数学与文化2——视觉完美性：数学与创造

创造在人类所有活动中扮演着一个重要的角色。本书是《数学与文化》丛书中的第二本，着重介绍数学、文化与众多领域的创造之间的紧密联系，这些领域包括建筑、当代艺术、地理、计算机绘图、文艺、戏剧和电影。近年来，得益于计算机绘图的出现，可视化在数学的某些部分中的角色越来越引人注目。这类新“可视化数学”必然会为艺术创造与数学之间的联系打开新路，本书收集了关于这些问题的论文。     

Cornea regeneration in the Pacific giant octopus,Octopus dofleini,and the common octopus,O. vulgaris

Summary Cornea regeneration in a Pacific giant octopus,Octopus dofleini, occurred within 10 days after the injury was observed. Surgical removal of the cornea in 2 common octopi,O. vulgaris experimentally duplicated this cornea regeneration within a 10-day period. It is, therefore, concluded that besides sucking discs, arms, and nerve fibres, octopi can also regenerated corneal tissue.The authors would like to thank U. E. Friese, B. Borowski, P. Burn, J.W. Atz, G.J. Nelson, H. Feinberg, P. Fenimore, C. Roper, M. Nixon, M. Segalla, G. Clark, D.O. Calligaro, J.M. Anderson and R.J. Koestler for assistance and advice. Illustrations were drawn by G.D. This work was supported by the New York Aquarium of the New York Zoological Society, while G.D. was at the New York Aquarium.     

Genome of the marsupial Monodelphis domestica reveals innovation in non-coding sequences

We report a high-quality draft of the genome sequence of the grey, short-tailed opossum (Monodelphis domestica). As the first metatherian ('marsupial') species to be sequenced, the opossum provides a unique perspective on the organization and evolution of mammalian genomes. Distinctive features of the opossum chromosomes provide support for recent theories about genome evolution and function, including a strong influence of biased gene conversion on nucleotide sequence composition, and a relationship between chromosomal characteristics and X chromosome inactivation. Comparison of opossum and eutherian genomes also reveals a sharp difference in evolutionary innovation between protein-coding and non-coding functional elements. True innovation in protein-coding genes seems to be relatively rare, with lineage-specific differences being largely due to diversification and rapid turnover in gene families involved in environmental interactions. In contrast, about 20% of eutherian conserved non-coding elements (CNEs) are recent inventions that postdate the divergence of Eutheria and Metatheria. A substantial proportion of these eutherian-specific CNEs arose from sequence inserted by transposable elements, pointing to transposons as a major creative force in the evolution of mammalian gene regulation.     

Miniature eye movements enhance fine spatial detail

Our eyes are constantly in motion. Even during visual fixation, small eye movements continually jitter the location of gaze. It is known that visual percepts tend to fade when retinal image motion is eliminated in the laboratory. However, it has long been debated whether, during natural viewing, fixational eye movements have functions in addition to preventing the visual scene from fading. In this study, we analysed the influence in humans of fixational eye movements on the discrimination of gratings masked by noise that has a power spectrum similar to that of natural images. Using a new method of retinal image stabilization, we selectively eliminated the motion of the retinal image that normally occurs during the intersaccadic intervals of visual fixation. Here we show that fixational eye movements improve discrimination of high spatial frequency stimuli, but not of low spatial frequency stimuli. This improvement originates from the temporal modulations introduced by fixational eye movements in the visual input to the retina, which emphasize the high spatial frequency harmonics of the stimulus. In a natural visual world dominated by low spatial frequencies, fixational eye movements appear to constitute an effective sampling strategy by which the visual system enhances the processing of spatial detail.     

Rapid Manufacturing of Non-Assembly Complex Micro-Devices by Microstereolithography

This paper introduces a non-assembly manufacturing case with microstereolithography technology. The design and manufacturing process of a pneumatic thrust bearing is described, and a special tessellation method is developed to further improve the capability of the manufacturing system thus bigger products can also be easily manufactured. Implemented in a layer-by-layer fashion, stereolithography has been used for the rapid manufacturing of complex devices, and it avoids the expensive assembly process in the traditional manufacturing. This paper presents that microstereolithography can produce high-resolution products with intricate details, small openings, and smooth surfaces. The potential of the microstereolithograhy technique is explored for the rapid manufacturing of small and complex objects.     

A murine lung cancer co-clinical trial identifies genetic modifiers of therapeutic response

Targeted therapies have demonstrated efficacy against specific subsets of molecularly defined cancers. Although most patients with lung cancer are stratified according to a single oncogenic driver, cancers harbouring identical activating genetic mutations show large variations in their responses to the same targeted therapy. The biology underlying this heterogeneity is not well understood, and the impact of co-existing genetic mutations, especially the loss of tumour suppressors, has not been fully explored. Here we use genetically engineered mouse models to conduct a 'co-clinical' trial that mirrors an ongoing human clinical trial in patients with KRAS-mutant lung cancers. This trial aims to determine if the MEK inhibitor selumetinib (AZD6244) increases the efficacy of docetaxel, a standard of care chemotherapy. Our studies demonstrate that concomitant loss of either p53 (also known as Tp53) or Lkb1 (also known as Stk11), two clinically relevant tumour suppressors, markedly impaired the response of Kras-mutant cancers to docetaxel monotherapy. We observed that the addition of selumetinib provided substantial benefit for mice with lung cancer caused by Kras and Kras and p53 mutations, but mice with Kras and Lkb1 mutations had primary resistance to this combination therapy. Pharmacodynamic studies, including positron-emission tomography (PET) and computed tomography (CT), identified biological markers in mice and patients that provide a rationale for the differential efficacy of these therapies in the different genotypes. These co-clinical results identify predictive genetic biomarkers that should be validated by interrogating samples from patients enrolled on the concurrent clinical trial. These studies also highlight the rationale for synchronous co-clinical trials, not only to anticipate the results of ongoing human clinical trials, but also to generate clinically relevant hypotheses that can inform the analysis and design of human studies.     

From pluripotency to forebrain patterning: an in vitro journey astride embryonic stem cells

Embryonic stem cells (ESCs) have been used extensively as in vitro models of neural development and disease, with special efforts towards their conversion into forebrain progenitors and neurons. The forebrain is the most complex brain region, giving rise to several fundamental structures, such as the cerebral cortex, the hypothalamus, and the retina. Due to the multiplicity of signaling pathways playing different roles at distinct times of embryonic development, the specification and patterning of forebrain has been difficult to study in vivo. Research performed on ESCs in vitro has provided a large body of evidence to complement work in model organisms, but these studies have often been focused more on cell type production than on cell fate regulation. In this review, we systematically reassess the current literature in the field of forebrain development in mouse and human ESCs with a focus on the molecular mechanisms of early cell fate decisions, taking into consideration the specific culture conditions, exogenous and endogenous molecular cues as described in the original studies. The resulting model of early forebrain induction and patterning provides a useful framework for further studies aimed at reconstructing forebrain development in vitro for basic research or therapy.     

The positional identity of mouse ES cell-generated neurons is affected by BMP signaling

We investigated the effects of bone morphogenetic proteins (BMPs) in determining the positional identity of neurons generated in vitro from mouse embryonic stem cells (ESCs), an aspect that has been neglected thus far. Classical embryological studies in lower vertebrates indicate that BMPs inhibit the default fate of pluripotent embryonic cells, which is both neural and anterior. Moreover, mammalian ESCs generate neurons more efficiently when cultured in a minimal medium containing BMP inhibitors. In this paper, we show that mouse ESCs produce, secrete, and respond to BMPs during in vitro neural differentiation. After neuralization in a minimal medium, differentiated ESCs show a gene expression profile consistent with a midbrain identity, as evaluated by the analysis of a number of markers of anterior–posterior and dorsoventral identity. We found that BMPs endogenously produced during neural differentiation mainly act by inhibiting the expression of a telencephalic gene profile, which was revealed by the treatment with Noggin or with other BMP inhibitors. To better characterize the effect of BMPs on positional fate, we compared the global gene expression profiles of differentiated ESCs with those of embryonic forebrain, midbrain, and hindbrain. Both Noggin and retinoic acid (RA) support neuronal differentiation of ESCs, but they show different effects on their positional identity: whereas RA supports the typical gene expression profile of hindbrain neurons, Noggin induces a profile characteristic of dorsal telencephalic neurons. Our findings show that endogenously produced BMPs affect the positional identity of the neurons that ESCs spontaneously generate when differentiating in vitro in a minimal medium. The data also support the existence of an intrinsic program of neuronal differentiation with dorsal telencephalic identity. Our method of ESC neuralization allows for fast differentiation of neural cells via the same signals found during in vivo embryonic development and for the acquisition of cortical identity by the inhibition of BMP alone.