Emergence of tables as first-graders cope with modelling tasks

In this action research, first-graders were challenged to cope with a sequence of modelling tasks involving an analysis of given situations and choices of mathematical tools. In the course of the sequence, they underwent a change in the nature of their problem-solving processes and developed modelling competencies. Moreover, during the task sequence, the first-graders spontaneously discovered the power of organizing problem data in a table. They did not merely use their existing mathematical knowledge, but also ‘reinvented’ tables as a new mathematical tool. This paper describes the gradual development of this tool as the children moved along the task sequence. Notably, the first-graders exhibited this progress in spite of having relatively little mathematical knowledge.     

Molecular structures and dynamics of the stepwise activation mechanism of a matrix metalloproteinase zymogen: challenging the cysteine switch dogma

Activation of matrix metalloproteinase zymogen (pro-MMP) is a vital homeostatic process, yet its molecular basis remains unresolved. Using stopped-flow X-ray spectroscopy of the active site zinc ion, we determined the temporal sequence of pro-MMP-9 activation catalyzed by tissue kallikrein protease in milliseconds to several minutes. The identity of three intermediates seen by X-ray spectroscopy was corroborated by molecular dynamics simulations and quantum mechanics/molecular mechanics calculations. The cysteine-zinc interaction that maintains enzyme latency is disrupted via active-site proton transfers that mediate transient metal-protein coordination events and eventual binding of water. Unexpectedly, these events ensue as a direct result of complexation of pro-MMP-9 and kallikrein and occur before proteolysis and eventual dissociation of the pro-peptide from the catalytic site. Here we demonstrate the synergism among long-range protein conformational transitions, local structural rearrangements, and fine atomic events in the process of zymogen activation.     

Cognitive‐Performance Recovery of Alzheimer's Disease Model Mice by Modulation of Early Soluble Amyloidal Assemblies

A rationally designed oligomerization inhibitor interacts with early intermediate assemblies of amyloid‐β polypeptide (Aβ) through the aromatic elements and inhibits their assembly into the toxic oligomers that cause Alzheimer's disease by a unique C^α‐methylation β‐breakage strategy. The electrostatic potential of the low‐energy conformation of the dipeptide inhibitor bound to Aβ is shown.

     

The game for the speed of convergence in repeated games of incomplete information

We consider an infinitely repeated two-person zero-sum game with incomplete information on one side, in which the maximizer is the (more) informed player. Such games have value v _∞ (p) for all 0≤p≤1. The informed player can guarantee that all along the game the average payoff per stage will be greater than or equal to v _∞ (p) (and will converge from above to v _∞ (p) if the minimizer plays optimally). Thus there is a conflict of interest between the two players as to the speed of convergence of the average payoffs-to the value v _∞ (p). In the context of such repeated games, we define a game for the speed of convergence, denoted SG _∞ (p), and a value for this game. We prove that the value exists for games with the highest error term, i.e., games in which v _n (p)− v _∞ (p) is of the order of magnitude of . In that case the value of SG _∞ (p) is of the order of magnitude of . We then show a class of games for which the value does not exist. Given any infinite martingale 𝔛^∞={X _k }^∞ _k=1, one defines for each n : V _n (𝔛^∞) ≔E∑ⁿ _k=1 |X _k+1 − X _k|. For our first result we prove that for a uniformly bounded, infinite martingale 𝔛^∞, V _n (𝔛^∞) can be of the order of magnitude of n ^1/2−ε, for arbitrarily small ε>0. Received January 1999/Final version April 2002     

Amine-tetrachloromethane charge transfer complexes: a structural and computational study

Abstract

Amine-tetrachloromethane charge-transfer complexes have recently been shown to be useful intermediates in transition-metal free solar light-assisted organic synthetic chemistry. Of particular promise is the complex of 1,4-diazabicyclo[2.2.2]octane (DABCO) which may serve as a starting point for several potential reactions involving oxidation of organic compounds. Here we disclose the crystal structure of the [DABCO???CCl₄] complex, and computational studies of two possible complex structures in their ground state, as well as in their first singlet and first triplet excited states.     

Faster algorithms for computing longest common increasing subsequences

We present algorithms for finding a longest common increasing subsequence of two or more input sequences. For two sequences of lengths n and m, where m?n, we present an algorithm with an output-dependent expected running time of and O(m) space, where ? is the length of an LCIS, σ is the size of the alphabet, and Sort is the time to sort each input sequence. For k?3 length-n sequences we present an algorithm which improves the previous best bound by more than a factor k for many inputs. In both cases, our algorithms are conceptually quite simple but rely on existing sophisticated data structures. Finally, we introduce the problem of longest common weakly-increasing (or non-decreasing) subsequences (LCWIS), for which we present an -time algorithm for the 3-letter alphabet case. For the extensively studied longest common subsequence problem, comparable speedups have not been achieved for small alphabets.     

Four (algorithms) in one (bag): an integrative framework of knowledge for teaching the standard algorithms of the basic arithmetic operations

In this article we present an integrative framework of knowledge for teaching the standard algorithms of the four basic arithmetic operations. The framework is based on a mathematical analysis of the algorithms, a connectionist perspective on teaching mathematics and an analogy with previous frameworks of knowledge for teaching arithmetic operations with rational numbers. In order to evaluate the potential applicability of the framework to task design, it was used for the design of mathematical learning tasks for teachers. The article includes examples of the tasks, their theoretical analysis, and empirical evidence of the sensitivity of the tasks to variations in teachers’ knowledge of the subject. This evidence is based on a study of 46 primary school teachers. The article concludes with remarks on the applicability of the framework to research and practice, highlighting its potential to encourage teaching the four algorithms with an emphasis on conceptual understanding.     

Silica-stabilized gold island films for transmission localized surface plasmon sensing

Ultrathin gold films prepared by evaporation of sub-percolation layers (typically up to 10 nm nominal thickness) onto transparent substrates form arrays of well-defined metal islands. Such films display a characteristic surface plasmon (SP) absorption band, conveniently measured by transmission spectroscopy. The SP band intensity and position are sensitive to the film morphology (island shape and inter-island separation) and the effective dielectric constant of the surrounding medium. The latter has been exploited for chemical and biological sensing in the transmission localized surface plasmon resonance (T-LSPR) mode. A major concern in the development of T-LSPR sensors based on Au island films is instability, manifested as change in the SP absorbance following immersion in organic solvents and aqueous solutions. The latter may present a problem in the use of Au island-based transducers for biological sensing, usually carried out in aqueous media. Here, we describe a facile method for stabilizing Au island films while maintaining a high sensitivity of the SP absorbance to analyte binding. Stabilization is achieved by coating the Au islands with an ultrathin silica layer, ca. 1.5 nm thick, deposited by a sol-gel procedure on an intermediate mercaptosilane monolayer. The silica coating is prepared using a modified literature procedure, where a change in the reaction conditions from room temperature to 90 degrees C shortened the deposition time from days to hours. The system was characterized by UV-vis spectroscopy, ellipsometry, XPS, HRSEM, AFM, and cyclic voltammetry. The ultrathin silica coating stabilizes the optical properties of the Au island films toward immersion in water, phosphate buffer saline (PBS), and various organic solvents, thus providing proper conditions where the optical response is sensitive only to changes in the effective dielectric constant of the immediate environment. The silica layer is thin enough to afford high T-LSPR sensitivity, while the hydroxyl groups on its surface enable chemical modification for binding of receptor molecules. The use of silica-encapsulated Au island films as a stable and effective platform for T-LSPR sensing is demonstrated.     

On the Fourier tails of bounded functions over the discrete cube

In this paper we consider bounded real-valued functions over the discrete cube, f: {−1, 1}ⁿ → [−1, 1]. Such functions arise naturally in theoretical computer science, combinatorics, and the theory of social choice. It is often interesting to understand when these functions essentially depend on few coordinates. Our main result is a dichotomy that includes a lower bound on how fast the Fourier coefficients of such functions can decay: we show that