Regularized Reduced Order Lippman-Schwinger-Lanczos Method for Inverse Scattering Problems in the Frequency Domain

Inverse scattering has a broad applicability in quantum mechanics, remote sensing, geophysical, and medical imaging. This paper presents a robust direct reduced order model (ROM) method for solving inverse scattering problems based on an efficient approximation of the resolvent operator regularizing the Lippmann-Schwinger-Lanczos (LSL) algorithm. We show that the efficiency of the method relies upon the weak dependence of the orthogonalized basis on the unknown potential in the Schr\"odinger equation by demonstrating that the Lanczos orthogonalization is equivalent to performing Gram-Schmidt on the ROM time snapshots. We then develop the LSL algorithm in the frequency domain with two levels of regularization. We show that the same procedure can be extended beyond the Schr\"odinger formulation to the Helmholtz equation, e.g., to imaging the conductivity using diffusive electromagnetic fields in conductive media with localized positive conductivity perturbations. Numerical experiments for Helmholtz and Schr\"odinger problems show that the proposed bi-level regularization scheme significantly improves the performance of the LSL algorithm, allowing for good reconstructions with noisy data and large data sets

Using tasks to explore teacher knowledge in situation-specific contexts

This article was published in the journal, Journal of Mathematics Teacher Education [© Springer] and the original publication is available at www.springerlink.comResearch often reports an overt discrepancy between theoretically/out-of context expressed teacher beliefs about mathematics and pedagogy and actual practice. In order to explore teacher knowledge in situation-specific contexts we have engaged mathematics teachers with classroom scenarios (Tasks) which: are hypothetical but grounded on learning and teaching issues that previous research and experience have highlighted as seminal; are likely to occur in actual practice; have purpose and utility; and, can be used both in (pre- and in-service) teacher education and research through generating access to teachers’ views and intended practices. The Tasks have the following structure: reflecting upon the learning objectives within a mathematical problem (and solving it); examining a flawed (fictional) student solution; and, describing, in writing, feedback to the student. Here we draw on the written responses to one Task (which involved reflecting on solutions of x+x−1=0 of 53 Greek in-service mathematics teachers in order to demonstrate the range of teacher knowledge (mathematical, didactical and pedagogical) that engagement with these tasks allows us to explore

Reconstruction of regulatory networks through temporal enrichment profiling and its application to H1N1 influenza viral infection

BACKGROUND: H1N1 influenza viruses were responsible for the 1918 pandemic that caused millions of deaths worldwide and the 2009 pandemic that caused approximately twenty thousand deaths. The cellular response to such virus infections involves extensive genetic reprogramming resulting in an antiviral state that is critical to infection control. Identifying the underlying transcriptional network driving these changes, and how this program is altered by virally-encoded immune antagonists, is a fundamental challenge in systems immunology. RESULTS: Genome-wide gene expression patterns were measured in human monocyte-derived dendritic cells (DCs) infected in vitro with seasonal H1N1 influenza A/New Caledonia/20/1999. To provide a mechanistic explanation for the timing of gene expression changes over the first 12 hours post-infection, we developed a statistically rigorous enrichment approach integrating genome-wide expression kinetics and time-dependent promoter analysis. Our approach, TIme-Dependent Activity Linker (TIDAL), generates a regulatory network that connects transcription factors associated with each temporal phase of the response into a coherent linked cascade. TIDAL infers 12 transcription factors and 32 regulatory connections that drive the antiviral response to influenza. To demonstrate the generality of this approach, TIDAL was also used to generate a network for the DC response to measles infection. The software implementation of TIDAL is freely available at http://tsb.mssm.edu/primeportal/?q=tidal_prog. CONCLUSIONS: We apply TIDAL to reconstruct the transcriptional programs activated in monocyte-derived human dendritic cells in response to influenza and measles infections. The application of this time-centric network reconstruction method in each case produces a single transcriptional cascade that recapitulates the known biology of the response with high precision and recall, in addition to identifying potentially novel antiviral factors. The ability to reconstruct antiviral networks with TIDAL enables comparative analysis of antiviral responses, such as the differences between pandemic and seasonal influenza infections

Changing classroom culture, curricula, and instruction for proof and proving: how amenable to scaling up, practicable for curricular integration, and capable of producing long-lasting effects are current interventions?

This paper is a commentary on the classroom interventions on the teaching and learning of proof reported in the seven empirical papers in this special issue. The seven papers show potential to enhance student learning in an area of mathematics that is not only notoriously difficult for students to learn and for teachers to teach, but also critically important to knowing and doing mathematics. Although the seven papers, and the intervention studies they report, vary in many ways—student population, content domain, goals and duration of the intervention, and theoretical perspectives, to name a few—they all provide valuable insight into ways in which classroom experiences might be designed to positively influence students’ learning to prove. In our commentary, we highlight the contributions and promise of the interventions in terms of whether and how they present capacity to change the classroom culture, the curriculum, or instruction. In doing so, we distinguish between works that aim to enhance students’ preparedness for, and competence in, proof and proving and works that explicitly foster appreciation for the need and importance of proof and proving. Finally, we also discuss briefly the interventions along three dimensions: how amenable to scaling up, how practicable for curricular integration, and how capable of producing long-lasting effects these interventions are

Inferring PDZ Domain Multi-Mutant Binding Preferences from Single-Mutant Data

Many important cellular protein interactions are mediated by peptide recognition domains. The ability to predict a domain's binding specificity directly from its primary sequence is essential to understanding the complexity of protein-protein interaction networks. One such recognition domain is the PDZ domain, functioning in scaffold proteins that facilitate formation of signaling networks. Predicting the PDZ domain's binding specificity was a part of the DREAM4 Peptide Recognition Domain challenge, the goal of which was to describe, as position weight matrices, the specificity profiles of five multi-mutant ERBB2IP-1 domains. We developed a method that derives multi-mutant binding preferences by generalizing the effects of single point mutations on the wild type domain's binding specificities. Our approach, trained on publicly available ERBB2IP-1 single-mutant phage display data, combined linear regression-based prediction for ligand positions whose specificity is determined by few PDZ positions, and single-mutant position weight matrix averaging for all other ligand columns. The success of our method as the winning entry of the DREAM4 competition, as well as its superior performance over a general PDZ-ligand binding model, demonstrates the advantages of training a model on a well-selected domain-specific data set

Post-traumatic stress disorder associated with life-threatening motor vehicle collisions in the WHO World Mental Health Surveys

BACKGROUND: Motor vehicle collisions (MVCs) are a substantial contributor to the global burden of disease and lead to subsequent post-traumatic stress disorder (PTSD). However, the relevant literature originates in only a few countries, and much remains unknown about MVC-related PTSD prevalence and predictors. METHODS: Data come from the World Mental Health Survey Initiative, a coordinated series of community epidemiological surveys of mental disorders throughout the world. The subset of 13 surveys (5 in high income countries, 8 in middle or low income countries) with respondents reporting PTSD after life-threatening MVCs are considered here. Six classes of predictors were assessed: socio-demographics, characteristics of the MVC, childhood family adversities, MVCs, other traumatic experiences, and respondent history of prior mental disorders. Logistic regression was used to examine predictors of PTSD. Mental disorders were assessed with the fully-structured Composite International Diagnostic Interview using DSM-IV criteria. RESULTS: Prevalence of PTSD associated with MVCs perceived to be life-threatening was 2.5 % overall and did not vary significantly across countries. PTSD was significantly associated with low respondent education, someone dying in the MVC, the respondent or someone else being seriously injured, childhood family adversities, prior MVCs (but not other traumatic experiences), and number of prior anxiety disorders. The final model was significantly predictive of PTSD, with 32 % of all PTSD occurring among the 5 % of respondents classified by the model as having highest PTSD risk. CONCLUSION: Although PTSD is a relatively rare outcome of life-threatening MVCs, a substantial minority of PTSD cases occur among the relatively small proportion of people with highest predicted risk. This raises the question whether MVC-related PTSD could be reduced with preventive interventions targeted to high-risk survivors using models based on predictors assessed in the immediate aftermath of the MVCs

A combinatorial optimization approach for diverse motif finding applications

BACKGROUND: Discovering approximately repeated patterns, or motifs, in biological sequences is an important and widely-studied problem in computational molecular biology. Most frequently, motif finding applications arise when identifying shared regulatory signals within DNA sequences or shared functional and structural elements within protein sequences. Due to the diversity of contexts in which motif finding is applied, several variations of the problem are commonly studied. RESULTS: We introduce a versatile combinatorial optimization framework for motif finding that couples graph pruning techniques with a novel integer linear programming formulation. Our approach is flexible and robust enough to model several variants of the motif finding problem, including those incorporating substitution matrices and phylogenetic distances. Additionally, we give an approach for determining statistical significance of uncovered motifs. In testing on numerous DNA and protein datasets, we demonstrate that our approach typically identifies statistically significant motifs corresponding to either known motifs or other motifs of high conservation. Moreover, in most cases, our approach finds provably optimal solutions to the underlying optimization problem. CONCLUSION: Our results demonstrate that a combined graph theoretic and mathematical programming approach can be the basis for effective and powerful techniques for diverse motif finding applications

How well can post‐traumatic stress disorder be predicted from pre‐trauma risk factors? An exploratory study in the WHO World Mental Health Surveys

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/108700/1/wps20150.pd

WHO World Mental Health Surveys International College Student Project: Prevalence and Distribution of Mental Disorders

Increasingly, colleges across the world are contending with rising rates of mental disorders, and in many cases, the demand for services on campus far exceeds the available resources. The present study reports initial results from the first stage of the WHO World Mental Health International College Student project, in which a series of surveys in 19 colleges across 8 countries (Australia, Belgium, Germany, Mexico, Northern Ireland, South Africa, Spain, United States) were carried out with the aim of estimating prevalence and basic sociodemographic correlates of common mental disorders among first-year college students. Web-based self-report questionnaires administered to incoming first-year students (45.5% pooled response rate) screened for six common lifetime and 12-month DSM-IV mental disorders: major depression, mania/hypomania, generalized anxiety disorder, panic disorder, alcohol use disorder, and substance use disorder. We focus on the 13,984 respondents who were full-time students: 35% of whom screened positive for at least one of the common lifetime disorders assessed and 31% screened positive for at least one 12-month disorder. Syndromes typically had onsets in early to middle adolescence and persisted into the year of the survey. Although relatively modest, the strongest correlates of screening positive were older age, female sex, unmarried-deceased parents, no religious affiliation, nonheterosexual identification and behavior, low secondary school ranking, and extrinsic motivation for college enrollment. The weakness of these associations means that the syndromes considered are widely distributed with respect to these variables in the student population. Although the extent to which cost-effective treatment would reduce these risks is unclear, the high level of need for mental health services implied by these results represents a major challenge to institutions of higher education and governments. (PsycINFO Database Record (c) 2018 APA, all rights reserved).status: publishe