计算的脑科学研究及其对数学教育的启示

脑科学研究发现,简单心算主要涉及算术事实的提取,依赖于左半球的语言中枢,而复杂心算激活了左侧顶—额叶网络和双侧颞下回,与视觉空间表征和视觉表象加工有关;精算主要激活左额叶下部区域,而估算激活了两半球更大的区域。在计算过程中所激活的脑区受年龄发展与个体差异以及训练的影响。研究对有效地促进儿童计算能力的发展提供了重要启示。     

Skull size and intelligence, and King Robert Bruce's IQ

An estimate of someone's IQ is a potentially informative personal datum. This study examines the association between external skull measurements and IQ scores, and uses the resulting regression equation to provide an estimate of the IQ of King Robert I of Scotland (Robert Bruce, 1274–1329). Participants were 48 relatively healthy Caucasian men (age 71–76 years) resident in Scotland. Using magnetic resonance imaging data, intracranial volume estimated from external skull length and width correlated greater than .5 (p < .001) with measured intracranial area, which correlates very highly with brain volume. IQ scores estimated from the National Adult Reading Test (NART) correlated .56 (p < .001) with measured intracranial area, and .49 (p < .01) with estimated intracranial volume based on external skull width and length. The partial correlation coefficient of this latter association was .25 (p = .09) after adjustment for measured intracranial area. Thus, actual intracranial area accounts for about 74% of the variance shared by NART and estimated intracranial volume. A cast of the skull of Robert Bruce was measured and its intracranial volume estimated. A regression equation between IQ and estimated intracranial volume, based on data from the 48 subjects, estimated the IQ of Robert Bruce at about 128 (95% confidence interval 106 to  130), i.e. almost two standard deviations above the mean. NART scores show a ceiling effect, so this estimated IQ might be an underestimate. Robert Bruce's estimated high IQ is congruent with his military, political and other intellectual achievements.     

A computational model of event segmentation from perceptual prediction

People tend to perceive ongoing continuous activity as series of discrete events. This partitioning of continuous activity may occur, in part, because events correspond to dynamic patterns that have recurred across different contexts. Recurring patterns may lead to reliable sequential dependencies in observers' experiences, which then can be used to guide perception. The current set of simulations investigated whether this statistical structure within events can be used 1) to develop stable internal representations that facilitate perception and 2) to learn when to update such representations in a self-organizing manner. These simulations demonstrate that experience with recurring patterns enables a system to accurately predict upcoming stimuli within an event, to identify boundaries between such events based on transient increases in prediction error, and to use such boundaries to improve prediction about subsequent activities.     

Decision-making deficit of a patient with axonal damage after traumatic brain injury

Patients with traumatic brain injury (TBI) were reported to have difficulty making advantageous decisions, but the underlying deficits of the network of brain areas involved in this process were not directly examined. We report a patient with TBI who demonstrated problematic behavior in situations of risk and complexity after cerebral injury from a traffic accident. The Iowa gambling task (IGT) was used to reveal his deficits in the decision-making process. To examine underlying deficits of the network of brain areas, we examined T1-weighted structural MRI, diffusion tensor imaging (DTI) and Tc-ECD SPECT in this patient. The patient showed abnormality in IGT. DTI-MRI results showed a significant decrease in fractional anisotropy (FA) in the fasciculus between the brain stem and cortical regions via the thalamus. He showed significant decrease in gray matter volumes in the bilateral insular cortex, hypothalamus, and posterior cingulate cortex, possibly reflecting Wallerian degeneration secondary to the fasciculus abnormalities. SPECT showed significant blood flow decrease in the broad cortical areas including the ventromedial prefrontal cortex (VM). Our study showed that the patient had dysfunctional decision-making process. Microstructural abnormality in the fasciculus, likely from the traffic accident, caused reduced afferent feedback to the brain, resulting in less efficient decision-making. Our findings support the somatic-marker hypothesis (SMH), where somatic feedback to the brain influences the decision-making process.     

Responsiveness and functional connectivity of the scene-sensitive retrosplenial complex in 7–11-year-old children

Brain imaging studies have identified two cortical areas, the parahippocampal place area (PPA) and the retrosplenial complex (RSC), that respond preferentially to the viewing of scenes. Contrary to the PPA, little is known about the functional maturation and cognitive control of the RSC. Here we used functional magnetic resonance imaging and tasks that required attention to scene (or face) images and suppression of face (or scene) images, respectively, to investigate task-dependent modulation of activity in the RSC and whole-brain functional connectivity (FC) of this area in 7–11-year-old children and young adults. We compared responsiveness of the RSC with that of the PPA. The RSC was selectively activated by scene images in both groups, albeit less than the PPA. Children modulated activity between the tasks similarly in the RSC and PPA, and to the same extent as adults in PPA, whereas adults modulated activity in the RSC less than in PPA. In children, the whole brain FC of the RSC was stronger in the Sf than Fs task between the left RSC and right fusiform gyrus. The between groups comparison suggested stronger FC in children than adults in the Sf task between the right RSC and the left inferior parietal lobule and intraparietal sulcus. Together the results suggest that the function of the RSC and the related networks undergo dynamic changes over the development from 7–11-year-old children to adulthood.     

Modeling Mental Spatial Reasoning About Cardinal Directions

This article presents research into human mental spatial reasoning with orientation knowledge. In particular, we look at reasoning problems about cardinal directions that possess multiple valid solutions (i.e., are spatially underdetermined), at human preferences for some of these solutions, and at representational and procedural factors that lead to such preferences. The article presents, first, a discussion of existing, related conceptual and computational approaches; second, results of empirical research into the solution preferences that human reasoners actually have; and, third, a novel computational model that relies on a parsimonious and flexible spatio‐analogical knowledge representation structure to robustly reproduce the behavior observed with human reasoners.     

A logical calculus for controlled monotonicity

In this paper we introduce a new deductive framework for analyzing processes displaying a kind of controlled monotonicity. In particular, we prove the cut-elimination theorem for a calculus involving series-parallel structures over partial orders which is built up from multi-level sequents, an interesting variant of Gentzen-style sequents. More broadly, our purpose is to provide a general, syntactical tool for grasping the combinatorics of non-monotonic processes.     

Novel fabrication of bulk Al with gradient grain size distributions via powder metallurgy

We describe a novel approach to synthesize gradient microstructures, defined hereafter as containing a broad but continuous distribution of grain sizes. These microstructures extend the concept of a bimodal grain size distribution and the ability to design with multiple length scales. We demonstrate the proposed approach via experiments involving cryogenic ball milling of Al–4.5Mg–0.4Mn–0.05Fe and Al–50Mg powder followed by subsequent consolidation. Our results reveal that the grains in the consolidated powder present a gradient size distribution ranging from <100 nm to >3 μm. Moreover, phase composition analysis revealed a unique “interfingered” structure where the two starting phases were intermixed in a complex three-dimensional mesh. Hardness studies of this gradient microstructure show average Vickers hardness values of 200 ± 2.6, 204 ± 4.3 and 266 ± 50 for macrohardness, microhardness and nanoindentation, respectively. The standard deviation values highlight that the gradient microstructure is disordered locally, but homogenous macroscopically.     

Exploring Factor Model Parameters across Continuous Variables with Local Structural Equation Models

Using an empirical data set, we investigated variation in factor model parameters across a continuous moderator variable and demonstrated three modeling approaches: multiple-group mean and covariance structure (MGMCS) analyses, local structural equation modeling (LSEM), and moderated factor analysis (MFA). We focused on how to study variation in factor model parameters as a function of continuous variables such as age, socioeconomic status, ability levels, acculturation, and so forth. Specifically, we formalized the LSEM approach in detail as compared with previous work and investigated its statistical properties with an analytical derivation and a simulation study. We also provide code for the easy implementation of LSEM. The illustration of methods was based on cross-sectional cognitive ability data from individuals ranging in age from 4 to 23 years. Variations in factor loadings across age were examined with regard to the age differentiation hypothesis. LSEM and MFA converged with respect to the conclusions. When there was a broad age range within groups and varying relations between the indicator variables and the common factor across age, MGMCS produced distorted parameter estimates. We discuss the pros of LSEM compared with MFA and recommend using the two tools as complementary approaches for investigating moderation in factor model parameters.     

The Consciousness (R)Evolution Paradigm

Consciousness represents the core of the new paradigm, the unitary, systemic vision, and comprehension that emerges in every field of science, culture, and spirituality. For centuries, consciousness has been divided from matter, the soul from the physical body. Now, in this historical beginning of globalization, we need a new holistic model, a global paradigm based on consciousness that can explain the unitary evolutionary process, the psychosomatic unity of human being, the neurophysiological roots of harmony between peoples and the way to personal and collective evolution of consciousness in order to realize a more conscious, peaceful, and sustainable planetary future. Consciousness is the key of human evolution.