Students´ language in computer-assisted tutoring of mathematical proofs

Truth and proof are central to mathematics. Proving (or disproving) seemingly simple statements often turns out to be one of the hardest mathematical tasks. Yet, doing proofs is rarely taught in the classroom. Studies on cognitive difficulties in learning to do proofs have shown that pupils and students not only often do not understand or cannot apply basic formal reasoning techniques and do not know how to use formal mathematical language, but, at a far more fundamental level, they also do not understand what it means to prove a statement or even do not see the purpose of proof at all. Since insight into the importance of proof and doing proofs as such cannot be learnt other than by practice, learning support through individualised tutoring is in demand. This volume presents a part of an interdisciplinary project, set at the intersection of pedagogical science, artificial intelligence, and (computational) linguistics, which investigated issues involved in provisioning computer-based tutoring of mathematical proofs through dialogue in natural language. The ultimate goal in this context, addressing the above-mentioned need for learning support, is to build intelligent automated tutoring systems for mathematical proofs. The research presented here has been focused on the language that students use while interacting with such a system: its linguistic propeties and computational modelling. Contribution is made at three levels: first, an analysis of language phenomena found in students´ input to a (simulated) proof tutoring system is conducted and the variety of students´ verbalisations is quantitatively assessed, second, a general computational processing strategy for informal mathematical language and methods of modelling prominent language phenomena are proposed, and third, the prospects for natural language as an input modality for proof tutoring systems is evaluated based on collected corpora

Low prevalence search for cancers in mammograms : evidence using laboratory experiments and computer aided detection

People miss a large proportion of targets when they only appear rarely. This Low Prevalence (LP) Effect could lead to serious consequences if it occurred in the real world task of searching for cancers in mammograms. Using a novel mammogram search task, we asked participants to search for a pre-specified cancer (Experiments 1-2) or a range of masses (Experiments 3-5) under high or low prevalence conditions. Experiment 1 showed that an LP Effect occurred using these stimuli. Experiment 2 tested an over-reliance hypothesis and showed that the use of Computer Aided Detection (CAD) led to fewer missed cancers with a valid CAD prompt yet, a large proportion of cancers were missed when CAD was incorrect. Experiment 3 - 5 showed that false alarms also increased when searching for a range of masses and that CAD reduced miss errors when it correctly cued the target but increased miss errors and false alarms when it did not. Furthermore, when a mass fell outside the CAD prompt it was more likely to be misidentified. No LP Effect was observed with the addition of CAD when people were asked to search for a range of targets. Theories and implications for mammogram search are discussed

Photofragmentation of SiF4 upon Si 2p and F 1s Core Excitation: Cation and Anion Yield Spectroscopy

We have studied the fragmentation dynamics of core-excited SiF4 by means of soft-x-ray photoexcitation and partial positive and negative ion yield measurements around the Si L2,3-shell and F K-shell ionization thresholds. All detectable ionic fragments are reported and we observe significant differences between the various partial ion yields near the Si 2p threshold. The differences are similar to our previous results from CH3Cl showing more extended fragmentation in correspondence to transitions to Rydberg states. At variance with smaller systems, we observe negative ion production in the shape resonance region. This can be related to the possibility in a relatively large system to dissipate positive charge over several channels

Low-Energy Nondipole Effects in Molecular Nitrogen Valence-Shell Photoionization

Observations are reported for the first time of significant nondipole effects in the photoionization of the outer-valence orbitals of diatomic molecules. Measured nondipole angular-distribution parameters for the 3sigmag, 1piu, and 2sigmau shells of N2 exhibit spectral variations with incident photon energies from thresholds to ~200 eV which are attributed via concomitant calculations to particular final-state symmetry waves arising from (E1)[direct-product](M1,E2) radiation-matter interactions first-order in photon momentum. Comparisons with previously reported K-edge studies in N2 verify linear scaling with photon momentum, accounting in part for the significantly enhanced nondipole behavior observed in inner-shell ionization at correspondingly higher momentum values in this molecule

Anion and Cation-yield Spectroscopy of Core-excited SF6

We report an extensive study on total and partial-ion-yield spectroscopy around both the S 2p and F 1s thresholds in SF6. All positive and negative single-ion channels have been measured. Below the F 1s threshold we detect a large variation in relative intensity of the resonant structures according to the specific channel monitored, indicating selective fragmentation. Above threshold, at variance with previous cases described by us, we detect high-intensity structures related to shape resonances not only in the cation channels but also for the anions. We discuss the applicability and limits of a model we have developed for the analysis of shape resonances in anion yields as a function of molecular size

48 Radioterapia chłoniaków narządu wzroku

Celem pracy jest przedstawienie wyników leczenia chłoniaków narządów wzroku ze szczególnym uwzględnieniem radioterapii.Materiał stanowiło 41 chorych (21 kobiet, 20 mężczyzn, w wieku 2,5–87 lat), z chłoniakiem złośliwym oczodołu lub aparatu ochronnego oka. Poza pełną oceną okulistyczną, morfologią z ręcznym rozmazem wykonano biopsję aspiracyjną cienkoigłową (BAC) i badania aspiratu: cytologiczne, immunocytochemiczne, genetyczno-molekularne, cytometrze przepływowym, ewentualnie badania histopatologiczne.Przy podejrzeniu o naciekanie oczodołu: USG RTG KT, z ewentualną równoczesną BAC lub MRI. U wszystkich RTG klatki piersiowej, USG jamy brzuszne, konsultację hematologiczną lub pediatryczną, przy podejrzeniu procesu uogólnionego – mielogram.WynikiU 18/41 chorych rozpoznano zmiany miejscowe: 16 – leczono tylko napromienianiem 20–40 G/T, 2 z naciekiem w powiece dolnej operacyjne + miejscowo Miyomycynę w kroplach. U 23 chorych z uogólnionym chłoniakiem zastosowano chemioterapię, w tym u 12 dodatkowo gammaterapię, a u jednego usunięcie operacyjne guza powieki z następowym napromienianiem.Uzyskanie bardzo dobrych efektów po radioterapii w przypadku form łagodnych chłoniaka i zlokalizowanych w oczodole lub aparacie ochronnym oka sugeruje stosowanie tej formy leczenia bez chemioterapii jako mniej obciążającej i równie skutecznej

Increased Responsiveness to Toll-Like Receptor 4 Stimulation in Peripheral Blood Mononuclear Cells from Patients with Recent Onset Rheumatoid Arthritis

Background. Cell signaling via Toll-like receptors (TLRs) leads to synovial inflammation in rheumatoid arthritis (RA). We aimed to assess effects of TLR2 and TLR4 stimulation on proinflammatory cytokine production by peripheral blood mononuclear cells (PBMCs) from patients with recent-onset RA, osteoarthrosis (OA), and healthy control (HC). Methods. PBMCs were stimulated with LPS, biglycan and cytokine mix. Cytokines were analyzed in supernatants with ELISA. Expression of toll-like receptors mRNA in leukocytes was analyzed using real-time qPCR. Results. PBMCs from RA patients spontaneously produced less IL-6 and TNFα than cells from OA and HC subjects. LPS increased cytokines' production in all groups. In RA patients increase was dramatic (30 to 48-fold and 17 to 31-fold, for respective cytokines) compared to moderate (2 to 8-fold) in other groups. LPS induced 15-HETE generation in PBMCs from RA (mean 251%) and OA patients (mean 43%), although only in OA group, the increase was significant. TLR2 and TLR4 gene expressions decreased in response to cytokine mix, while LPS enhanced TLR2 expression in HC and depressed TLR4 expression in OA patients. Conclusion. PBMCs from recent-onset RA patients are overresponsive to stimulation with bacterial lipopolysaccharide. TLR expression is differentially regulated in healthy and arthritic subjects

Nearest-Neighbor-Atom Core-Hole Transfer in Isolated Molecules

A new phenomenon sensitive only to next-door-neighbor atoms in isolated molecules is demonstrated using angle-resolved photoemission of site-selective core electrons. Evidence for this interatomic core-to-core electron interaction is observable only by measuring nondipolar angular distributions of photoelectrons. In essence, the phenomenon acts as a very fine atomic-scale sensor of nearest-neighbor elemental identity

Nondipole Effects in the Photoionization of Xe 4d5/2 and 4d3/2: Evidence for Quadrupole Satellites

Measurements of nondipole parameters in spin-orbit-resolved Xe 4d photoionization demonstrate dynamical differences arising from relativistic effects. The experimental data do not agree with relativistic random-phase approximation calculations of single ionization dipole and quadrupole channels. It is suggested that the discrepancy is due to the omission of multiple-excitation quadrupole channels, i.e., quadrupole satellite transitions

Second-order Nonlinearities of Anionic 3-dicyanomethylen-5,5-dimethyle-1-[2-(4-hydroxyphenyl)ethenyl)]-cyclohexene

Due to the connecting one π-conjugated group with the two backside donor and acceptor groups, anionic 3-dicyanomethylen-5,5-dimethyle-1-[2-(4-hydroxyphenyl)ethenyl)]-cyclohexene (1) might possess nonlinear optical (NLO) properties. To estimate the potential for second-order NLO behaviour; the electric dipole moments and dispersion-free dipole polarizabilities and first hyperpolarizabilities have been determined by density functional theory (DFT) at B3LYP/6-31++G(d, p) level. Quantum mechanical calculations using time-dependent Hartree-Fock (TDHF) procedure have been utilized to evaluate frequency-dependent second-order nonlinearities of 1. The one-photon absorption (OPA) characterization of 1 has been theoretically obtained by means of configuration interaction (CI) with 6-31G basis set. Our theoretical results on the maximum OPA wavelength, second-order susceptibilities and corresponding microscopic NLO responses are accorded with the previous experimental observations of the investigated compound. The highest occupied molecular orbitals, the lowest unoccupied molecular orbitals and the HOMO-LUMO band gaps for 1 have been also examined by DFT/B3LYP method