Fractional regularization matrices for linear discrete ill-posed problems

The numerical solution of linear discrete ill-posed problems typically requires regularization. Two of the most popular regularization methods are due to Tikhonov and Lavrentiev. These methods require the choice of a regularization matrix. Common choices include the identity matrix and finite difference approximations of a derivative operator. It is the purpose of the present paper to explore the use of fractional powers of the matrices {Mathematical expression} (for Tikhonov regularization) and A (for Lavrentiev regularization) as regularization matrices, where A is the matrix that defines the linear discrete ill-posed problem. Both small- and large-scale problems are considered. © 2013 Springer Science+Business Media Dordrecht

Spin waves cause non-linear friction

Energy dissipation is studied for a hard magnetic tip that scans a soft magnetic substrate. The dynamics of the atomic moments are simulated by solving the Landau-Lifshitz-Gilbert (LLG) equation numerically. The local energy currents are analysed for the case of a Heisenberg spin chain taken as substrate. This leads to an explanation for the velocity dependence of the friction force: The non-linear contribution for high velocities can be attributed to a spin wave front pushed by the tip along the substrate.Comment: 5 pages, 9 figure

Spin waves cause non-linear friction

Energy dissipation is studied for a hard magnetic tip that scans a soft magnetic substrate. The dynamics of the atomic moments are simulated by solving the Landau-Lifshitz-Gilbert (LLG) equation numerically. The local energy currents are analysed for the case of a Heisenberg spin chain taken as substrate. This leads to an explanation for the velocity dependence of the friction force: The non-linear contribution for high velocities can be attributed to a spin wave front pushed by the tip along the substrate.Comment: 5 pages, 9 figure

SORTCERY—A High–Throughput Method to Affinity Rank Peptide Ligands

Uncovering the relationships between peptide and protein sequences and binding properties is critical for successfully predicting, re-designing and inhibiting protein–protein interactions. Systematically collected data that link protein sequence to binding are valuable for elucidating determinants of protein interaction but are rare in the literature because such data are experimentally difficult to generate. Here we describe SORTCERY, a high-throughput method that we have used to rank hundreds of yeast-displayed peptides according to their affinities for a target interaction partner. The procedure involves fluorescence-activated cell sorting of a library, deep sequencing of sorted pools and downstream computational analysis. We have developed theoretical models and statistical tools that assist in planning these stages. We demonstrate SORTCERY's utility by ranking 1026 BH3 (Bcl-2 homology 3) peptides with respect to their affinities for the anti-apoptotic protein Bcl-x[subscript L]. Our results are in striking agreement with measured affinities for 19 individual peptides with dissociation constants ranging from 0.1 to 60 nM. High-resolution ranking can be used to improve our understanding of sequence–function relationships and to support the development of computational models for predicting and designing novel interactions.National Institutes of Health (U.S.) (Award GM096466)German Academic Scholarship Foundation (Grant RE 3111/1-1

Generating High-Accuracy Peptide-Binding Data in High Throughput with Yeast Surface Display and SORTCERY

Library methods are widely used to study protein-protein interactions, and high-throughput screening or selection followed by sequencing can identify a large number of peptide ligands for a protein target. In this chapter, we describe a procedure called "SORTCERY" that can rank the affinities of library members for a target with high accuracy. SORTCERY follows a three-step protocol. First, fluorescence-activated cell sorting (FACS) is used to sort a library of yeast-displayed peptide ligands according to their affinities for a target. Second, all sorted pools are deep sequenced. Third, the resulting data are analyzed to create a ranking. We demonstrate an application of SORTCERY to the problem of ranking peptide ligands for the anti-apoptotic regulator Bcl-xL.National Institute of General Medical Sciences (U.S.) (Award GM096466

LWR core thermal-hydraulic analysis : assessment and comparison of the range of applicability of the codes COBRA IIIC/MIT and COBRA IV-I

Based on the M.S. thesis of the first author in the M.I.T. Dept. of Nuclear Engineering, 1978.This report summarizes the result of studies concerning the range of applicability of two subchannel codes for a variety of thermal-hydraulic analyses. The subchannel codes used include COBRA IIIC/MIT and the newly developed code, COBRA IV-I which is considered the benchmark code for the purpose of this report. Hence, through the comparisons of the two codes, the applicability of COBRA IIIC/MIT is assessed with respect to COBRA IV-I. A variety of LWR thermal-hydraulic analyses are examined. Results of both codes for steady-state and transient analyses are compared. The types of analysis include BWR bundle-wide analysis, a simulated rod ejection and loss of flow transients for a PWR. The system parameters were changed drastically to reach extreme coolant conditions, thereby establishing upper limits. In addition to these cases, both codes are compared to experimental data including measured coolant exit temperatures in a core, interbundle mixing for inlet flow upset cases and two-subchannel flow blockage measurements. The comparisons showed that, overall, COBRA IIIC/MIT predicts most thermal-hydraulic parameters quite satisfactorily. However, the clad temperature predictions differ from those calculated by COBRA IV-I and appear to be in error. These incorrect predictions are caused by the discontinuity in the heat transfer coefficient at the start of boiling. Hence, if the heat transfer package is corrected, then COBRA IIIC/MIT should be just as applicable as the implicit option of COBRA IV-I.Final report for research project sponsored by Long Island Lighting Company and others under the MIT Energy Laboratory Electric Utility Program