Perceiving Structure in Mathematical Expressions

Despite centuries of using mathematical notation, surprisingly little is known about how mathematicians perceive equations. The present experiment provides an initial step in understanding what sort of internal representation is used by experienced mathematicians. In particular, we examined if mathematical syntax plays a role in how mathematicians encode algebraic equations, or if just a simple memory strategy is used. Participants in the experiment performed a memory recognition task that required them to identify both well-formed (syntactically correct) and non-well-formed sub-expressions of equations. As hypothesised, performance was significantly better for well-formed sub-expressions, a result which suggests that mathematicians do indeed use an internal representation based on mathematical syntax to encode equations

HYDRAULIC CONDUCTIVITY AND HYDROSTRATIGRAPHY OF THE PLATTEVILLE FORMATION, TWIN CITIES METROPOLITAN AREA, MINNESOTA

Point data and descriptive information provided as part of the supplemental GIS data.This report synthesizes a large body of data that provide a better understanding of the hydrogeologic characteristics of the Ordovician Platteville Formation in the Twin Cities Metropolitan Area (TCMA). The carbonate-dominated Platteville Formation plays an important role in the TCMA hydrogeologic system by limiting vertical infiltration of relatively recent water to the more commonly utilized aquifers beneath it. Furthermore, it has been impacted by numerous contaminant plumes, which threaten the water quality in domestic wells and the large number (dozens) of springs along the Mississippi River and its tributaries. Hydraulic conductivity data are synthesized and interpreted across a range of scales, with the recognition of variable user needs. For example, generalized bulk hydraulic conductivity for parts of the Platteville Formation may be useful for modeling water budgets through relatively large areas. In contrast, more site-specific needs such as development of remediation strategies and prediction of flow paths may be facilitated by considering the large range in hydraulic conductivity, measured at a number of scales, and by recognizing the location of fast-flow secondary pore networks as well as key aquitards.The Metropolitan Counci

Performance and Agreement of Risk Stratification Instruments for Postoperative Delirium in Persons Aged 50 Years or Older

Several risk stratification instruments for postoperative delirium in older people have been developed because early interventions may prevent delirium. We investigated the performance and agreement of nine commonly used risk stratification instruments in an independent validation cohort of consecutive elective and emergency surgical patients aged >= 50 years with >= 1 risk factor for postoperative delirium. Data was collected prospectively. Delirium was diagnosed according to DSM-IV-TR criteria. The observed incidence of postoperative delirium was calculated per risk score per risk stratification instrument. In addition, the risk stratification instruments were compared in terms of area under the receiver operating characteristic (ROC) curve (AUC), and positive and negative predictive value. Finally, the positive agreement between the risk stratification instruments was calculated. When data required for an exact implementation of the original risk stratification instruments was not available, we used alternative data that was comparable. The study population included 292 patients: 60% men; mean age (SD), 66 (8) years; 90% elective surgery. The incidence of postoperative delirium was 9%. The maximum observed incidence per risk score was 50% (95% CI, 15-85%); for eight risk stratification instruments, the maximum observed incidence per risk score was = 0.11). Positive predictive values of the risk stratification instruments varied between 0-25%, negative predictive values between 89-95%. Positive agreement varied between 0-66%. No risk stratification instrument showed clearly superior performance. In conclusion, in this independent validation cohort, the performance and agreement of commonly used risk stratification instruments for postoperative delirium was poor. Although some caution is needed because the risk stratification instruments were not implemented exactly as described in the original studies, we think that their usefulness in clinical practice can be questioned

Free energy and molecular dynamics calculations for the cubic-tetragonal phase transition in zirconia

The high-temperature cubic-tetragonal phase transition of pure stoichiometric zirconia is studied by molecular dynamics (MD) simulations and within the framework of the Landau theory of phase transformations. The interatomic forces are calculated using an empirical, self-consistent, orthogonal tight-binding (SC-TB) model, which includes atomic polarizabilities up to the quadrupolar level. A first set of standard MD calculations shows that, on increasing temperature, one particular vibrational frequency softens. The temperature evolution of the free energy surfaces around the phase transition is then studied with a second set of calculations. These combine the thermodynamic integration technique with constrained MD simulations. The results seem to support the thesis of a second-order phase transition but with unusual, very anharmonic behaviour above the transition temperature

Hybrid Monte Carlo with Fat Link Fermion Actions

The use of APE smearing or other blocking techniques in lattice fermion actions can provide many advantages. There are many variants of these fat link actions in lattice QCD currently, such as FLIC fermions. The FLIC fermion formalism makes use of the APE blocking technique in combination with a projection of the blocked links back into the special unitary group. This reunitarisation is often performed using an iterative maximisation of a gauge invariant measure. This technique is not differentiable with respect to the gauge field and thus prevents the use of standard Hybrid Monte Carlo simulation algorithms. The use of an alternative projection technique circumvents this difficulty and allows the simulation of dynamical fat link fermions with standard HMC and its variants. The necessary equations of motion for FLIC fermions are derived, and some initial simulation results are presented. The technique is more general however, and is straightforwardly applicable to other smearing techniques or fat link actions

A lattice calculation of the nucleon's spin-dependent structure function g_2 revisited

Our previous calculation of the spin-dependent structure function g_2 is revisited. The interest in this structure function is to a great extent motivated by the fact that it receives contributions from twist-two as well as from twist-three operators already in leading order of 1/Q^2 thus offering the unique possibility of directly assessing higher-twist effects. In our former calculation the lattice operators were renormalized perturbatively and mixing with lower-dimensional operators was ignored. However, the twist-three operator which gives rise to the matrix element d_2 mixes non-perturbatively with an operator of lower dimension. Taking this effect into account leads to a considerably smaller value of d_2, which is consistent with the experimental data.Comment: 25 pages, 11 figure

Relative energetics and structural properties of zirconia using a self-consistent tight-binding model

We describe an empirical, self-consistent, orthogonal tight-binding model for zirconia, which allows for the polarizability of the anions at dipole and quadrupole levels and for crystal field splitting of the cation d orbitals. This is achieved by mixing the orbitals of different symmetry on a site with coupling coefficients driven by the Coulomb potentials up to octapole level. The additional forces on atoms due to the self-consistency and polarizabilities are exactly obtained by straightforward electrostatics, by analogy with the Hellmann-Feynman theorem as applied in first-principles calculations. The model correctly orders the zero temperature energies of all zirconia polymorphs. The Zr-O matrix elements of the Hamiltonian, which measure covalency, make a greater contribution than the polarizability to the energy differences between phases. Results for elastic constants of the cubic and tetragonal phases and phonon frequencies of the cubic phase are also presented and compared with some experimental data and first-principles calculations. We suggest that the model will be useful for studying finite temperature effects by means of molecular dynamics.Comment: to be published in Physical Review B (1 march 2000

Lambda and Antilambda polarization from deep inelastic muon scattering

We report results of the first measurements of Lambda and Antilambda polarization produced in deep inelastic polarized muon scattering on the nucleon. The results are consistent with an expected trend towards positive polarization with increasing x_F. The polarizations of Lambda and Antilambda appear to have opposite signs. A large negative polarization for Lambda at low positive x_F is observed and is not explained by existing models.A possible interpretation is presented.Comment: 9 pages, 2 figure

Shadowing in Inelastic Scattering of Muons on Carbon, Calcium and Lead at Low XBj

Nuclear shadowing is observed in the per-nucleon cross-sections of positive muons on carbon, calcium and lead as compared to deuterium. The data were taken by Fermilab experiment E665 using inelastically scattered muons of mean incident momentum 470 GeV/c. Cross-section ratios are presented in the kinematic region 0.0001 < XBj <0.56 and 0.1 < Q**2 < 80 GeVc. The data are consistent with no significant nu or Q**2 dependence at fixed XBj. As XBj decreases, the size of the shadowing effect, as well as its A dependence, are found to approach the corresponding measurements in photoproduction.Comment: 22 pages, incl. 6 figures, to be published in Z. Phys.

The multiple roles of myelin protein genes during the development of the oligodendrocyte

It has become clear that the products of several of the earliest identified myelin protein genes perform functions that extend beyond the myelin sheath. Interestingly, these myelin proteins, which comprise proteolipid protein, 2′,3′-cyclic nucleotide 3′-phosphodiesterase and the classic and golli MBPs (myelin basic proteins), play important roles during different stages of oligodendroglial development. These non-myelin-related functions are varied and include roles in the regulation of process outgrowth, migration, RNA transport, oligodendrocyte survival and ion channel modulation. However, despite the wide variety of cellular functions performed by the different myelin genes, the route by which they achieve these many functions seems to converge upon a common mechanism involving Ca2+ regulation, cytoskeletal rearrangements and signal transduction. In the present review, the newly emerging functions of these myelin proteins will be described, and these will then be discussed in the context of their contribution to oligodendroglial development