Random Costs in Combinatorial Optimization

The random cost problem is the problem of finding the minimum in an exponentially long list of random numbers. By definition, this problem cannot be solved faster than by exhaustive search. It is shown that a classical NP-hard optimization problem, number partitioning, is essentially equivalent to the random cost problem. This explains the bad performance of heuristic approaches to the number partitioning problem and allows us to calculate the probability distributions of the optimum and sub-optimum costs.Comment: 4 pages, Revtex, 2 figures (eps), submitted to PR

On the combination of omics data for prediction of binary outcomes

Enrichment of predictive models with new biomolecular markers is an important task in high-dimensional omic applications. Increasingly, clinical studies include several sets of such omics markers available for each patient, measuring different levels of biological variation. As a result, one of the main challenges in predictive research is the integration of different sources of omic biomarkers for the prediction of health traits. We review several approaches for the combination of omic markers in the context of binary outcome prediction, all based on double cross-validation and regularized regression models. We evaluate their performance in terms of calibration and discrimination and we compare their performance with respect to single-omic source predictions. We illustrate the methods through the analysis of two real datasets. On the one hand, we consider the combination of two fractions of proteomic mass spectrometry for the calibration of a diagnostic rule for the detection of early-stage breast cancer. On the other hand, we consider transcriptomics and metabolomics as predictors of obesity using data from the Dietary, Lifestyle, and Genetic determinants of Obesity and Metabolic syndrome (DILGOM) study, a population-based cohort, from Finland

Context and Content of Teaching Conversations: Exploring How to Promote Sharing of Innovative Teaching Knowledge Between Science Faculty

Background: Change strategies may leverage interpersonal relationships and conversations to spread teaching innovations among science faculty. Knowledge sharing refers to the process by which individuals transfer information and thereby spread innovative ideas within an organization. We use knowledge sharing as a lens for identifying factors that encourage productive teaching-related conversations between individuals, characterizing the context and content of these discussions, and understanding how peer interactions may shape instructional practices. In this study, we interview 19 science faculty using innovative teaching practices about the teaching-focused conversations they have with diferent discussion partners. Results: This qualitative study describes characteristics of the relationship between discussion partners, what they discuss with respect to teaching, the amount of help-seeking that occurs, and the perceived impacts of these conversations on their teaching. We highlight the role of ofce location and course overlap in bringing faculty together and characterize the range of topics they discuss, such as course delivery and teaching strategies. We note the tendency of faculty to seek out partners with relevant expertise and describe how faculty perceive their discussion partners to infuence their instructional practices and personal afect. Finally, we elaborate on how these themes vary depending on the relationship between discussion partners. Conclusions: The knowledge sharing framework provides a useful lens for investigating how various factors afect faculty conversations around teaching. Building on this framework, our results lead us to propose two hypotheses for how to promote sharing teaching knowledge among faculty, thereby identifying productive directions for further systematic inquiry. In particular, we propose that productive teaching conversations might be cultivated by fostering collaborative teaching partnerships and developing departmental structures to facilitate sharing of teaching expertise. We further suggest that social network theories and other examinations of faculty behavior can be useful approaches for researching the mechanisms that drive teaching reform

Innovative Teaching Knowledge Stays with Users

Programs seeking to transform undergraduate science, technology, engineering, and mathematics courses often strive for participating faculty to share their knowledge of innovative teaching practices with other faculty in their home departments. Here, we provide interview, survey, and social network analyses revealing that faculty who use innovative teaching practices preferentially talk to each other, suggesting that greater steps are needed for information about innovative practices to reach faculty more broadly

Development of the Cooperative Adoption Factors Instrument to Measure Factors Associated with Instructional Practice in the Context of Institutional Change

Background: Many institutional and departmentally focused change efforts have sought to improve teaching in STEM through the promotion of evidence-based instructional practices (EBIPs). Even with these efforts, EBIPs have not become the predominant mode of teaching in many STEM departments. To better understand institutional change efforts and the barriers to EBIP implementation, we developed the Cooperative Adoption Factors Instrument (CAFI) to probe faculty member characteristics beyond demographic attributes at the individual level. The CAFI probes multiple constructs related to institutional change including perceptions of the degree of mutual advantage of taking an action (strategic complements), trust and interconnectedness among colleagues (interdependence), and institutional attitudes toward teaching (climate). Results: From data collected across five STEM fields at three large public research universities, we show that the CAFI has evidence of internal structure validity based on exploratory and confirmatory factor analysis. The scales have low correlations with each other and show significant variation among our sampled universities as demonstrated by ANOVA. We further demonstrate a relationship between the strategic complements and climate factors with EBIP adoption through use of a regression analysis. In addition to these factors, we also find that indegree, a measure of opinion leadership, correlates with EBIP adoption. Conclusions: The CAFI uses the CACAO model of change to link the intended outcome of EBIP adoption with perception of EBIPs as mutually reinforcing (strategic complements), perception of faculty having their fates intertwined (interdependence), and perception of institutional readiness for change (climate). Our work has established that the CAFI is sensitive enough to pick up on differences between three relatively similar institutions and captures significant relationships with EBIP adoption. Our results suggest that the CAFI is likely to be a suitable tool to probe institutional change efforts, both for change agents who wish to characterize the local conditions on their respective campuses to support effective planning for a change initiative and for researchers who seek to follow the progression of a change initiative. While these initial findings are very promising, we also recommend that CAFI be administered in different types of institutions to examine the degree to which the observed relationships hold true across contexts

Fine and ultrafine particle number and size measurements from industrial combustion processes : primary emissions field data

This study is to our knowledge the first to present the results of on-line measurements of residual nanoparticle numbers downstream of the flue gas treatment systems of a wide variety of medium- and large-scale industrial installations. Where available, a semi-quantitative elemental composition of the sampled particles is carried out using a Scanning Electron Microscope coupled with an Energy Dispersive Spectrometer (SEM-EDS). The semi-quantitative elemental composition as a function of the particle size is presented. EU's Best Available Technology documents (BAT) show removal efficiencies of Electrostatic Precipitator (ESP) and bag filter dedusting systems exceeding 99% when expressed in terms of weight. Their efficiency decreases slightly for particles smaller than 1 mu m but when expressed in terms of weight, still exceeds 99% for bag filters and 96% for ESP. This study reveals that in terms of particle numbers, residual nanoparticles (NP) leaving the dedusting systems dominate by several orders of magnitude. In terms of weight, all installations respect their emission limit values and the contribution of NP to weight concentrations is negligible, despite their dominance in terms of numbers. Current World Health Organisation regulations are expressed in terms of PM2.5 wt concentrations and therefore do not reflect the presence or absence of a high number of NP. This study suggests that research is needed on possible additional guidelines related to NP given their possible toxicity and high potential to easily enter the blood stream when inhaled by humans

Phase Transition in the Number Partitioning Problem

Number partitioning is an NP-complete problem of combinatorial optimization. A statistical mechanics analysis reveals the existence of a phase transition that separates the easy from the hard to solve instances and that reflects the pseudo-polynomiality of number partitioning. The phase diagram and the value of the typical ground state energy are calculated.Comment: minor changes (references, typos and discussion of results

Number partitioning as random energy model

Number partitioning is a classical problem from combinatorial optimisation. In physical terms it corresponds to a long range anti-ferromagnetic Ising spin glass. It has been rigorously proven that the low lying energies of number partitioning behave like uncorrelated random variables. We claim that neighbouring energy levels are uncorrelated almost everywhere on the energy axis, and that energetically adjacent configurations are uncorrelated, too. Apparently there is no relation between geometry (configuration) and energy that could be exploited by an optimization algorithm. This ``local random energy'' picture of number partitioning is corroborated by numerical simulations and heuristic arguments.Comment: 8+2 pages, 9 figures, PDF onl