The Interplay Between Fairness and Randomness in a Spatial Computer Game

This article describes how children use an expressive microworld to articulate ideas about how to make a game seem fair with the use of randomness. Our aim in this study is to disentangle different flavours of fairness and to find out how children used each flavour to make sense of potentially complex behaviour. In order to achieve this, a spatial computer game was designed to enable children to examine the consequences of their attempts to make the game fair. The study investigates how 23 children, aged between 5.5 and 8 years, engaged in constructing a crucial part of a mechanism for a fair spatial lottery machine (microworld). In particular, the children tried to construct a fair game given a situation in which the key elements happened randomly. The children could select objects, determine their properties, and arrange their spatial layout in the machine. The study is based on task-based interviewing of children who were interacting with the computer game. The study shows that children have various cognitive resources for constructing a random fair environment. The spatial arrangement, the visualisation and the manipulations in the lottery machine allow us gain a view into the children’s thinking of the two central concepts, fairness and randomness. The paper reports on two main strategies by which the children attempted to achieve a balance in the lottery machine. One involves arranging the balls symmetrically and the other randomly. We characterize the nature of the thinking in these two strategies: the first we see as deterministic and the latter as stochastic, exploiting the random collisions of the ball. In this article we trace how the children’s thinking moved between these two perspectives.

Stable and Oriented Liquid Crystal Droplets Stabilized by Imidazolium Ionic Liquids

Liquid crystals represent a fascinating intermediate state of matter, with dynamic yet organized molecular features and untapped opportunities in sensing. Several works report the use of liquid crystal droplets formed by microfluidics and stabilized by surfactants such as sodium dodecyl sulfate (SDS). In this work, we explore, for the first time, the potential of surface-active ionic liquids of the imidazolium family as surfactants to generate in high yield, stable and oriented liquid crystal droplets. Our results show that [C₁₂MIM][Cl], in particular, yields stable, uniform and monodisperse droplets (diameter 74 ± 6 µm; PDI = 8%) with the liquid crystal in a radial configuration, even when compared with the standard SDS surfactant. These findings reveal an additional application for ionic liquids in the field of soft matter.     

Normal correlation coefficient of non-normal variables using piece-wise linear approximation

The correlation coefficient of non-normal variables is expressed as a function of the correlation coefficient of normal variables using piece-wise linear approximation of each univariate transform of normal to anything, and the second order moments of a multiply truncated bivariate normal distribution. For the inverse problem, an algorithm iterates this analytic function in order to assign a normal correlation coefficient to two non-normal variables. The algorithm is applied for the generation of randomized bivariate samples with given correlation coefficient and marginal distributions and used in a randomization test for bivariate nonlinearity. The test correctly does not reject the null hypothesis of linear correlation if the nonlinearity is plausible and due to the sample transform alone.     

A Versatile Monomer for Preparing Well-Defined Functional Polycarbonates and Poly(ester-carbonates)

Despite the increasing demands for functional degradable biomaterials, strategies for generating materials with modular compositions and well-defined functionalities from common building blocks are still lacking. Here we report an azido-functionalized cyclic carbonate monomer, AzDXO, that exhibited controlled/"living" ring-opening polymerization kinetics under the catalysis of 1,8-diazabicyclo[5.4.0]-undec-7-ene. Homopolymerization of AzDXO and copolymerization of AzDXO with lactide resulted in polycarbonate and poly(ester-carbonates) with well-defined composition and narrow polydispersity. Further side-chain functionalizations of these polymers were accomplished under facile conditions via copper-catalyzed or copper-free strain-promoted azido-alkyne cyclcoaddition. This versatile monomer building block, obtainable in two steps without tedious purifications, provides a practical solution to the preparation of well-defined functional polycarbonates and poly(ester-carbonates).     

A Chemogenetic Approach for the Optical Monitoring of Voltage in Neurons

Optical monitoring of neuronal voltage using fluorescent indicators is a powerful approach for the interrogation of the cellular and molecular logic of the nervous system. Herein, a semisynthetic tethered voltage indicator (STeVI1) based upon nile red is described that displays voltage sensitivity when genetically targeted to neuronal membranes. This environmentally sensitive probe allows for wash‐free imaging and faithfully detects supra‐ and sub‐threshold activity in neurons.     

Use of fat suppression in R₂ relaxometry with MRI for the quantification of tissue iron overload in beta-thalassemic patients

Purpose

To assess the performance and results of R₂ relaxometry using a fat-suppressed (FS) multiecho sequence and compare these to conventional R₂ relaxometry in estimating tissue iron overload.

Materials and Methods

Relaxation rate values (R₂=1/T2) of the liver, spleen, pancreas and vertebral bone marrow (VBM) were estimated in 21 patients with β-thalassemia major, using a respiratory-triggered 16-echo Carr-Purcell-Meiboom-Gill (CPMG) spin-echo sequence before (R₂) and after (R₂ FS) the application of chemically selective fat suppression.

Results

Hepatic and splenic R₂ FS values correlated with respective R₂ values (r=0.98 and r=0.96, P<.001), whereas correlations between R₂ FS and R₂ values for pancreas and VBM were not statistically significant. Bland–Altman plots show disagreement between R₂ and R₂ FS values, particularly for pancreas and VBM. Hepatic, pancreatic and VBM R₂ FS values correlated with serum ferritin (r=0.88, P<.001; r=0.51, P<.003; and r=0.75, P<.002, respectively). Hepatic R₂ FS values correlated with splenic R₂ FS (r=0.77, P<.03), pancreatic R₂ FS (r=0.61, P<.006) and VBM R₂ FS values (r=0.70, P<.001), whereas pancreatic R₂ FS values correlated also with VMB R₂ FS values. On the contrary, among the R₂ values of the above tissues, obtained without fat suppression, only hepatic R₂ values correlated with serum ferritin, whereas no correlation was documented between hepatic and pancreatic or VBM R₂ values. The application of fat suppression did not improve breathing or flow artifacts.

Conclusion

Application of fat suppression in the standard CPMG sequence improved the capability of MRI in noninvasive quantification of iron, particularly in lipid-rich tissues, such as vertebral bone marrow (VBM) and pancreas.     

Convergence of Birkhoff Normal form for Essentially Isochronous Systems

We reconsider the problem of the convergence of Birkhoff's normal form for a system of perturbed harmonic oscillators, under the condition that the system is essentially isochronous. In contrast with previous proofs based on the so called quadratically convergent method, the present proof uses only classical expansions in a parameter. This allows us to bring into light some mechanisms of accumulation of small divisors, which can be useful in more complicated and interesting cases. These same mechanisms allow us to prove the theorem with the Bruno condition on the frequencies in a very natural way.