Colossal infrared and terahertz magneto-optical activity in a two-dimensional Dirac material

When two-dimensional electron gases (2DEGs) are exposed to magnetic field, they resonantly absorb electromagnetic radiation via electronic transitions between Landau levels (LLs). In 2DEGs with a Dirac spectrum, such as graphene, theory predicts an exceptionally high infrared magneto-absorption, even at zero doping. However, the measured LL magneto-optical effects in graphene have been much weaker than expected because of imperfections in the samples available so far for such experiments. Here we measure magneto-transmission and Faraday rotation in high-mobility encapsulated monolayer graphene using a custom designed setup for magneto-infrared microspectroscopy. Our results show a strongly enhanced magneto-optical activity in the infrared and terahertz ranges characterized by a maximum allowed (50%) absorption of light, a 100% magnetic circular dichroism as well as a record high Faraday rotation. Considering that sizeable effects have been already observed at routinely achievable magnetic fields, our findings demonstrate a new potential of magnetic tuning in 2D Dirac materials for long-wavelength optoelectronics and plasmonics.Comment: 14 pages, 4 figure

Formation of new stellar populations from gas accreted by massive young star clusters

Stars in star clusters are thought to form in a single burst from a common progenitor cloud of molecular gas. However, massive, old globular clusters -- with ages greater than 10 billion years and masses of several hundred thousand solar masses -- often harbour multiple stellar populations, indicating that more than one star-forming event occurred during their lifetimes. Colliding stellar winds from late-stage, asymptotic-giant-branch stars are often invoked as second-generation star-formation trigger. The initial cluster masses should be at least 10 times more massive than they are today for this to work. However, large populations of clusters with masses greater than a few million solar masses are not found in the local Universe. Here we report on three 1-2 billion-year-old, massive star clusters in the Magellanic Clouds, which show clear evidence of burst-like star formation that occurred a few hundred million years after their initial formation era. We show that such clusters could accrete sufficient gas reservoirs to form new stars if the clusters orbited in their host galaxies' gaseous discs throughout the period between their initial formation and the more recent bursts of star formation. This may eventually give rise to the ubiquitous multiple stellar populations in globular clusters.Comment: 10 pages, 11 figures, Authors' version of a letter published in Nature (27 January 2016), including Methods and Extended Dat

Provable Acceleration of Heavy Ball beyond Quadratics for a Class of Polyak-\L{}ojasiewicz Functions when the Non-Convexity is Averaged-Out

Heavy Ball (HB) nowadays is one of the most popular momentum methods in non-convex optimization. It has been widely observed that incorporating the Heavy Ball dynamic in gradient-based methods accelerates the training process of modern machine learning models. However, the progress on establishing its theoretical foundation of acceleration is apparently far behind its empirical success. Existing provable acceleration results are of the quadratic or close-to-quadratic functions, as the current techniques of showing HB's acceleration are limited to the case when the Hessian is fixed. In this work, we develop some new techniques that help show acceleration beyond quadratics, which is achieved by analyzing how the change of the Hessian at two consecutive time points affects the convergence speed. Based on our technical results, a class of Polyak-\L{}ojasiewicz (PL) optimization problems for which provable acceleration can be achieved via HB is identified. Moreover, our analysis demonstrates a benefit of adaptively setting the momentum parameter. (Update: 08/29/2023) Erratum is added in Appendix J. This is an updated version that fixes an issue in the previous version. An additional condition needs to be satisfied for the acceleration result of HB beyond quadratics in this work, which naturally holds when the dimension is one or, more broadly, when the Hessian is diagonal. We elaborate on the issue in Appendix J.Comment: (ICML 2022) Proceedings of the 39th International Conference on Machine Learning

HAZniCS -- Software Components for Multiphysics Problems

We introduce the software toolbox HAZniCS for solving interface-coupled multiphysics problems. HAZniCS is a suite of modules that combines the well-known FEniCS framework for finite element discretization with solver and graph library HAZmath. The focus of the paper is on the design and implementation of a pool of robust and efficient solver algorithms which tackle issues related to the complex interfacial coupling of the physical problems often encountered in applications in brain biomechanics. The robustness and efficiency of the numerical algorithms and methods is shown in several numerical examples, namely the Darcy-Stokes equations that model flow of cerebrospinal fluid in the human brain and the mixed-dimensional model of electrodiffusion in the brain tissue

Rational approximation preconditioners for multiphysics problems

We consider a class of mathematical models describing multiphysics phenomena interacting through interfaces. On such interfaces, the traces of the fields lie (approximately) in the range of a weighted sum of two fractional differential operators. We use a rational function approximation to precondition such operators. We first demonstrate the robustness of the approximation for ordinary functions given by weighted sums of fractional exponents. Additionally, we present more realistic examples utilizing the proposed preconditioning techniques in interface coupling between Darcy and Stokes equations

Near-infrared photoresponse sensitization of solvent additive processed poly(3-hexylthiophene)/fullerene solar cells by a low band gap polymer

With the aim of extending the photoresponse of the poly(3-hexylthiophene)/[6,6]-phenyl-C61-butyric acid methyl ester photovoltaic system into the near-infrared region, a low band gap polymer poly [2,1,3-benzothiadiazole-4,7-diyl[4,4-bis(2-ethylhexyl)-4H-cyclopenta[2,1-b:3,4-b\u27]dithiophene-2, 6-diyl]] was incorporated to make ternary blend solar cells. Solvent additive 1,8-diiodooctane (DIO) was applied to optimize the phase separation in a one-step active layer preparation. Devices fabricated with DIO additive demonstrate an improvement of device power conversion efficiency by 17%, which can be attributed to favorable microscopic structure of the ternary blend with 1:1:0.2 composition processed with DIO and extended absorption on the red side of the visible spectrum up to 900 nm

Extragradient Type Methods for Riemannian Variational Inequality Problems

Riemannian convex optimization and minimax optimization have recently drawn considerable attention. Their appeal lies in their capacity to adeptly manage the non-convexity of the objective function as well as constraints inherent in the feasible set in the Euclidean sense. In this work, we delve into monotone Riemannian Variational Inequality Problems (RVIPs), which encompass both Riemannian convex optimization and minimax optimization as particular cases. In the context of Euclidean space, it is established that the last-iterates of both the extragradient (EG) and past extragradient (PEG) methods converge to the solution of monotone variational inequality problems at a rate of $O\left(\frac{1}{\sqrt{T}}\right)$ (Cai et al., 2022). However, analogous behavior on Riemannian manifolds remains an open question. To bridge this gap, we introduce the Riemannian extragradient (REG) and Riemannian past extragradient (RPEG) methods. We demonstrate that both exhibit $O\left(\frac{1}{\sqrt{T}}\right)$ last-iterate convergence. Additionally, we show that the average-iterate convergence of both REG and RPEG is $O\left(\frac{1}{{T}}\right)$, aligning with observations in the Euclidean case (Mokhtari et al., 2020). These results are enabled by judiciously addressing the holonomy effect so that additional complications in Riemannian cases can be reduced and the Euclidean proof inspired by the performance estimation problem (PEP) technique or the sum-of-squares (SOS) technique can be applied again

Investigating gait-responsive somatosensory cueing from a wearable device to improve walking in Parkinson’s disease

Freezing-of-gait (FOG) and impaired walking are common features of Parkinson’s disease (PD). Provision of external stimuli (cueing) can improve gait, however, many cueing methods are simplistic, increase task loading or have limited utility in a real-world setting. Closed-loop (automated) somatosensory cueing systems have the potential to deliver personalised, discrete cues at the appropriate time, without requiring user input. Further development of cue delivery methods and FOG-detection are required to achieve this. In this feasibility study, we aimed to test if FOG-initiated vibration cues applied to the lower-leg via wearable devices can improve gait in PD, and to develop real-time FOG-detection algorithms. 17 participants with Parkinson’s disease and daily FOG were recruited. During 1 h study sessions, participants undertook 4 complex walking circuits, each with a different intervention: continuous rhythmic vibration cueing (CC), responsive cueing (RC; cues initiated by the research team in response to FOG), device worn with no cueing (NC), or no device (ND). Study sessions were grouped into 3 stages/blocks (A-C), separated by a gap of several weeks, enabling improvements to circuit design and the cueing device to be implemented. Video and onboard inertial measurement unit (IMU) data were analyzed for FOG events and gait metrics. RC significantly improved circuit completion times demonstrating improved overall performance across a range of walking activities. Step frequency was significantly enhanced by RC during stages B and C. During stage C, > 10 FOG events were recorded in 45% of participants without cueing (NC), which was significantly reduced by RC. A machine learning framework achieved 83% sensitivity and 80% specificity for FOG detection using IMU data. Together, these data support the feasibility of closed-loop cueing approaches coupling real-time FOG detection with responsive somatosensory lower-leg cueing to improve gait in PD

Geographic and species association of hepatitis B virus genotypes in non-human primates

AbstractInfection with hepatitis B virus (HBV) has been detected in human populations thoughout the world, as well as in a number of ape species (Pan troglodytes, Gorilla gorilla, gibbons [Nomascus and Hylobates species] and Pongo pygmaeus). To investigate the distribution of naturally occurring HBV infection in these species and other African Old World monkey species (Cercopithecidae), we screened 137 plasma samples from mainly wild caught animals by polymerase chain reaction (PCR) using several of highly conserved primers from the HB surface (HBs) gene, and for HBs antigen (HBsAg) by ELISA. None of the 93 Cercopithecidae screened (6 species) showed PCR or serology evidence for HBV infection; in contrast 2 from 8 chimpanzees and 5 from 22 gibbons were PCR-positive with each set of primers.Complete genome sequences from each of the positive apes were obtained and compared with all previously published complete and surface gene sequences. This extended phylogenetic analysis indicated that HBV variants from orangutans were interspersed by with HBV variants from southerly distributed gibbon species (H. agilis and H. moloch) occupying overlapping or adjacent habitat ranges with orangutans; in contrast, HBV variants from gibbon species in mainland Asia were phylogenetically distinct. A geographical rather than (sub)species association of HBV would account for the distribution of HBV variants in different subspecies of chimpanzees in Africa, and explain the inlier position of the previously described lowland gorilla sequence in the chimpanzee clade. These new findings have a number of implication for understanding the origins and epidemiology of HBV infection in non-human primates