‘Negative of my money,positive of her money’: secondary students’ ways of relating equations to a debt context

We interviewed 40 students each in grades 7 and 11 to investigate their integer-related reasoning. In one task, the students were asked to write and interpret equations related to a story problem about borrowing money from a friend. All the students solved the story problem correctly. However, they reasoned about the problem in different ways. Many students represented the situation numerically without invoking negative numbers, whereas others wrote equations involving negative numbers. When asked to interpret equations involving negative numbers in relation to the story, students did so in two ways. Their responses reflect distinct perspectives concerning the relationship between arithmetic equations and borrowing/owing. We discuss these findings and their implications regarding the role of contexts in integer instruction.     

Automata on ordinals and automaticity of linear orders

We investigate structures recognizable by finite state automata with an input tape of length a limit ordinal. At limits, the set of states which appear unboundedly often before the limit are mapped to a limit state. We describe a method for proving non-automaticity and apply this to determine the optimal bounds for the ranks of linear orders recognized by such automata.     

Measuring the Stability of Results From Supervised Statistical Learning

Stability is a major requirement to draw reliable conclusions when interpreting results from supervised statistical learning. In this article, we present a general framework for assessing and comparing the stability of results, which can be used in real-world statistical learning applications as well as in simulation and benchmark studies. We use the framework to show that stability is a property of both the algorithm and the data-generating process. In particular, we demonstrate that unstable algorithms (such as recursive partitioning) can produce stable results when the functional form of the relationship between the predictors and the response matches the algorithm. Typical uses of the framework in practical data analysis would be to compare the stability of results generated by different candidate algorithms for a dataset at hand or to assess the stability of algorithms in a benchmark study. Code to perform the stability analyses is provided in the form of an R package. Supplementary material for this article is available online.     

Prostate‐Cancer‐Targeted N‐(2‐Hydroxypropyl)methacrylamide Copolymer/Docetaxel Conjugates

Biodistribution, pharmacokinetics, and efficacy of prostate‐cancer‐targeted HPMA copolymer/DTX conjugates are evaluated in nude mice bearing prostate cancer C4‐2 xenografts. PSMA‐specific monoclonal antibodies 3F/11 are used as the targeting moiety. Control conjugates contain either non‐specific IgG or no IgG. The ratios of tumor accumulation to total background organs (heart, lung, kidney, liver, spleen and blood) accumulation increase substantially with time for the targeted conjugate, and the ratio at 48 h is 7‐fold higher than that at 6 h. Preliminary evaluation of the efficacy of the conjugates in vivo show tumor growth inhibition for all HPMA copolymer/DTX conjugates.

     

Total synthesis of (+)-cyperolone

The total synthesis of (+)-cyperolone, an eudesmane-derived sesquiterpenoid from Cyperus rotundus, is described. The de novo synthesis was accomplished via a 15 step sequence starting from (R)-(-)-carvone. The synthetic route features a platinum-catalyzed cycloisomerization to rapidly construct the bicyclic core from a 3-silyloxy-1,5-enyne intermediate.     

A collision algorithm for anisotropic disperse flows based on ellipsoidal parcel representations

In this study, a new approach to the prediction of collision probabilities is proposed, which is specifically derived for Lagrangian Monte Carlo simulations of highly anisotropic disperse flows. The collision probability formulation eliminates the influence of the collision mesh by introduction of a parcel diameter. Two non-parametric parcel diameter estimators are given, an isotropic parcel diameter estimator for homogeneous droplet clouds, and an anisotropic parcel diameter estimator for inhomogeneous droplet clouds of reduced dimensionality, which obtains an ellipsoidal parcel representation from a weighted principal component analysis of the parcel population. The new formulation effectively reduces the parameters for spatial resolution from two (mesh size, number of parcels) to one (number of parcels only). For validation, simple synthetic test cases are run that allow a comparison of the collision probability formulation to purely stochastic and purely deterministic schemes. Dependence on numerical parameters is tested exemplary with a highly anisotropic hollow-cone spray for gasoline direct injection.     

Ultraviolet resonance Raman spectroscopy of locked single‐stranded oligo(dA) reveals conformational implications of the locked ribose in LNA

We report here the first UV resonance Raman spectroscopic (UVRRS) study on locked nucleic acid (LNA) oligomers. Locking a base in nucleic acid (NA) oligomers produces a conformational change in the glycosyl bond between backbone and base. We present evidence of this change in LNAs when compared to their natural analogs using UVRRS. Wavenumber downshifts and peak amplitude increases, especially of the ∼1481 cm⁻¹ peak that is a spectral marker for part of the glycosyl bond, correlate with the fraction of locked bases when single‐stranded oligomers incorporating up to three locked bases were examined. By varying the position of the locked base within a fixed length sequence, we conclude that one, or at most two bases, on either side of the lock is affected. We further conclude from these data, and previously published reports, that the conformation of LNA is determined by imidazole–imidazole and pyrimidine–pyrimidine repulsion and imidazole–pyrimidine attraction in contrast to dispersion attraction‐dependent aggregation in the B conformation of DNA. Copyright © 2009 John Wiley & Sons, Ltd.     

Entanglement witnesses and geometry of entanglement of two-qutrit states

We construct entanglement witnesses with regard to the geometric structure of the Hilbert-Schmidt space and investigate the geometry of entanglement. In particular, for a two-parameter family of two-qutrit states that are part of the magic simplex, we calculate the Hilbert-Schmidt measure of entanglement. We present a method to detect bound entanglement which is illustrated for a three-parameter family of states. In this way, we discover new regions of bound entangled states. Furthermore, we outline how to use our method to distinguish entangled from separable states.