The 'algebra as object' analogy: a view from school

Treating algebraic symbols as objects (eg. “‘a’ means ‘apple’”) is a means of introducing elementary simplification of algebra, but causes problems further on. This current school-based research included an examination of texts still in use in the mathematics department, and interviews with mathematics teachers, year 7 pupils and then year 10 pupils asking them how they would explain, “3a + 2a = 5a” to year 7 pupils. Results included the notion that the ‘algebra as object’ analogy can be found in textbooks in current usage, including those recently published. Teachers knew that they were not ‘supposed’ to use the analogy but not always clear why, nevertheless stating methods of teaching consistent with an‘algebra as object’ approach. Year 7 pupils did not explicitly refer to ‘algebra as object’, although some of their responses could be so interpreted. In the main, year 10 pupils used ‘algebra as object’ to explain simplification of algebra, with some complicated attempts to get round the limitations. Further research would look to establish whether the appearance of ‘algebra as object’ in pupils’ thinking between year 7 and 10 is consistent and, if so, where it arises. Implications also are for on-going teacher training with alternatives to introducing such simplification.

Spoken word recognition in adolescents with autism spectrum disorders and specific language impairment

Spoken word recognition, during gating, appears intact in specific language impairment (SLI). This study used gating to investigate the process in adolescents with autism spectrum disorders plus language impairment (ALI). Adolescents with ALI, SLI, and typical language development (TLD), matched on nonverbal IQ listened to gated words that varied in frequency (low/high) and number of phonological onset neighbors (low/high density). Adolescents with ALI required more speech input to initially identify low-frequency words with low competitor density than those with SLI and those with TLD, who did not differ. These differences may be due to less well specified word form representations in ALI.

A search for invariant relative satellite motion

This report presents the canonical Hamiltonian formulation of relative satellite motion. The unperturbed Hamiltonian model is shown to be equivalent to the well known Hill-Clohessy-Wilshire (HCW) linear formulation. The in°uence of perturbations of the nonlinear Gravitational potential and the oblateness of the Earth; J2 perturbations are also modelled within the Hamiltonian formulation. The modelling incorporates eccentricity of the reference orbit. The corresponding Hamiltonian vector ¯elds are computed and implemented in Simulink. A numerical method is presented aimed at locating periodic or quasi-periodic relative satellite motion. The numerical method outlined in this paper is applied to the Hamiltonian system. Although the orbits considered here are weakly unstable at best, in the case of eccentricity only, the method ¯nds exact periodic orbits. When other perturbations such as nonlinear gravitational terms are added, drift is signicantly reduced and in the case of the J2 perturbation with and without the nonlinear gravitational potential term, bounded quasi-periodic solutions are found. Advantages of using Newton's method to search for periodic or quasi-periodic relative satellite motion include simplicity of implementation, repeatability of solutions due to its non-random nature, and fast convergence. Given that the use of bounded or drifting trajectories as control references carries practical di±culties over long-term missions, Principal Component Analysis (PCA) is applied to the quasi-periodic or slowly drifting trajectories to help provide a closed reference trajectory for the implementation of closed loop control. In order to evaluate the e®ect of the quality of the model used to generate the periodic reference trajectory, a study involving closed loop control of a simulated master/follower formation was performed. 2 The results of the closed loop control study indicate that the quality of the model employed for generating the reference trajectory used for control purposes has an important in°uence on the resulting amount of fuel required to track the reference trajectory. The model used to generate LQR controller gains also has an e®ect on the e±ciency of the controller.

Collision prediction of a moving object within a virtual world

This paper provides a solution for predicting moving/moving and moving/static collisions of objects within a virtual environment. Feasible prediction in real-time virtual worlds can be obtained by encompassing moving objects within a sphere and static objects within a convex polygon. Fast solutions are then attainable by describing the movement of objects parametrically in time as a polynomial.

Improving sequence-based fold recognition by using 3D model quality assessment

Motivation: The ability of a simple method (MODCHECK) to determine the sequence–structure compatibility of a set of structural models generated by fold recognition is tested in a thorough benchmark analysis. Four Model Quality Assessment Programs (MQAPs) were tested on 188 targets from the latest LiveBench-9 automated structure evaluation experiment. We systematically test and evaluate whether the MQAP methods can successfully detect native-likemodels. Results: We show that compared with the other three methods tested MODCHECK is the most reliable method for consistently performing the best top model selection and for ranking the models. In addition, we show that the choice of model similarity score used to assess a model's similarity to the experimental structure can influence the overall performance of these tools. Although these MQAP methods fail to improve the model selection performance for methods that already incorporate protein three dimension (3D) structural information, an improvement is observed for methods that are purely sequence-based, including the best profile–profile methods. This suggests that even the best sequence-based fold recognition methods can still be improved by taking into account the 3D structural information.

Prediction of novel and analogous folds using fragment assembly and fold recognition

A number of new and newly improved methods for predicting protein structure developed by the Jones–University College London group were used to make predictions for the CASP6 experiment. Structures were predicted with a combination of fold recognition methods (mGenTHREADER, nFOLD, and THREADER) and a substantially enhanced version of FRAGFOLD, our fragment assembly method. Attempts at automatic domain parsing were made using DomPred and DomSSEA, which are based on a secondary structure parsing algorithm and additionally for DomPred, a simple local sequence alignment scoring function. Disorder prediction was carried out using a new SVM-based version of DISOPRED. Attempts were also made at domain docking and “microdomain” folding in order to build complete chain models for some targets.

Improvement of the GenTHREADER method for genomic fold recognition

Motivation: In order to enhance genome annotation, the fully automatic fold recognition method GenTHREADER has been improved and benchmarked. The previous version of GenTHREADER consisted of a simple neural network which was trained to combine sequence alignment score, length information and energy potentials derived from threading into a single score representing the relationship between two proteins, as designated by CATH. The improved version incorporates PSI-BLAST searches, which have been jumpstarted with structural alignment profiles from FSSP, and now also makes use of PSIPRED predicted secondary structure and bi-directional scoring in order to calculate the final alignment score. Pairwise potentials and solvation potentials are calculated from the given sequence alignment which are then used as inputs to a multi-layer, feed-forward neural network, along with the alignment score, alignment length and sequence length. The neural network has also been expanded to accommodate the secondary structure element alignment (SSEA) score as an extra input and it is now trained to learn the FSSP Z-score as a measurement of similarity between two proteins. Results: The improvements made to GenTHREADER increase the number of remote homologues that can be detected with a low error rate, implying higher reliability of score, whilst also increasing the quality of the models produced. We find that up to five times as many true positives can be detected with low error rate per query. Total MaxSub score is doubled at low false positive rates using the improved method.

Benchmarking secondary structure prediction for fold recognition

If secondary structure predictions are to be incorporated into fold recognition methods, an assessment of the effect of specific types of errors in predicted secondary structures on the sensitivity of fold recognition should be carried out. Here, we present a systematic comparison of different secondary structure prediction methods by measuring frequencies of specific types of error. We carry out an evaluation of the effect of specific types of error on secondary structure element alignment (SSEA), a baseline fold recognition method. The results of this evaluation indicate that missing out whole helix or strand elements, or predicting the wrong type of element, is more detrimental than predicting the wrong lengths of elements or overpredicting helix or strand. We also suggest that SSEA scoring is an effective method for assessing accuracy of secondary structure prediction and perhaps may also provide a more appropriate assessment of the “usefulness” and quality of predicted secondary structure, if secondary structure alignments are to be used in fold recognition.

What are the baselines for protein fold recognition?

What constitutes a baseline level of success for protein fold recognition methods? As fold recognition benchmarks are often presented without any thought to the results that might be expected from a purely random set of predictions, an analysis of fold recognition baselines is long overdue. Given varying amounts of basic information about a protein—ranging from the length of the sequence to a knowledge of its secondary structure—to what extent can the fold be determined by intelligent guesswork? Can simple methods that make use of secondary structure information assign folds more accurately than purely random methods and could these methods be used to construct viable hierarchical classifications?

A multinomial model of applying recognition to judge between multiple alternatives

Proponents of the “fast and frugal” approach to decision-making suggest that inferential judgments are best made on the basis of limited information. For example, if only one of two cities is recognized and the task is to judge which city has the larger population, the recognition heuristic states that the recognized city should be selected. In preference choices with >2 options, it is also standard to assume that a “consideration set”, based upon some simple criterion, is established to reduce the options available. A multinomial processing tree model is outlined which provides the basis for estimating the extent to which recognition is used as a criterion in establishing a consideration set for inferential judgments.

Spectrally invariant approximation within atmospheric radiative transfer

Certain algebraic combinations of single scattering albedo and solar radiation reflected from, or transmitted through, vegetation canopies do not vary with wavelength. These ‘‘spectrally invariant relationships’’ are the consequence of wavelength independence of the extinction coefficient and scattering phase function in veg- etation. In general, this wavelength independence does not hold in the atmosphere, but in cloud-dominated atmospheres the total extinction and total scattering phase function vary only weakly with wavelength. This paper identifies the atmospheric conditions under which the spectrally invariant approximation can accu- rately describe the extinction and scattering properties of cloudy atmospheres. The validity of the as- sumptions and the accuracy of the approximation are tested with 1D radiative transfer calculations using publicly available radiative transfer models: Discrete Ordinate Radiative Transfer (DISORT) and Santa Barbara DISORT Atmospheric Radiative Transfer (SBDART). It is shown for cloudy atmospheres with cloud optical depth above 3, and for spectral intervals that exclude strong water vapor absorption, that the spectrally invariant relationships found in vegetation canopy radiative transfer are valid to better than 5%. The physics behind this phenomenon, its mathematical basis, and possible applications to remote sensing and climate are discussed.

Does high-frequency repetitive transcranial magnetic stimulation produce residual and/or cumulative effects within an experimental session?

A common procedure for studying the effects on cognition of repetitive transcranial magnetic stimulation (rTMS) is to deliver rTMS concurrent with task performance, and to compare task performance on these trials versus on trials without rTMS. Recent evidence that TMS can have effects on neural activity that persist longer than the experimental session itself, however, raise questions about the assumption of the transient nature of rTMS that underlies many concurrent (or "online") rTMS designs. To our knowledge, there have been no studies in the cognitive domain examining whether the application of brief trains of rTMS during specific epochs of a complex task may have effects that spill over into subsequent task epochs, and perhaps into subsequent trials. We looked for possible immediate spill-over and longer-term cumulative effects of rTMS in data from two studies of visual short-term delayed recognition. In 54 subjects, 10-Hz rTMS trains were applied to five different brain regions during the 3-s delay period of a spatial task, and in a second group of 15 subjects, electroencephalography (EEG) was recorded while 10-Hz rTMS was applied to two brain areas during the 3-s delay period of both spatial and object tasks. No evidence for immediate effects was found in the comparison of the memory probe-evoked response on trials that were vs. were not preceded by delay-period rTMS. No evidence for cumulative effects was found in analyses of behavioral performance, and of EEG signal, as a function of task block. The implications of these findings, and their relation to the broader literature on acute vs. long-lasting effects of rTMS, are considered.

Keeping the world at hand: rapid visuomotor processing for hand-object interactions

The existence of hand-centred visual processing has long been established in the macaque premotor cortex. These hand-centred mechanisms have been thought to play some general role in the sensory guidance of movements towards objects, or, more recently, in the sensory guidance of object avoidance movements. We suggest that these hand-centred mechanisms play a specific and prominent role in the rapid selection and control of manual actions following sudden changes in the properties of the objects relevant for hand-object interactions. We discuss recent anatomical and physiological evidence from human and non-human primates, which indicates the existence of rapid processing of visual information for hand-object interactions. This new evidence demonstrates how several stages of the hierarchical visual processing system may be bypassed, feeding the motor system with hand-related visual inputs within just 70 ms following a sudden event. This time window is early enough, and this processing rapid enough, to allow the generation and control of rapid hand-centred avoidance and acquisitive actions, for aversive and desired objects, respectively

Empathy and emotion recognition in people with autism, first-degree relatives, and controls

Empathy is the lens through which we view others' emotion expressions, and respond to them. In this study, empathy and facial emotion recognition were investigated in adults with autism spectrum conditions (ASC; N=314), parents of a child with ASC (N=297) and IQ-matched controls (N=184). Participants completed a self-report measure of empathy (the Empathy Quotient [EQ]) and a modified version of the Karolinska Directed Emotional Faces Task (KDEF) using an online test interface. Results showed that mean scores on the EQ were significantly lower in fathers (p<0.05) but not mothers (p>0.05) of children with ASC compared to controls, whilst both males and females with ASC obtained significantly lower EQ scores (p<0.001) than controls. On the KDEF, statistical analyses revealed poorer overall performance by adults with ASC (p<0.001) compared to the control group. When the 6 distinct basic emotions were analysed separately, the ASC group showed impaired performance across five out of six expressions (happy, sad, angry, afraid and disgusted). Parents of a child with ASC were not significantly worse than controls at recognising any of the basic emotions, after controlling for age and non-verbal IQ (all p>0.05). Finally, results indicated significant differences between males and females with ASC for emotion recognition performance (p<0.05) but not for self-reported empathy (p>0.05). These findings suggest that self-reported empathy deficits in fathers of autistic probands are part of the 'broader autism phenotype'. This study also reports new findings of sex differences amongst people with ASC in emotion recognition, as well as replicating previous work demonstrating empathy difficulties in adults with ASC. The use of empathy measures as quantitative endophenotypes for ASC is discussed.