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COMPUTATIONAL PITFALLS OF HIGH-ORDER METHODS FOR NONLINEAR EQUATIONS
Sen, Syamal K.,Agarwal, Ravi P.,Khattri, Sanjay K. The Korean Society for Computational and Applied M 2012 Journal of applied mathematics & informatics Vol.30 No.3
Several methods with order higher than that of Newton methods which are of order 2 have been reported in literature for solving nonlinear equations. The focus of most of these methods was to economize on/minimize the number of function evaluations per iterations. We have demonstrated here that there are several computational pit-falls, such as the violation of fixed-point theorem, that one could encounter while using these methods. Further it was also shown that the overall computational complexity could be more in these high-order methods than that in the second-order Newton method.
Rani, Mukta,Nischal, Anuradha,Sahoo, Ganesh Chandra,Khattri, Sanjay Asian Pacific Journal of Cancer Prevention 2013 Asian Pacific journal of cancer prevention Vol.14 No.12
The G-protein coupled receptor 87 (GPR87) is a recently discovered orphan GPCR which means that the search of their endogenous ligands has been a novel challenge. GPR87 has been shown to be overexpressed in squamous cell carcinomas (SCCs) or adenocarcinomas in lungs and bladder. The 3D structure of GPR87 was here modeled using two templates (2VT4 and 2ZIY) by a threading method. Functional assignment of GPR87 by SVM revealed that along with transporter activity, various novel functions were predicted. The 3D structure was further validated by comparison with structural features of the templates through Verify-3D, ProSA and ERRAT for determining correct stereochemical parameters. The resulting model was evaluated by Ramachandran plot and good 3D structure compatibility was evidenced by DOPE score. Molecular dynamics simulation and solvation of protein were studied through explicit spherical boundaries with a harmonic restraint membrane water system. A DRY-motif (Asp-Arg-Tyr sequence) was found at the end of transmembrane helix3, where GPCR binds and thus activation of signals is transduced. In a search for better inhibitors of GPR87, in silico modification of some substrate ligands was carried out to form polar interactions with Arg115 and Lys296. Thus, this study provides early insights into the structure of a major drug target for SCCs.
Dwivedi, Shailendra,Singh, Sarvesh,Goel, Apul,Khattri, Sanjay,Mandhani, Anil,Sharma, Praveen,Misra, Sanjeev,Pant, Kamlesh Kumar Asian Pacific Journal of Cancer Prevention 2015 Asian Pacific journal of cancer prevention Vol.16 No.8
Background: It has been hypothesized that IL-18 (pro-) and IL-10 (anti-) inflammatory genetic variants at -607 C/A-137G/C and -819C/T,-592C/A, respectively, may generate susceptibility and severity risk with various modes of tobacco exposure in prostate carcinoma (PCa) patients. IL-18 is a pro-inflammatory cytokine expressed on various cells including prostate gland elements, and is a key mediator of immune responses with anti-cancerous properties. IL-10 is an anti-inflammatory cytokine that is associated with tumour malignancy which causes immune escape. Materials and Methods: The present study was conducted with 540 subjects, comprising 269 prostate carcinoma patients and 271 controls. Genotyping was performed by PCR-RFLP and confirmed by real time PCR probe-based methods. Results: The findings indicated that the mutant heterozygous and homozygous genotype CC and GC+CC showed significant negative associations (p=0.01, OR=0.21; 95% CI: 0.08-0.51 and p=0.011, OR=0.43; 95% CI: 0.22-0.81, respectively) thus, less chance to be diagnosed as cancer against GG genotype of tobacco smoking patients. In addition, a heterozygous GC genotype at the same locus of IL-18 pro-inflammatory cytokine may aggravate the severity (OR=2.82; 95%CI 1.09-7.29 :p=001) so that patients are more likely to be diagnosed in advanced stage than with the GG wild homozygous genotype. Our results also illustrated that anti-inflammatory cytokine (IL-10) genetic variants, although showing no significant association with susceptibility to cancer of the prostate, may gave profound effects on severity of the disease, as -819 TC (OR=4.60; 95%CI 1.35-15.73), and -592 AC (OR=5.04; 95%CI 1.08-25.43) of IL-10 in tobacco chewers and combined users (both chewers and smokers) respectively, are associated with diagnosis in more advanced stage than with other variants. Conclusions: We conclude that promoter genetic variants of IL-18 and IL-10 with various modes of tobacco exposure may affect not only susceptibility risk but also severity in prostate cancer.
On the convergence of Broyden's method in Hilbert spaces
Argyros, I.K.,Cho, Y.J.,Khattri, S.K. Elsevier [etc.] 2014 Applied Mathematics and Computation Vol.242 No.-
In this paper, we present a new semilocal convergence analysis for an inverse free Broyden's method in a Hilbert space setting. In the analysis, we apply our new idea of recurrent functions concepts of divided differences of order one and Lipschitz/center-Lipschitz conditions on the operator involved. Our analysis extends the applicability of Broyden's method in cases not covered before. Finally, we give an example to illustrate the main result in this paper.
COMPUTATIONAL PITFALLS OF HIGH-ORDER METHODS FOR NONLINEAR EQUATIONS
Syamal K. Sen,Ravi P. Agarwal,Sanjay K. Khattri 한국전산응용수학회 2012 Journal of applied mathematics & informatics Vol.30 No.3
Several methods with order higher than that of Newton methods which are of order 2 have been reported in literature for solving nonlinear equations. The focus of most of these methods was to economize on/minimize the number of function evaluations per iterations. We have demonstrated here that there are several computational pit-falls, such as the violation of fixed-point theorem, that one could encounter while using these methods. Further it was also shown that the overall computational complexity could be more in these high-order methods than that in the second-order Newton method.
Santhosh Kumar Devadas,Minal Khairnar,Sumathi S Hiregoudar,Shashank Ojha,Sachin Punatar,Alok gupta,Anant Gokarn,Pallavi Bhole,Sadhana Kannan,Navin Khattry 대한혈액학회 2017 Blood Research Vol.52 No.4
Background: Stem cell units (SCUs) that are cryopreserved prior to both autologous and allogeneic hematopoietic stem cell transplants (for donor lymphocyte infusion) remain unused or partially used several times, and become an increased burden to blood banks/SCU repositories. Because of the scarcity of data regarding the duration for which the storage is useful, there is no general consensus regarding disposal of SCUs. Methods: We conducted a retrospective audit of SCU utilization in 435 patients who planned to undergo either autologous stem cell transplantation (auto-SCT) (N=239) or allogeneic stem cell transplantation (allo-SCT) (N=196) at a tertiary cancer care center between November 2007 to January 2015. Results: Our cohort consisted of 1,728 SCUs stored for conducting auto-SCT and 729 SCUs stored for conducting donor lymphocyte infusions (DLIs) after allo-SCT. Stem cells were not in-fused in 12.5% of patients who had planned to undergo auto-SCT, and 80% of patients who underwent allo-SCT never received DLI. Forty-one percent of SCUs intended for use in auto-SCT remained unutilized, with a second auto-SCT being performed only in 4 patients. Ninety-four percent of SCUs intended for carrying out DLIs remained unused, with only minimal usage observed one year after undergoing allo-SCT. Conclusion: The duration of storage of unused SCUs needs to be debated upon, so that a consensus can be reached regarding the ethical disposal of SCU.
Santhosh Kumar Devadas,Minal Khairnar,Sumathi S Hiregoudar,Shashank Ojha,Sachin Punatar,Alok gupta,Anant Gokarn,Pallavi Bhole,Sadhana Kannan,Navin Khattry 대한혈액학회 2017 Blood Research Vol.51 No.4
Background: Stem cell units (SCUs) that are cryopreserved prior to both autologous and allogeneic hematopoietic stem cell transplants (for donor lymphocyte infusion) remain unused or partially used several times, and become an increased burden to blood banks/SCU repositories. Because of the scarcity of data regarding the duration for which the storage is useful, there is no general consensus regarding disposal of SCUs. Methods: We conducted a retrospective audit of SCU utilization in 435 patients who planned to undergo either autologous stem cell transplantation (auto-SCT) (N=239) or allogeneic stem cell transplantation (allo-SCT) (N=196) at a tertiary cancer care center between November 2007 to January 2015. Results: Our cohort consisted of 1,728 SCUs stored for conducting auto-SCT and 729 SCUs stored for conducting donor lymphocyte infusions (DLIs) after allo-SCT. Stem cells were not in-fused in 12.5% of patients who had planned to undergo auto-SCT, and 80% of patients who underwent allo-SCT never received DLI. Forty-one percent of SCUs intended for use in auto-SCT remained unutilized, with a second auto-SCT being performed only in 4 patients. Ninety-four percent of SCUs intended for carrying out DLIs remained unused, with only minimal usage observed one year after undergoing allo-SCT. Conclusion: The duration of storage of unused SCUs needs to be debated upon, so that a consensus can be reached regarding the ethical disposal of SCU.