Informal proof, formal proof, formalism

Increases in the use of automated theorem-provers have renewed focus on the relationship between the informal proofs normally found in mathematical research and fully formalised derivations. Whereas some claim that any correct proof will be underwritten by a fully formal proof, sceptics demur. In this paper I look at the relevance of these issues for formalism, construed as an anti-platonistic metaphysical doctrine. I argue that there are strong reasons to doubt that all proofs are fully formalisable, if formal proofs are required to be finitary, but that, on a proper view of the way in which formal proofs idealise actual practice, this restriction is unjustified and formalism is not threatened

Developing a Personal Pedagogy of Conducting

When conductors in academic institutions are required to teach a course or private lessons in conducting, they most often resort to their own training and recycle the ideas and methods of their own teachers. Over time it is typical for them to try new approaches and techniques, to discover and implement new resources and literature, and to develop their own personal conducting pedagogy. Through an examination of conducting texts as well as current conducting course syllabi from various American universities and colleges, some conclusions about current conducting pedagogical practices can be drawn. After consideration of the material and a summary of current practice, this paper presents several sample syllabi and a description of the process for teaching a basic conducting class. These materials serve as a model for the approach that could be taken by the readers in the development of their own personal conducting pedagogy

Putnam, Gödel and mathematical realism revisited

I revisit my 1993 paper on Putnam and mathematical realism focusing on the indispensability argument and how it has fared over the years. This argument starts from the claim that mathematics is an indispensable part of science and draws the conclusion, from holistic considerations about confirmation, that the ontology of science includes abstract objects as well as the physical entities science deals with

Conservation of a microRNA cluster in parasitic nematodes and profiling of miRNAs in excretory-secretory products and microvesicles of Haemonchus contortus

microRNAs are small non-coding RNAs that are important regulators of gene expression in a range of animals, including nematodes. We have analysed a cluster of four miRNAs from the pathogenic nematode species Haemonchus contortus that are closely linked in the genome. We find that the cluster is conserved only in clade V parasitic nematodes and in some ascarids, but not in other clade III species nor in clade V free-living nematodes. Members of the cluster are present in parasite excretory-secretory products and can be detected in the abomasum and draining lymph nodes of infected sheep, indicating their release in vitro and in vivo. As observed for other parasitic nematodes, H. contortus adult worms release extracellular vesicles (EV). Small RNA libraries were prepared from vesicle-enriched and vesicle-depleted supernatants from both adult worms and L4 stage larvae. Comparison of the miRNA species in the different fractions indicated that specific miRNAs are packaged within vesicles, while others are more abundant in vesicle-depleted supernatant. Hierarchical clustering analysis indicated that the gut is the likely source of vesicle-associated miRNAs in the L4 stage, but not in the adult worm. These findings add to the growing body of work demonstrating that miRNAs released from parasitic helminths may play an important role in host-parasite interactions

The Influence of Operational Resources and Activities on Indirect Personnel Costs: A Multilevel Modeling Approach

Indirect activities often represent an underemphasized, yet significant, contributing source of costs for organizations. In order to manage indirect costs, organizations must understand how these costs behave relative to changes in operational resources and activities. This is of particular interest to the Air Force and its sister services, because recent and projected reductions in defense spending are forcing reductions in their operational variables, and insufficient research exists to help them understand how this may influence indirect costs. Furthermore, although academic research on indirect costs has advanced the knowledge behind the modeling and behavior of indirect costs, significant gaps in the literature remain. Our research provides important and timely advances to the indirect cost literature. First, our research disaggregates the indirect cost pool and focuses on indirect personnel costs, which represent 33% of all Air Force indirect costs and are a leading source of indirect costs in many organizations. Second, we employ a multilevel modeling approach to capture the hierarchical nature of an enterprise, allowing us to assess the influence that each level of an organization has on indirect cost behavior and relationships. Third, we identify the operational variables that influence indirect personnel costs in the Air Force enterprise, providing Air Force decision-makers with evidence-based knowledge to inform decisions regarding budget reduction strategies

Searches for New Quarks and Leptons Produced in Z-Boson Decay

We have searched for events with new-particle topologies in 390 hadronic Z decays with the Mark II detector at the SLAC Linear Collider. We place 95%-confidence-level lower limits of 40.7 GeV/c^2 for the top-quark mass, 42.0 GeV/c^2 for the mass of a fourth-generation charge - 1/3 quark, and 41.3 GeV/c^2 for the mass of an unstable Dirac neutral lepton

Measurement of Z Decays into Lepton Pairs

We present measurements by the Mark II experiment of the ratios of the leptonic partial widths of the Z boson to the hadronic partial width. The results are Γ_(ee)/Γ_(had)=0.037_(-0.012^()+0.016),Γ_(µµ)/Γ_(had)=0.053-_(0.015)^(+0.020), and Γ_(ττ)/Γ_(had)=0.066_(-0.017)^(+0.021), in good agreement with the standard-model prediction of 0.048. From the average leptonic width result, Γ_(ll)/Γ_(had)=0.053_(-0.009)^(+0.010), we derive Γ_(had)=1.56_(-0.24)^(+0.28) GeV. We find for the vector coupling constants of the tau and muon v_τ^2=0.31±0.31_(-0.30)^(+0.43) and v_μ^2=0.05±0.30_(-0.23)^(+0.34)

Functional strength training versus movement performance therapy for upper limb motor recovery early after stroke: a RCT

Background: Not all stroke survivors respond to the same form of physical therapy in the same way early after stroke. The response is variable and a detailed understanding of the interaction between specific physical therapies and neural structure and function is needed. Objectives: To determine if upper limb recovery is enhanced more by functional strength training (FST) than by movement performance therapy (MPT), to identify the differences in the neural correlates of response to (1) FST and (2) MPT and to determine whether or not pretreatment neural characteristics can predict recovery in response to (1) FST and (2) MPT. Design: Randomised, controlled, observer-blind, multicentre trial with embedded explanatory investigations. An independent facility used computer-generated randomisation for participants’ group allocation. Setting: In-patient rehabilitation, participants’ homes, university movement analysis facilities and NHS or university neuroimaging departments in the UK. Participants: People who were between 2 and 60 days after stroke in the territory of the anterior cerebral circulation, with some voluntary muscle contraction in the more affected upper limb but not full function. Interventions: Routine rehabilitation [conventional physical therapy (CPT)] plus either MPT or FST in equal doses during a 6-week intervention phase. FST was progressive resistive exercise provided during training of functional tasks. MPT was therapist ‘hands-on’ sensory input and guidance for production of smooth and accurate movement. Main outcomes: Action Research Arm Test (ARAT) score for clinical efficacy. Neural measures were made of corticocortical [fractional anisotropy (FA) from corpus callosum midline], corticospinal connectivity (asymmetry of corticospinal tracts FA) and resting motor threshold of paretic biceps brachii (pBB) and extensor carpi radialis muscles (derived from transcranial magnetic stimulation). Analysis: Change in ARAT scores were analysed using analysis of covariance models adjusted for baseline variables and randomisation strata. Correlation coefficients were calculated between change in neural measures and change in ARAT score per group and for the whole sample. An interaction term was calculated for each baseline neural measure and ARAT score change from baseline to outcome. Results: A total of 288 participants were randomised [mean age 72.2 (standard deviation 12.5) years; mean ARAT score of 25.5 (18.2); n = 283]. For the 240 participants with ARAT measurements at baseline and outcome, the mean change scores were FST + CPT = 9.70 (11.72) and MPT + CPT = 7.90 (9.18). The group difference did not reach statistical significance (least squares mean difference 1.35, 95% confidence interval –1.20 to 3.90; p = 0.298). Correlations between ARAT change scores and baseline neural values ranged from –0.147 (p = 0.385) for whole-sample corticospinal connectivity (n = 37) to 0.199 (p = 0.320) for MPT + CPT resting motor threshold pBB (n = 27). No statistically significant interaction effects were found between baseline neural variables and change in ARAT score. There were no differences between groups in adverse events. Limitations: The number of participants in the embedded explanatory investigation was lower than expected. Conclusions: The small difference in upper limb improvement in response to FST and MPT did not reach statistical significance. Baseline neural measures neither correlated with upper limb recovery nor predicted therapy response. Future work: Needs to continue investigation of the variability of response to specific physical therapies in people early after stroke. Trial registration: Current Controlled Trials ISRCTN19090862 and National Research Ethics Service reference number 11/EE/0524. Funding: This project was funded by the Efficacy and Mechanism Evaluation programme, a Medical Research Council and National Institute for Health Research partnership