Backtracking New Q-Newton's method, Schr\"oder's theorem, and Linear Conjugacy

A new variant of Newton's method - named Backtracking New Q-Newton's method (BNQN) - which has strong theoretical guarantee, is easy to implement, and has good experimental performance, was recently introduced by the third author. Experiments performed previously showed some remarkable properties of the basins of attractions for finding roots of polynomials and meromorphic functions using BNQN. In particular, it seems that for finding roots of polynomials of degree 2, the basins of attraction of the dynamics for BNQN are the same as that for Newton's method (the latter is the classical Schr\"oder's result in Complex Dynamics). In this paper, we show that indeed the picture we obtain when finding roots of polynomials of degree 2 is the same as that in Sch\"oder's result, with a remarkable difference: on the boundary line of the basins, the dynamics of Newton's method is chaotic, while the dynamics of BNQN is more smooth. On the way to proving the result, we show that BNQN (in any dimension) is invariant under conjugation by linear operators of the form $A=cR$, where $R$ is unitary and $c>0$ a constant. This again illustrates the similarity-difference relation between BNQN and Newton's method.Comment: 29 pages. Comments are welcome

Backtracking New Q-Newton's method, Newton's flow, Voronoi's diagram and Stochastic root finding

A new variant of Newton's method - named Backtracking New Q-Newton's method (BNQN) - which has strong theoretical guarantee, is easy to implement, and has good experimental performance, was recently introduced by the third author. Experiments performed previously showed some remarkable properties of the basins of attractions for finding roots of polynomials and meromorphic functions, with BNQN. In general, they look more smooth than that of Newton's method. In this paper, we continue to experimentally explore in depth this remarkable phenomenon, and connect BNQN to Newton's flow and Voronoi's diagram. This link poses a couple of challenging puzzles to be explained. Experiments also indicate that BNQN is more robust against random perturbations than Newton's method and Random Relaxed Newton's method.Comment: 48 pages. Some typos are fixed. Comments are welcome!. arXiv admin note: text overlap with arXiv:2312.1216

Emergence of Superlattice Dirac Points in Graphene on Hexagonal Boron Nitride

The Schr\"odinger equation dictates that the propagation of nearly free electrons through a weak periodic potential results in the opening of band gaps near points of the reciprocal lattice known as Brillouin zone boundaries. However, in the case of massless Dirac fermions, it has been predicted that the chirality of the charge carriers prevents the opening of a band gap and instead new Dirac points appear in the electronic structure of the material. Graphene on hexagonal boron nitride (hBN) exhibits a rotation dependent Moir\'e pattern. In this letter, we show experimentally and theoretically that this Moir\'e pattern acts as a weak periodic potential and thereby leads to the emergence of a new set of Dirac points at an energy determined by its wavelength. The new massless Dirac fermions generated at these superlattice Dirac points are characterized by a significantly reduced Fermi velocity. The local density of states near these Dirac cones exhibits hexagonal modulations indicating an anisotropic Fermi velocity.Comment: 16 pages, 6 figure

Ripple Texturing of Suspended Graphene Atomic Membranes

Graphene is the nature's thinnest elastic membrane, with exceptional mechanical and electrical properties. We report the direct observation and creation of one-dimensional (1D) and 2D periodic ripples in suspended graphene sheets, using spontaneously and thermally induced longitudinal strains on patterned substrates, with control over their orientations and wavelengths. We also provide the first measurement of graphene's thermal expansion coefficient, which is anomalously large and negative, ~ -7x10^-6 K^-1 at 300K. Our work enables novel strain-based engineering of graphene devices.Comment: 15 pages, 4 figure

Tuning a Circular p-n Junction in Graphene from Quantum Confinement to Optical Guiding

The motion of massless Dirac-electrons in graphene mimics the propagation of photons. This makes it possible to control the charge-carriers with components based on geometrical-optics and has led to proposals for an all-graphene electron-optics platform. An open question arising from the possibility of reducing the component-size to the nanometer-scale is how to access and understand the transition from optical-transport to quantum-confinement. Here we report on the realization of a circular p-n junction that can be continuously tuned from the nanometer-scale, where quantum effects are dominant, to the micrometer scale where optical-guiding takes over. We find that in the nanometer-scale junction electrons are trapped in states that resemble atomic-collapse at a supercritical charge. As the junction-size increases, the transition to optical-guiding is signaled by the emergence of whispering-gallery modes and Fabry-Perot interference. The creation of tunable junctions that straddle the crossover between quantum-confinement and optical-guiding, paves the way to novel design-architectures for controlling electronic transport.Comment: 16 pages, 4 figure

Realization of a Tunable Artificial Atom at a Supercritically Charged Vacancy in Graphene

The remarkable electronic properties of graphene have fueled the vision of a graphene-based platform for lighter, faster and smarter electronics and computing applications. One of the challenges is to devise ways to tailor its electronic properties and to control its charge carriers. Here we show that a single atom vacancy in graphene can stably host a local charge and that this charge can be gradually built up by applying voltage pulses with the tip of a scanning tunneling microscope (STM). The response of the conduction electrons in graphene to the local charge is monitored with scanning tunneling and Landau level spectroscopy, and compared to numerical simulations. As the charge is increased, its interaction with the conduction electrons undergoes a transition into a supercritical regime 6-11 where itinerant electrons are trapped in a sequence of quasi-bound states which resemble an artificial atom. The quasi-bound electron states are detected by a strong enhancement of the density of states (DOS) within a disc centered on the vacancy site which is surrounded by halo of hole states. We further show that the quasi-bound states at the vacancy site are gate tunable and that the trapping mechanism can be turned on and off, providing a new mechanism to control and guide electrons in grapheneComment: 18 pages and 5 figures plus 14 pages and 15 figures of supplementary information. Nature Physics advance online publication, Feb 22 (2016

Suppressive effects of Schizandra chinensis Baillon water extract on allergy-related cytokine generation and degranulation in IgE-antigen complex-stimulated RBL-2H3 cells

Schizandra chinensis Baillon is a traditional folk medicine plant that is used to treat and prevent several inflammatory diseases and cancer in Korea, but the underlying mechanisms involved in its anti-allergic activity are not fully understood. This study was designed to investigate mechanisms of anti-allergic activity of a Schizandra chinensis Baillon water extract (SCWE) in immunoglobulin E (IgE)-antigen complex-stimulated RBL2H3 cells and to assess whether gastric and intestinal digestion affects the anti-allergic properties of SCWE. Oxidative stress is an important consequence of the allergic inflammatory response. The antioxidant activities of SCWE increased in a concentration-dependent manner. RBL-2H3 cells were sensitized with monoclonal anti-dinitrophenol (DNP) specific IgE, treated with SCWE, and challenged with the antigen DNP-human serum albumin. SCWE inhibited β-hexosaminidase release and expression of interleukin (IL)-4, IL-13, and tumor necrosis factor-alpha (TNF-α) mRNA and protein in IgE-antigen complex-stimulated RBL2H3 cells. We found that digested SCWE fully maintained its antioxidant activity and anti-allergic activity against the IgE-antigen complex-induced activation of RBL-2H3 cells. SCWE may be useful for preventing allergic diseases, such as asthma. Thus, SCWE could be used as a natural functional ingredient for allergic diseases in the food and/or pharmaceutical industries

Towards the use of hydrogels in the treatment of limbal stem cell deficiency

Corneal blindness caused by limbal stem cell deficiency (LSCD) is a prevailing disorder worldwide. Clinical outcomes for LSCD therapy using amniotic membrane (AM) are unpredictable. Hydrogels can eliminate limitations of standard therapy for LSCD, because they present all the advantages of AM (i.e. biocompatibility, inertness and a biodegradable structure) but unlike AM, they are structurally uniform and can be easily manipulated to alter mechanical and physical properties. Hydrogels can be delivered with minimum trauma to the ocular surface and do not require extensive serological screening before clinical application. The hydrogel structure is also amenable to modifications which direct stem cell fate. In this focussed review we highlight hydrogels as biomaterial substrates which may replace and/or complement AM in the treatment of LSCD

Migraine triggers in Asian countries: a narrative review

BackgroundMigraine is one of the most common neurological disorders worldwide. Clinical characteristics of migraine may be somewhat different across ethnic groups. Although factors such as stress, lack of sleep, and fasting are known as migraine triggers, the discussion about geographical differences of migraine triggers in Asia is lacking.MethodsIn this study, we performed a narrative review on migraine triggers in Asia. We searched PubMed for relevant papers published between January 2000 and February 2022.ResultsForty-two papers from 13 Asian countries were included. Stress and sleep are the most frequently reported migraine triggers in Asia. There were some differences in migraine triggers in Asian countries: fatigue and weather common in Eastern Asia and fasting common in Western Asia.ConclusionMajority of the common triggers reported by patients with migraine in Asia were stress and sleep, similar to those reported globally, thus showing they are universally important. Some triggers linked to internal homeostasis are influenced by culture (e.g., alcohol, food/eating habit), and triggers related to environmental homeostasis, such as weather, are highly heterogenous between regions

The limited usefulness of real-time 3-dimensional echocardiography in obtaining normal reference ranges for right ventricular volumes

<p>Abstract</p> <p>Background</p> <p>To obtain normal reference ranges and intraobserver variability for right ventricular (RV) volume indexes (VI) and ejection fraction (EF) from apical recordings with real-time 3-dimensional echocardiography (RT3DE), and similarly for RV area indexes (AI) and area fraction (AF) with 2-dimensional echocardiography (2DE).</p> <p>Methods</p> <p>166 participants; 79 males and 87 females aged between 29–79 years and considered free from clinical and subclinical cardiovascular disease. Normal ranges are defined as 95% reference values and reproducibility as coefficients of variation (CV) for repeated measurements.</p> <p>Results</p> <p>None of the apical recordings with RT3DE and 2DE included the RV outflow tract. Upper reference values were 62 ml/m²for RV end-diastolic (ED) VI and 24 ml/m²for RV end-systolic (ES) VI. Lower normal reference value for RVEF was 41%. The respective reference ranges were 17 cm²/m²for RVEDAI, 11 cm²/m²for RVESAI and 27% for RVAF. Males had higher upper normal values for RVEDVI, RVESVI and RVEDAI, and a lower limit than females for RVEF and RVAF. Weak but significant negative correlations between age and RV dimensions were found with RT3DE, but not with 2DE. CVs for repeated measurements ranged between 10% and 14% with RT3DE and from 5% to 14% with 2DE.</p> <p>Conclusion</p> <p>Although the normal ranges for RVVIs and RVAIs presented in this study reflect RV inflow tract dimensions only, the data presented may still be regarded as a useful tool in clinical practice, especially for RVEF and RVAF.</p