPC-PC/Thr ratio. The accuracy of MRS in detecting metastases was 75% in patients who received NACT (n=9) as compared to 96% in those who did not (n=21). Our results demonstrate the potential of in vitro MRS in characterizing the metabolite profile of the axillary nodes with breast cancer metastases. It detected axillary metastases with reasonable accuracy and can be complementary to histopathological evaluation and immunohistochemistry.     

Biochemical characterization of metastatic lymph nodes of breast cancer patients by in vitro 1H magnetic resonance spectroscopy: a pilot study

Using one-dimensional (1D) and two-dimensional (2D) proton nuclear magnetic resonance (NMR) methods, the perchloric acid extract of involved (n = 11) and noninvolved (n = 12) axillary lymph nodes (ALN) of breast cancer patients was investigated. Resonances from 40 metabolites such as lactate (Lac), glucose, several amino acids (alanine, lysine, glutamic acid, glutamine, etc.), nucleotides (adenosine triphosphate, guanosine triphosphate, uridine triphosphate, uridine monophosphate, etc.), membrane metabolites [glycerophosphocholine (GPC), phosphocoline (PC), phosphoethanolamine (PE), choline] were unambiguously assigned in both the involved and noninvolved ALN. The concentration of PC/GPC (p = 0.002) was significantly higher in the involved compared to noninvolved nodes. In addition, the concentration of glycolytic product Lac (p = 0.0001) was also found to be significantly higher in involved nodes. Increased concentration of membrane metabolites PC/GPC may be attributed to increased membrane synthesis in malignant cells and, therefore, suggests the presence of metastatic cells in lymph nodes. The higher concentration of Lac is indicative of the presence of malignant cells that derive energy via anaerobic glycolytic pathway. Present results demonstrate the potentials of in vitro proton NMR in detecting malignant cells in ALN and such studies may have an important bearing in determining the prognosis of breast cancer patients.     

Skeletal muscle metabolism in Duchenne muscular dystrophy (DMD): an in-vitro proton NMR spectroscopy study

The metabolic differences in the skeletal muscle of patients with Duchenne muscular dystrophy (DMD) and normal subjects (controls) were investigated using in-vitro high-resolution proton NMR spectroscopy. In all, 56 metabolites were unambiguously identified in the perchloric acid extract of muscle tissue using one- and two-dimensional NMR. The concentrations of glycolytic substrate glucose (Glc; p < 0.05), gluconeogenic amino acids such as glutamine (Gln; p < 0.05) and alanine (Ala; p < 0.05) and the glycolytic product lactate (Lac; p < 0.05) were statistically significantly lower in DMD patients as compared to controls. A significant reduction in the concentrations of total creatine (TCr; p < 0.05), glycerophosphoryl choline + phosphoryl choline + carnitine (GPC/PC/Car; p < 0.05), choline (Cho; p < 0.05) and acetate (Ace; p < 0.05) was also observed in these patients. Decrease in the level of glucose may be attributed to the reduction in the concentrations of gluconeogenic substrates or membrane abnormalities in degenerated muscle of DMD patients. Lower levels of choline containing compounds indicate membrane abnormalities. Decrease in the concentration of lactate in the muscle of DMD patients may be due to the reduction in anaerobic glycolytic activity or lower substrate concentration. The decrease in the concentration of acetate may reflect reduced transport of fatty acids into mitochondria due to decreased concentration of carnitine in DMD patients. Kreb's cycle intermediate alpha-ketoglutarate was observed only in the diseased muscle, which is suggestive of predominant oxidative metabolism for energy generation.