On A Conjecture of Tian

We study Tian's $\alpha$-invariant in comparison with the $\alpha_1$-invariant for pairs $(S_d,H)$ consisting of a smooth surface $S_d$ of degree $d$ in the projective three-dimensional space and a hyperplane section $H$. A conjecture of Tian asserts that $\alpha(S_d,H)=\alpha_1(S_d,H)$. We show that this is indeed true for $d=4$ (the result is well known for $d\leqslant 3$), and we show that $\alpha(S_d,H)<\alpha_1(S_d,H)$ for $d\geqslant 8$ provided that $S_d$ is general enough. We also construct examples of $S_d$, for $d=6$ and $d=7$, for which Tian's conjecture fails. We provide a candidate counterexample for $S_5$.Comment: Final version. To appear in Mathematische Zeitschrif

Instantons and Killing spinors

We investigate instantons on manifolds with Killing spinors and their cones. Examples of manifolds with Killing spinors include nearly Kaehler 6-manifolds, nearly parallel G_2-manifolds in dimension 7, Sasaki-Einstein manifolds, and 3-Sasakian manifolds. We construct a connection on the tangent bundle over these manifolds which solves the instanton equation, and also show that the instanton equation implies the Yang-Mills equation, despite the presence of torsion. We then construct instantons on the cones over these manifolds, and lift them to solutions of heterotic supergravity. Amongst our solutions are new instantons on even-dimensional Euclidean spaces, as well as the well-known BPST, quaternionic and octonionic instantons.Comment: 40 pages, 2 figures v2: author email addresses and affiliations adde

Nonlinear response of the vacuum Rabi resonance

On the level of single atoms and photons, the coupling between atoms and the electromagnetic field is typically very weak. By employing a cavity to confine the field, the strength of this interaction can be increased many orders of magnitude to a point where it dominates over any dissipative process. This strong-coupling regime of cavity quantum electrodynamics has been reached for real atoms in optical cavities, and for artificial atoms in circuit QED and quantum-dot systems. A signature of strong coupling is the splitting of the cavity transmission peak into a pair of resolvable peaks when a single resonant atom is placed inside the cavity - an effect known as vacuum Rabi splitting. The circuit QED architecture is ideally suited for going beyond this linear response effect. Here, we show that increasing the drive power results in two unique nonlinear features in the transmitted heterodyne signal: the supersplitting of each vacuum Rabi peak into a doublet, and the appearance of additional peaks with the characteristic sqrt(n) spacing of the Jaynes-Cummings ladder. These constitute direct evidence for the coupling between the quantized microwave field and the anharmonic spectrum of a superconducting qubit acting as an artificial atom.Comment: 6 pages, 4 figures. Supplementary Material and Supplementary Movies are available at http://www.eng.yale.edu/rslab/publications.htm

Oxidative stress-dependent cyclooxygenase-2-derived prostaglandin F2α impairs endothelial function in renovascular hypertensive rats

Abstract Aims: The role of endothelium-derived contracting factors (EDCFs) in regulating renovascular function is yet to be elucidated in renovascular hypertension (RH). The current study investigated whether oxidative stress-dependent cyclooxygenase (COX)-2-derived prostaglandin F(2alpha) (PGF(2alpha)) impairs endothelial function in renal arteries of renovascular hypertensive rats (RHR). Results: Renal hypertension was induced in rats by renal artery stenosis of both kidneys using the 2-kidney 2-clip model. Acute treatment with reactive oxygen species (ROS) scavengers, COX-2 inhibitors, and thromboxane-prostanoid receptor antagonists, but not COX-1 inhibitors, improved endothelium-dependent relaxations and eliminated endothelium-dependent contractions in RHR renal arteries. Five weeks of treatment with celecoxib or tempol reduced blood pressure, increased renal blood flow, and restored endothelial function in RHRs. Increased ROS production in RHR arteries was inhibited by ROS scavengers, but unaffected by COX-2 inhibitors; whereas increased PGF(2alpha) release was reduced by both ROS scavengers and COX-2 inhibitors. ROS also induced COX-2-dependent contraction in RHR renal arteries, which was accompanied by the release of COX-2-derived PGF(2alpha). Further, chronic tempol treatment reduced COX-2 and BMP4 upregulation, p38MAPK phosphorylation, and the nitrotyrosine level in RHR renal arteries. Conclusion: These findings demonstrate the functional importance of oxidative stress, which serves as an initiator of increased COX-2 activity, and that COX-2-derived PGF(2alpha) plays an important role in mediating endothelial dysfunction in RH. Innovation: The current study, thus, suggests that drugs targeting oxidative stress-dependent COX-2-derived PGF(2alpha) may be useful in the prevention and management of RH. Antioxid. Redox Signal. 16, 363-373.published_or_final_versio

Rectification of electronic heat current by a hybrid thermal diode

We report the realization of an ultra-efficient low-temperature hybrid heat current rectifier, thermal counterpart of the well-known electric diode. Our design is based on a tunnel junction between two different elements: a normal metal and a superconducting island. Electronic heat current asymmetry in the structure arises from large mismatch between the thermal properties of these two. We demonstrate experimentally temperature differences exceeding $60$ mK between the forward and reverse thermal bias configurations. Our device offers a remarkably large heat rectification ratio up to $\sim 140$ and allows its prompt implementation in true solid-state thermal nanocircuits and general-purpose electronic applications requiring energy harvesting or thermal management and isolation at the nanoscale.Comment: 8 pages, 6 color figure

Antisense epidermal growth factor receptor RNA transfection in human glioblastoma cells down-regulates telomerase activity and telomere length

Epidermal growth factor receptor is overexpressed and/or amplified in up to 50% of glioblastomas, suggesting an important role of this gene in glial tumorigenesis and progression. In the present study we demonstrated that epidermal growth factor receptor is involved in regulation of telomerase activity in glioblastoma. Antisense-epidermal growth factor receptor approach was used to inhibit epidermal growth factor receptor expression of glioblastoma U87MG cells. Telomerase activity in antisense-epidermal growth factor receptor cells decreased by up to 54 folds compared with control cells. Moreover, the telomere lengths of antisense-epidermal growth factor receptor cells were shortened. In addition, the tumorigenicity of antisense-epidermal growth factor receptor cells was significantly inhibited. Taken together, there were strong correlations between tumorigenicity and epidermal growth factor receptor expression levels, and between tumorigenicity and telomerase activity. These results provide evidence that epidermal growth factor receptor plays an important role in the regulation of telomerase activity of glioma cells. Our findings provide new insights into both the biological functions of epidermal growth factor receptor and the regulation of telomerase activity. The inhibition of telomerase activity triggered by antisense-epidermal growth factor receptor treatment may reflect yet another mechanism of antisense-epidermal growth factor receptor approach in tumour suppression

Bridging Time Scales in Cellular Decision Making with a Stochastic Bistable Switch

Cellular transformations which involve a significant phenotypical change of the cell's state use bistable biochemical switches as underlying decision systems. In this work, we aim at linking cellular decisions taking place on a time scale of years to decades with the biochemical dynamics in signal transduction and gene regulation, occuring on a time scale of minutes to hours. We show that a stochastic bistable switch forms a viable biochemical mechanism to implement decision processes on long time scales. As a case study, the mechanism is applied to model the initiation of follicle growth in mammalian ovaries, where the physiological time scale of follicle pool depletion is on the order of the organism's lifespan. We construct a simple mathematical model for this process based on experimental evidence for the involved genetic mechanisms. Despite the underlying stochasticity, the proposed mechanism turns out to yield reliable behavior in large populations of cells subject to the considered decision process. Our model explains how the physiological time constant may emerge from the intrinsic stochasticity of the underlying gene regulatory network. Apart from ovarian follicles, the proposed mechanism may also be of relevance for other physiological systems where cells take binary decisions over a long time scale.Comment: 14 pages, 4 figure

Dairy consumption and cardiometabolic diseases: systematic review and updated meta-analyses of prospective cohort studies

Purpose of Review Dairy products contain both beneficial and harmful nutrients in relation to cardiometabolic diseases. Here, we provide the latest scientific evidence regarding the relationship between dairy products and cardiometabolic diseases by reviewing the literature and updating meta-analyses of observational studies. Recent Findings We updated our previous meta-analyses of cohort studies on type 2 diabetes, coronary heart disease (CHD), and stroke with nine studies and confirmed previous results. Total dairy and low-fat dairy (per 200 g/d) were inversely associated with a 3–4% lower risk of diabetes. Yogurt was non-linearly inversely associatedwith diabetes (RR = 0.86, 95%CI: 0.83–0.90 at 80 g/ d). Total dairy and milk were not associated with CHD (RR~1.0). An increment of 200 g of daily milk intake was associated with an 8% lower risk of stroke. Summary The latest scientific evidence confirmed neutral or beneficial associations between dairy products and risk of cardiometabolic diseases

X-ray emission from isolated neutron stars

X-ray emission is a common feature of all varieties of isolated neutron stars (INS) and, thanks to the advent of sensitive instruments with good spectroscopic, timing, and imaging capabilities, X-ray observations have become an essential tool in the study of these objects. Non-thermal X-rays from young, energetic radio pulsars have been detected since the beginning of X-ray astronomy, and the long-sought thermal emission from cooling neutron star's surfaces can now be studied in detail in many pulsars spanning different ages, magnetic fields, and, possibly, surface compositions. In addition, other different manifestations of INS have been discovered with X-ray observations. These new classes of high-energy sources, comprising the nearby X-ray Dim Isolated Neutron Stars, the Central Compact Objects in supernova remnants, the Anomalous X-ray Pulsars, and the Soft Gamma-ray Repeaters, now add up to several tens of confirmed members, plus many candidates, and allow us to study a variety of phenomena unobservable in "standard'' radio pulsars.Comment: Chapter to be published in the book of proceedings of the 1st Sant Cugat Forum on Astrophysics, "ICREA Workshop on the high-energy emission from pulsars and their systems", held in April, 201

Baryonic symmetries and M5 branes in the AdS_4/CFT_3 correspondence

We study U(1) symmetries dual to Betti multiplets in the AdS_4/CFT_3 correspondence for M2 branes at Calabi-Yau four-fold singularities. Analysis of the boundary conditions for vector fields in AdS_4 allows for a choice where wrapped M5 brane states carrying non-zero charge under such symmetries can be considered. We begin by focusing on isolated toric singularities without vanishing six-cycles, and study in detail the cone over Q^{111}. The boundary conditions considered are dual to a CFT where the gauge group is U(1)^2 x SU(N)^4. We find agreement between the spectrum of gauge-invariant baryonic-type operators in this theory and wrapped M5 brane states. Moreover, the physics of vacua in which these symmetries are spontaneously broken precisely matches a dual gravity analysis involving resolutions of the singularity, where we are able to match condensates of the baryonic operators, Goldstone bosons and global strings. We also argue more generally that theories where the resolutions have six-cycles are expected to receive non-perturbative corrections from M5 brane instantons. We give a general formula relating the instanton action to normalizable harmonic two-forms, and compute it explicitly for the Q^{222} example. The holographic interpretation of such instantons is currently unclear.Comment: 92 pages, 10 figure