The role of 'S' level mathematics

The role of 'S' level mathematic

Derivation and analysis of a computationally efficient discrete Backus-Gilbert footprint-matching algorithm

Includes bibliographical references.A computationally efficient discrete Backus-Gilbert (BG) method is derived that is subject to minimization constraints appropriate for footprint-matching applications. The method is flexible, since computational cost can be traded for accuracy. A comparison of the discrete BG method with a non-discrete BG method shows that the new method can be 250% more efficient while maintaining the same accuracy as traditional approaches. In addition, optimization approaches are used to further enhance the computational performance of the discretized BG method. A singular value decomposition approximation is applied that increases the computational efficiencies 43% to 106% while maintaining similar accuracies to the original discretized algorithm. Accuracies of the optimization were found to be scene dependent. In addition, alternative quadrature methods were also tested for several idealized simulated scenes. The results suggest that accuracy improvements could be made using customized quadrature methods that would be employed along known physical data discontinuities (such as along coastlines in microwave imagery data). In addition, regularization behaviors are also discussed; with a particular emphasis on the extension of the method for use with unnormalized gain functions. This work demonstrates that for some gain function configurations local biases can be intrinsic to the system. The flexibility of the discrete BG method allowed for several of the optimizations to be performed in a straightforward manner. Many additional optimizations are likely possible. Due to the lower computational cost of the method, this work is applicable toward applications in which noise may vary dynamically (such as in RFI-contaminated environments). The computational flexibility of the method also makes it well suited to computationally constrained problems such as 4D data assimilation of remote sensing observations.Research supported by the DoD Center for Geosciences/Atmospheric Research at CSU under Cooperative Agreement #DAAL01-98-0078 with the Army Research Laboratory

Multiple gene aberrations and breast cancer: lessons from super-responders.

BackgroundThe presence of multiple molecular aberrations in patients with breast cancer may correlate with worse outcomes.Case presentationsWe performed in-depth molecular analysis of patients with estrogen receptor-positive, HER2-negative, hormone therapy-refractory breast cancer, who achieved partial or complete responses when treated with anastrozole and everolimus. Tumors were analyzed using a targeted next generation sequencing (NGS) assay in a Clinical Laboratory Improvement Amendments laboratory. Genomic libraries were captured for 3,230 exons in 182 cancer-related genes plus 37 introns from 14 genes often rearranged in cancer and sequenced to high coverage. Patients received anastrozole (1 g PO daily) and everolimus (5 or 10 mg PO daily). Thirty-two patients with breast cancer were treated on study and 5 (16 %) achieved a partial or complete response. Primary breast tissue was available for NGS testing in three of the responders (partial response with progression free survival of 11 and 14 months, respectively; complete response with progression free survival of 9+ months). The following molecular aberrations were observed: PTEN loss by immunohistochemistry, CCDN1 and FGFR1 amplifications, and PRKDC re-arrangement (NGS) (patient #1); PIK3CA and PIK3R1 mutations, and CCDN1, FGFR1, MYC amplifications (patient #2); TP53 mutation, CCNE1, IRS2 and MCL1 amplifications (patient #3). Some (but not all) of these aberrations converge on the PI3K/AKT/mTOR pathway, perhaps accounting for response.ConclusionsPatients with estrogen receptor-positive breast cancer can achieve significant responses on a combination of anastrozole and everolimus, even in the presence of multiple molecular aberrations. Further study of next generation sequencing-profiled tumors for convergence and resistance pathways is warranted

The A Priori Prediction of Vibrational Circular Dichroism Spectra: a New Approach to the Study of the Stereochemistry of Chiral Molecules

A theory of Vibrational Circular Dichroism (VCD) has been developed by the author and implemented at the ab initio self- -consistent field (SCF) level of approximation. VCD spectra calculated from this theory for several small chiral organic molecules are in excellent overall agreement with experiment, when basis sets of adequate sophistication are used and when the ab initio SCF force fields are scaled following the procedure of Pulay and coworkers. VCD spectroscopy, together with a pri ori theoretical calculations, now affords a new technique for the study of the stereochemistry of chiral molecules

Processing Satellite Data for Slant Total Electron Content Measurements

A method, system, and apparatus provide the ability to estimate ionospheric observables using space-borne observations. Space-borne global positioning system (GPS) data of ionospheric delay are obtained from a satellite. The space-borne GPS data are combined with ground-based GPS observations. The combination is utilized in a model to estimate a global three-dimensional (3D) electron density field

Next generation sequencing of exceptional responders with BRAF-mutant melanoma: implications for sensitivity and resistance.

BackgroundPatients with BRAF mutation-positive advanced melanoma respond well to matched therapy with BRAF or MEK inhibitors, but often quickly develop resistance.MethodsTumor tissue from ten patients with advanced BRAF mutation-positive melanoma who achieved partial response (PR) or complete response (CR) on BRAF and/or MEK inhibitors was analyzed using next generation sequencing (NGS) assay. Genomic libraries were captured for 3230 exons in 182 cancer-related genes plus 37 introns from 14 genes often rearranged in cancer and sequenced to average median depth of 734X with 99% of bases covered >100X.ResultsThree of the ten patients (median number of prior therapies = 2) attained prolonged CR (duration = 23.6+ to 28.7+ months); seven patients achieved either a PR or a short-lived CR. One patient who achieved CR ongoing at 28.7+ months and had tissue available close to the time of initiating BRAF inhibitor therapy had only a BRAF mutation. Abnormalities in addition to BRAF mutation found in other patients included: mutations in NRAS, APC and NF1; amplifications in BRAF, aurora kinase A, MYC, MITF and MET; deletions in CDKN2A/B and PAX5; and, alterations in RB1 and ATM. Heterogeneity between patients and molecular evolution within patients was noted.ConclusionNGS identified potentially actionable DNA alterations that could account for resistance in patients with BRAF mutation-positive advanced melanoma who achieved a PR or CR but whose tumors later progressed. A subset of patients with advanced melanoma may harbor only a BRAF mutation and achieve a durable CR on BRAF pathway inhibitors

Ionospheric Simulation System for Satellite Observations and Global Assimilative Model Experiments - ISOGAME

Modeling and imaging the Earth's ionosphere as well as understanding its structures, inhomogeneities, and disturbances is a key part of NASA's Heliophysics Directorate science roadmap. This invention provides a design tool for scientific missions focused on the ionosphere. It is a scientifically important and technologically challenging task to assess the impact of a new observation system quantitatively on our capability of imaging and modeling the ionosphere. This question is often raised whenever a new satellite system is proposed, a new type of data is emerging, or a new modeling technique is developed. The proposed constellation would be part of a new observation system with more low-Earth orbiters tracking more radio occultation signals broadcast by Global Navigation Satellite System (GNSS) than those offered by the current GPS and COSMIC observation system. A simulation system was developed to fulfill this task. The system is composed of a suite of software that combines the Global Assimilative Ionospheric Model (GAIM) including first-principles and empirical ionospheric models, a multiple- dipole geomagnetic field model, data assimilation modules, observation simulator, visualization software, and orbit design, simulation, and optimization software