Newton's Easy Quadratures ``Omitted for the Sake of Brevity'

In the 1687 Principia, Newton gave a solution to the direct problem (given the orbit and center of force, find the central force) for a conic-section with a focal center of force (answer: a reciprocal square force) and for a spiral orbit with a polar center of force (answer: a reciprocal cube force). He did not, however, give solutions for the two corresponding inverse problems (given the force and center of force, find the orbit). He gave a cryptic solution to the inverse problem of a reciprocal cube force, but offered no solution for the reciprocal square force. Some take this omission as an indication that Newton could not solve the reciprocal square, for, they ask, why else would he not select this important problem? Others claim that ``it is child's play' for him, as evidenced by his 1671 catalogue of quadratures (tables of integrals). The answer to that question is obscured for all who attempt to work through Newton's published solution of the reciprocal cube force because it is done in the synthetic geometric style of the 1687 Principia rather than in the analytic algebraic style that Newton employed until 1671. In response to a request from David Gregory in 1694, however, Newton produced an analytic version of the body of the proof, but one which still had a geometric conclusion. Newton's charge is to find both ``the orbit' and ``the time in orbit.' In the determination of the dependence of the time on orbital position, t(r), Newton evaluated an integral of the form ∫dx/x <sup>n</sup> to calculate a finite algebraic equation for the area swept out as a function of the radius, but he did not write out the analytic expression for time t = t(r), even though he knew that the time t is proportional to that area. In the determination of the orbit, θ (r), Newton obtained an integral of the form ∫dx/√(1−x<sup>2</sup>) for the area that is proportional to the angle θ, an integral he had shown in his 1669 On Analysis by Infinite Equations to be equal to the arcsin(x). Since the solution must therefore contain a transcendental function, he knew that a finite algebraic solution for θ=θ(r) did not exist for ``the orbit' as it had for ``the time in orbit.' In contrast to these two solutions for the inverse cube force, however, it is not possible in the inverse square solution to generate a finite algebraic expression for either ``the orbit' or ``the time in orbit.' In fact, in Lemma 28, Newton offers a demonstration that the area of an ellipse cannot be given by a finite equation. I claim that the limitation of Lemma 28 forces Newton to reject the inverse square force as an example and to choose instead the reciprocal cube force as his example in Proposition 41. (Received August 14, 2002) Published online March 26, 2003 Communicated by G. Smith     

A massive phytoplankton bloom induced by an ecosystem-scale iron fertilization experiment in the equatorial Pacific Ocean

The seeding of an expanse of surface waters in the equatorial Pacific Ocean with low concentrations of dissolved iron triggered a massive phytoplankton bloom which consumed large quantities of carbon dioxide and nitrate that these microscopic plants cannot fully utilize under natural conditions. These and other observations provide unequivocal support for the hypothesis that phytoplankton growth in this oceanic region is limited by iron bioavailability.     

Detecting MoS2 and MoSe2 with optical contrast simulation

Optical imaging is a promising method to identify and locate 2D materials efficiently and non-invasively. By putting a 2D material on a substrate, the nanolayer will add to an optical path and create a contrast to the case when the nanolayer is absent. This optical contrast imaging can be used to identify the 2D material and its number of layers. To make the optical imaging process in the laboratories an effective tool, Fresnel Law as a model was used to simulate the optical imaging results of 2D materials(graphene, Mo S2 and MoSe_2) on top of different thickness of SiO_2 and Si wafer in the present investigation. The results provide the details of the optimal conditions(optimal light wavelength and optimal SiO_2 thickness) to identify and locate single to few 2D nanolayers, which can be used directly in laboratories. The optical contrasts of 1–5 layers of molybdenum disulfide(MoS_2) and molybdenum diselenide(MoSe_2) were simulated. To the best of our knowledge, it is the first time that the optical contrast results of MoSe_2 have been reported. In particular, this work highlights the sensitivity of the model on the accuracy of the refractive indices used. It is demonstrated that through computational modeling that optical contrast can allow effective determination of number of layers in few layer 2D materials.     

Inhibition of nociceptors by TRPV1-mediated entry of impermeant sodium channel blockers

Most local anaesthetics used clinically are relatively hydrophobic molecules that gain access to their blocking site on the sodium channel by diffusing into or through the cell membrane. These anaesthetics block sodium channels and thereby the excitability of all neurons, not just sensory neurons. We tested the possibility of selectively blocking the excitability of primary sensory nociceptor (pain-sensing) neurons by introducing the charged, membrane-impermeant lidocaine derivative QX-314 through the pore of the noxious-heat-sensitive TRPV1 channel. Here we show that charged sodium-channel blockers can be targeted into nociceptors by the application of TRPV1 agonists to produce a pain-specific local anaesthesia. QX-314 applied externally had no effect on the activity of sodium channels in small sensory neurons when applied alone, but when applied in the presence of the TRPV1 agonist capsaicin, QX-314 blocked sodium channels and inhibited excitability. Inhibition by co-applied QX-314 and capsaicin was restricted to neurons expressing TRPV1. Injection of QX-314 together with capsaicin into rat hindpaws produced a long-lasting (more than 2 h) increase in mechanical and thermal nociceptive thresholds. Long-lasting decreases in pain sensitivity were also seen with regional injection of QX-314 and capsaicin near the sciatic nerve; however, in contrast to the effect of lidocaine, the application of QX-314 and capsaicin together was not accompanied by motor or tactile deficits.     

Coupling superconducting qubits via a cavity bus

Superconducting circuits are promising candidates for constructing quantum bits (qubits) in a quantum computer; single-qubit operations are now routine, and several examples of two-qubit interactions and gates have been demonstrated. These experiments show that two nearby qubits can be readily coupled with local interactions. Performing gate operations between an arbitrary pair of distant qubits is highly desirable for any quantum computer architecture, but has not yet been demonstrated. An efficient way to achieve this goal is to couple the qubits to a 'quantum bus', which distributes quantum information among the qubits. Here we show the implementation of such a quantum bus, using microwave photons confined in a transmission line cavity, to couple two superconducting qubits on opposite sides of a chip. The interaction is mediated by the exchange of virtual rather than real photons, avoiding cavity-induced loss. Using fast control of the qubits to switch the coupling effectively on and off, we demonstrate coherent transfer of quantum states between the qubits. The cavity is also used to perform multiplexed control and measurement of the qubit states. This approach can be expanded to more than two qubits, and is an attractive architecture for quantum information processing on a chip.     

A reversible wet/dry adhesive inspired by mussels and geckos

The adhesive strategy of the gecko relies on foot pads composed of specialized keratinous foot-hairs called setae, which are subdivided into terminal spatulae of approximately 200 nm (ref. 1). Contact between the gecko foot and an opposing surface generates adhesive forces that are sufficient to allow the gecko to cling onto vertical and even inverted surfaces. Although strong, the adhesion is temporary, permitting rapid detachment and reattachment of the gecko foot during locomotion. Researchers have attempted to capture these properties of gecko adhesive in synthetic mimics with nanoscale surface features reminiscent of setae; however, maintenance of adhesive performance over many cycles has been elusive, and gecko adhesion is greatly diminished upon full immersion in water. Here we report a hybrid biologically inspired adhesive consisting of an array of nanofabricated polymer pillars coated with a thin layer of a synthetic polymer that mimics the wet adhesive proteins found in mussel holdfasts. Wet adhesion of the nanostructured polymer pillar arrays increased nearly 15-fold when coated with mussel-mimetic polymer. The system maintains its adhesive performance for over a thousand contact cycles in both dry and wet environments. This hybrid adhesive, which combines the salient design elements of both gecko and mussel adhesives, should be useful for reversible attachment to a variety of surfaces in any environment.     

Genetic variants in novel pathways influence blood pressure and cardiovascular disease risk

Blood pressure is a heritable trait influenced by several biological pathways and responsive to environmental stimuli. Over one billion people worldwide have hypertension (≥140?mm?Hg systolic blood pressure or ≥90?mm?Hg diastolic blood pressure). Even small increments in blood pressure are associated with an increased risk of cardiovascular events. This genome-wide association study of systolic and diastolic blood pressure, which used a multi-stage design in 200,000 individuals of European descent, identified sixteen novel loci: six of these loci contain genes previously known or suspected to regulate blood pressure (GUCY1A3-GUCY1B3, NPR3-C5orf23, ADM, FURIN-FES, GOSR2, GNAS-EDN3); the other ten provide new clues to blood pressure physiology. A genetic risk score based on 29 genome-wide significant variants was associated with hypertension, left ventricular wall thickness, stroke and coronary artery disease, but not kidney disease or kidney function. We also observed associations with blood pressure in East Asian, South Asian and African ancestry individuals. Our findings provide new insights into the genetics and biology of blood pressure, and suggest potential novel therapeutic pathways for cardiovascular disease prevention.     

Evidence for a spin-aligned neutron-proton paired phase from the level structure of (92)Pd

Shell structure and magic numbers in atomic nuclei were generally explained by pioneering work that introduced a strong spin-orbit interaction to the nuclear shell model potential. However, knowledge of nuclear forces and the mechanisms governing the structure of nuclei, in particular far from stability, is still incomplete. In nuclei with equal neutron and proton numbers (N = Z), enhanced correlations arise between neutrons and protons (two distinct types of fermions) that occupy orbitals with the same quantum numbers. Such correlations have been predicted to favour an unusual type of nuclear superfluidity, termed isoscalar neutron-proton pairing, in addition to normal isovector pairing. Despite many experimental efforts, these predictions have not been confirmed. Here we report the experimental observation of excited states in the N = Z = 46 nucleus (92)Pd. Gamma rays emitted following the (58)Ni((36)Ar,2n)(92)Pd fusion-evaporation reaction were identified using a combination of state-of-the-art high-resolution γ-ray, charged-particle and neutron detector systems. Our results reveal evidence for a spin-aligned, isoscalar neutron-proton coupling scheme, different from the previous prediction. We suggest that this coupling scheme replaces normal superfluidity (characterized by seniority coupling) in the ground and low-lying excited states of the heaviest N = Z nuclei. Such strong, isoscalar neutron-proton correlations would have a considerable impact on the nuclear level structure and possibly influence the dynamics of rapid proton capture in stellar nucleosynthesis.     

An integrated semiconductor device enabling non-optical genome sequencing

The seminal importance of DNA sequencing to the life sciences, biotechnology and medicine has driven the search for more scalable and lower-cost solutions. Here we describe a DNA sequencing technology in which scalable, low-cost semiconductor manufacturing techniques are used to make an integrated circuit able to directly perform non-optical DNA sequencing of genomes. Sequence data are obtained by directly sensing the ions produced by template-directed DNA polymerase synthesis using all-natural nucleotides on this massively parallel semiconductor-sensing device or ion chip. The ion chip contains ion-sensitive, field-effect transistor-based sensors in perfect register with 1.2 million wells, which provide confinement and allow parallel, simultaneous detection of independent sequencing reactions. Use of the most widely used technology for constructing integrated circuits, the complementary metal-oxide semiconductor (CMOS) process, allows for low-cost, large-scale production and scaling of the device to higher densities and larger array sizes. We show the performance of the system by sequencing three bacterial genomes, its robustness and scalability by producing ion chips with up to 10 times as many sensors and sequencing a human genome.     

An actively accreting massive black hole in the dwarf starburst galaxy Henize 2-10

Supermassive black holes are now thought to lie at the heart of every giant galaxy with a spheroidal component, including our own Milky Way. The birth and growth of the first 'seed' black holes in the earlier Universe, however, is observationally unconstrained and we are only beginning to piece together a scenario for their subsequent evolution. Here we report that the nearby dwarf starburst galaxy Henize?2-10 (refs 5 and 6) contains a compact radio source at the dynamical centre of the galaxy that is spatially coincident with a hard X-ray source. From these observations, we conclude that Henize?2-10 harbours an actively accreting central black hole with a mass of approximately one million solar masses. This nearby dwarf galaxy, simultaneously hosting a massive black hole and an extreme burst of star formation, is analogous in many ways to galaxies in the infant Universe during the early stages of black-hole growth and galaxy mass assembly. Our results confirm that nearby star-forming dwarf galaxies can indeed form massive black holes, and that by implication so can their primordial counterparts. Moreover, the lack of a substantial spheroidal component in Henize?2-10 indicates that supermassive black-hole growth may precede the build-up of galaxy spheroids.