Higher-order principal component pursuit via tensor approximation and convex optimization

Recovering the low-rank structure of data matrix from sparse errors arises in the principal component pursuit （PCP）. This paper exploits the higher-order generalization of matrix recovery, named higher-order principal component pursuit （HOPCP）, since it is critical in multi-way data analysis. Unlike the convexification （nuclear norm） for matrix rank function, the tensorial nuclear norm is stil an open problem. While existing preliminary works on the tensor completion field provide a viable way to indicate the low complexity estimate of tensor, therefore, the paper focuses on the low multi-linear rank tensor and adopt its convex relaxation to formulate the convex optimization model of HOPCP. The paper further propose two algorithms for HOPCP based on alternative minimization scheme： the augmented Lagrangian alternating direction method （ALADM） and its truncated higher-order singular value decomposition （ALADM-THOSVD） version. The former can obtain a high accuracy solution while the latter is more efficient to handle the computationally intractable problems. Experimental results on both synthetic data and real magnetic resonance imaging data show the applicability of our algorithms in high-dimensional tensor data processing.     

The age of synthesis: From cognitive science to converging technologies and hereafter

This paper describes the development of two of the most important scientific disciplines in the last quarter of the 20th century, cognitive science, which emerged in 1975, and nano-bio-info-cogno (NBIC) converging technologies, which emerged in 2000. In this century, we will achieve cross-disciplinary integration, innovation in comprehensive knowledge and comprehensive devel opment in human resources. NBIC converging technologies will greatly expand human cognition and communication, improve human health, enhance social outcomes, strengthen national security and unify science and education. Cognitive science and converging technologies will have major effects on the future human development. I argue that the 21st century represents an age of synthesis, reflected in the continual reintegration between scientific disciplines in recent times. This new age of synthesis will require innovations in thought and methodology that differ from those underlying the age of analysis in the 20th century. I predict that these developments will allow every individual to realize comprehensive development. Accordingly, the education system will be transformed, and a comprehensive human resources system will be created.     

On-chip natural assembly of silicon photonic bandgap crystals.

Photonic bandgap crystals can reflect light for any direction of propagation in specific wavelength ranges. This property, which can be used to confine, manipulate and guide photons, should allow the creation of all-optical integrated circuits. To achieve this goal, conventional semiconductor nanofabrication techniques have been adapted to make photonic crystals. A potentially simpler and cheaper approach for creating three-dimensional periodic structures is the natural assembly of colloidal microspheres. However, this approach yields irregular, polycrystalline photonic crystals that are difficult to incorporate into a device. More importantly, it leads to many structural defects that can destroy the photonic bandgap. Here we show that by assembling a thin layer of colloidal spheres on a silicon substrate, we can obtain planar, single-crystalline silicon photonic crystals that have defect densities sufficiently low that the bandgap survives. As expected from theory, we observe unity reflectance in two crystalline directions of our photonic crystals around a wavelength of 1.3 micrometres. We also show that additional fabrication steps, intentional doping and patterning, can be performed, so demonstrating the potential for specific device applications.     

Programmable and autonomous computing machine made of biomolecules.

Devices that convert information from one form into another according to a definite procedure are known as automata. One such hypothetical device is the universal Turing machine, which stimulated work leading to the development of modern computers. The Turing machine and its special cases, including finite automata, operate by scanning a data tape, whose striking analogy to information-encoding biopolymers inspired several designs for molecular DNA computers. Laboratory-scale computing using DNA and human-assisted protocols has been demonstrated, but the realization of computing devices operating autonomously on the molecular scale remains rare. Here we describe a programmable finite automaton comprising DNA and DNA-manipulating enzymes that solves computational problems autonomously. The automaton's hardware consists of a restriction nuclease and ligase, the software and input are encoded by double-stranded DNA, and programming amounts to choosing appropriate software molecules. Upon mixing solutions containing these components, the automaton processes the input molecule via a cascade of restriction, hybridization and ligation cycles, producing a detectable output molecule that encodes the automaton's final state, and thus the computational result. In our implementation 1012 automata sharing the same software run independently and in parallel on inputs (which could, in principle, be distinct) in 120 microl solution at room temperature at a combined rate of 109 transitions per second with a transition fidelity greater than 99.8%, consuming less than 10-10 W.     

Superconductivity in CaCuO2 as a result of field-effect doping.

Understanding the doping mechanisms in the simplest superconducting copper oxide-the infinite-layer compound ACuO2 (where A is an alkaline earth metal)-is an excellent way of investigating the pairing mechanism in high-transition-temperature (high-Tc) superconductors more generally. Gate-induced modulation of the carrier concentration to obtain superconductivity is a powerful means of achieving such understanding: it minimizes the effects of potential scattering by impurities, and of structural modifications arising from chemical dopants. Here we report the transport properties of thin films of the infinite-layer compound CaCuO2 using field-effect doping. At high hole- and electron-doping levels, superconductivity is induced in the nominally insulating material. Maximum values of Tc of 89 K and 34 K are observed respectively for hole- and electron-type doping of around 0.15 charge carriers per CuO2. We can explore the whole doping diagram of the CuO2 plane while changing only a single electric parameter, the gate voltage.     

Visualizing single-molecule diffusion in mesoporous materials

Periodic mesoporous materials formed through the cooperative self-assembly of surfactants and framework building blocks can assume a variety of structures, and their widely tuneable properties make them attractive hosts for numerous applications. Because the molecular movement in the pore system is the most important and defining characteristic of porous materials, it is of interest to learn about this behaviour as a function of local structure. Generally, individual fluorescent dye molecules can be used as molecular beacons with which to explore the structure of--and the dynamics within--these porous hosts, and single-molecule fluorescence techniques provide detailed insights into the dynamics of various processes, ranging from biology to heterogeneous catalysis. However, optical microscopy methods cannot directly image the mesoporous structure of the host system accommodating the diffusing molecules, whereas transmission electron microscopy provides detailed images of the porous structure, but no dynamic information. It has therefore not been possible to 'see' how molecules diffuse in a real nanoscale pore structure. Here we present a combination of electron microscopic mapping and optical single-molecule tracking experiments to reveal how a single luminescent dye molecule travels through linear or strongly curved sections of a mesoporous channel system. In our approach we directly correlate porous structures detected by transmission electron microscopy with the diffusion dynamics of single molecules detected by optical microscopy. This opens up new ways of understanding the interactions of host and guest.     

Enhanced biological carbon consumption in a high CO2 ocean

The oceans have absorbed nearly half of the fossil-fuel carbon dioxide (CO2) emitted into the atmosphere since pre-industrial times, causing a measurable reduction in seawater pH and carbonate saturation. If CO2 emissions continue to rise at current rates, upper-ocean pH will decrease to levels lower than have existed for tens of millions of years and, critically, at a rate of change 100 times greater than at any time over this period. Recent studies have shown effects of ocean acidification on a variety of marine life forms, in particular calcifying organisms. Consequences at the community to ecosystem level, in contrast, are largely unknown. Here we show that dissolved inorganic carbon consumption of a natural plankton community maintained in mesocosm enclosures at initial CO2 partial pressures of 350, 700 and 1,050 microatm increases with rising CO2. The community consumed up to 39% more dissolved inorganic carbon at increased CO2 partial pressures compared to present levels, whereas nutrient uptake remained the same. The stoichiometry of carbon to nitrogen drawdown increased from 6.0 at low CO2 to 8.0 at high CO2, thus exceeding the Redfield carbon:nitrogen ratio of 6.6 in today's ocean. This excess carbon consumption was associated with higher loss of organic carbon from the upper layer of the stratified mesocosms. If applicable to the natural environment, the observed responses have implications for a variety of marine biological and biogeochemical processes, and underscore the importance of biologically driven feedbacks in the ocean to global change.     

Coupled 142Nd-143Nd evidence for a protracted magma ocean in Mars

Resolving early silicate differentiation timescales is crucial for understanding the chemical evolution and thermal histories of terrestrial planets. Planetary-scale magma oceans are thought to have formed during early stages of differentiation, but the longevity of such magma oceans is poorly constrained. In Mars, the absence of vigorous convection and plate tectonics has limited the scale of compositional mixing within its interior, thus preserving the early stages of planetary differentiation. The SNC (Shergotty-Nakhla-Chassigny) meteorites from Mars retain 'memory' of these events. Here we apply the short-lived 146Sm-142Nd and the long-lived 147Sm-143Nd chronometers to a suite of shergottites to unravel the history of early silicate differentiation in Mars. Our data are best explained by progressive crystallization of a magma ocean with a duration of approximately 100 million years after core formation. This prolonged solidification requires the existence of a primitive thick atmosphere on Mars that reduces the cooling rate of the interior.     

Drosophila TCTP is essential for growth and proliferation through regulation of dRheb GTPase

Cellular growth and proliferation are coordinated during organogenesis. Misregulation of these processes leads to pathological conditions such as cancer. Tuberous sclerosis (TSC) is a benign tumour syndrome caused by mutations in either TSC1 or TSC2 tumour suppressor genes. Studies in Drosophila and other organisms have identified TSC signalling as a conserved pathway for growth control. Activation of the TSC pathway is mediated by Rheb (Ras homologue enriched in brain), a Ras superfamily GTPase. Rheb is a direct target of TSC2 and is negatively regulated by its GTPase-activating protein activity. However, molecules required for positive regulation of Rheb have not been identified. Here we show that a conserved protein, translationally controlled tumour protein (TCTP), is an essential new component of the TSC-Rheb pathway. Reducing Drosophila TCTP (dTCTP) levels reduces cell size, cell number and organ size, which mimics Drosophila Rheb (dRheb) mutant phenotypes. dTCTP is genetically epistatic to Tsc1 and dRheb, but acts upstream of dS6k, a downstream target of dRheb. dTCTP directly associates with dRheb and displays guanine nucleotide exchange activity with it in vivo and in vitro. Human TCTP (hTCTP) shows similar biochemical properties compared to dTCTP and can rescue dTCTP mutant phenotypes, suggesting that the function of TCTP in the TSC pathway is evolutionarily conserved. Our studies identify TCTP as a direct regulator of Rheb and a potential therapeutic target for TSC disease.