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

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)

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

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

The evolutionary dynamics of variant antigen genes in Babesia reveal a history of genomic innovation underlying host-parasite interaction

Babesia spp. are tick-borne, intraerythrocytic hemoparasites that use antigenic variation to resist host immunity, through sequential modification of the parasite-derived variant erythrocyte surface antigen (VESA) expressed on the infected red blood cell surface. We identified the genomic processes driving antigenic diversity in genes encoding VESA (ves1) through comparative analysis within and between three Babesia species, (B. bigemina, B. divergens and B. bovis). Ves1 structure diverges rapidly after speciation, notably through the evolution of shortened forms (ves2) from 5′ ends of canonical ves1 genes. Phylogenetic analyses show that ves1 genes are transposed between loci routinely, whereas ves2 genes are not. Similarly, analysis of sequence mosaicism shows that recombination drives variation in ves1 sequences, but less so for ves2, indicating the adoption of different mechanisms for variation of the two families. Proteomic analysis of the B. bigemina PR isolate shows that two dominant VESA1 proteins are expressed in the population, whereas numerous VESA2 proteins are co-expressed, consistent with differential transcriptional regulation of each family. Hence, VESA2 proteins are abundant and previously unrecognized elements of Babesia biology, with evolutionary dynamics consistently different to those of VESA1, suggesting that their functions are distinct

Killing Tensors and Conformal Killing Tensors from Conformal Killing Vectors

Koutras has proposed some methods to construct reducible proper conformal Killing tensors and Killing tensors (which are, in general, irreducible) when a pair of orthogonal conformal Killing vectors exist in a given space. We give the completely general result demonstrating that this severe restriction of orthogonality is unnecessary. In addition we correct and extend some results concerning Killing tensors constructed from a single conformal Killing vector. A number of examples demonstrate how it is possible to construct a much larger class of reducible proper conformal Killing tensors and Killing tensors than permitted by the Koutras algorithms. In particular, by showing that all conformal Killing tensors are reducible in conformally flat spaces, we have a method of constructing all conformal Killing tensors (including all the Killing tensors which will in general be irreducible) of conformally flat spaces using their conformal Killing vectors.Comment: 18 pages References added. Comments and reference to 2-dim case. Typos correcte