Quantum simulation of partial differential equations via Schrodingerisation

We present a simple new way - called Schrodingerisation - to simulate general linear partial differential equations via quantum simulation. Using a simple new transform, referred to as the warped phase transformation, any linear partial differential equation can be recast into a system of Schrodinger's equations - in real time - in a straightforward way. This can be seen directly on the level of the dynamical equations without more sophisticated methods. This approach is not only applicable to PDEs for classical problems but also those for quantum problems - like the preparation of quantum ground states, Gibbs states and the simulation of quantum states in random media in the semiclassical limit

Joint Correcting and Refinement for Balanced Low-Light Image Enhancement

Low-light image enhancement tasks demand an appropriate balance among brightness, color, and illumination. While existing methods often focus on one aspect of the image without considering how to pay attention to this balance, which will cause problems of color distortion and overexposure etc. This seriously affects both human visual perception and the performance of high-level visual models. In this work, a novel synergistic structure is proposed which can balance brightness, color, and illumination more effectively. Specifically, the proposed method, so-called Joint Correcting and Refinement Network (JCRNet), which mainly consists of three stages to balance brightness, color, and illumination of enhancement. Stage 1: we utilize a basic encoder-decoder and local supervision mechanism to extract local information and more comprehensive details for enhancement. Stage 2: cross-stage feature transmission and spatial feature transformation further facilitate color correction and feature refinement. Stage 3: we employ a dynamic illumination adjustment approach to embed residuals between predicted and ground truth images into the model, adaptively adjusting illumination balance. Extensive experiments demonstrate that the proposed method exhibits comprehensive performance advantages over 21 state-of-the-art methods on 9 benchmark datasets. Furthermore, a more persuasive experiment has been conducted to validate our approach the effectiveness in downstream visual tasks (e.g., saliency detection). Compared to several enhancement models, the proposed method effectively improves the segmentation results and quantitative metrics of saliency detection. The source code will be available at https://github.com/woshiyll/JCRNet

Quantum simulation for time-dependent Hamiltonians -- with applications to non-autonomous ordinary and partial differential equations

Non-autonomous dynamical systems appear in a very wide range of interesting applications, both in classical and quantum dynamics, where in the latter case it corresponds to having a time-dependent Hamiltonian. However, the quantum simulation of these systems often needs to appeal to rather complicated procedures involving the Dyson series, considerations of time-ordering, requirement of time steps to be discrete and/or requiring multiple measurements and postselection. These procedures are generally much more complicated than the quantum simulation of time-independent Hamiltonians. Here we propose an alternative formalism that turns any non-autonomous unitary dynamical system into an autonomous unitary system, i.e., quantum system with a time-independent Hamiltonian, in one higher dimension, while keeping time continuous. This makes the simulation with time-dependent Hamiltonians not much more difficult than that of time-independent Hamiltonians, and can also be framed in terms of an analogue quantum system evolving continuously in time. We show how our new quantum protocol for time-dependent Hamiltonians can be performed in a resource-efficient way and without measurements, and can be made possible on either continuous-variable, qubit or hybrid systems. Combined with a technique called Schrodingerisation, this dilation technique can be applied to the quantum simulation of any linear ODEs and PDEs, and nonlinear ODEs and certain nonlinear PDEs, with time-dependent coefficients

Time complexity analysis of quantum algorithms via linear representations for nonlinear ordinary and partial differential equations

We construct quantum algorithms to compute the solution and/or physical observables of nonlinear ordinary differential equations (ODEs) and nonlinear Hamilton-Jacobi equations (HJE) via linear representations or exact mappings between nonlinear ODEs/HJE and linear partial differential equations (the Liouville equation and the Koopman-von Neumann equation). The connection between the linear representations and the original nonlinear system is established through the Dirac delta function or the level set mechanism. We compare the quantum linear systems algorithms based methods and the quantum simulation methods arising from different numerical approximations, including the finite difference discretisations and the Fourier spectral discretisations for the two different linear representations, with the result showing that the quantum simulation methods usually give the best performance in time complexity. We also propose the Schr\"odinger framework to solve the Liouville equation for the HJE, since it can be recast as the semiclassical limit of the Wigner transform of the Schr\"odinger equation. Comparsion between the Schr\"odinger and the Liouville framework will also be made.Comment: quantum algorithms,linear representations,noninea

Regulation of <i>Arabidopsis</i> root development by receptor-like kinase RGIR1 and abiotic stress

In deze studie werd een Arabidopsis mutant geïndentificeerd met een kortere wortelfenotype die gemuteerd is in het At2g37050 locus. Het gen werd Root Growth Inhibition Receptor 1 (RGIR1) genoemd en codeert voor een leucine-rich repeat kinase behorende tot de LRR-I RLK subfamilie van Arabidopsis. Zaailingen van de knock-out mutant vertoonden een significant gereduceerde wortellengte en -oppervlakte in vergelijking met het wildtype op agar, terwijl deze mutanten geen verschil in bladfenotype op agar en grond lieten zien. Hiruit werd geconcludeerd dat RGIR1 alleen een rol speelt in wortelgroei en -ontwikkeling. Onder invloed van de ethyleen precursor ACC, zout of koude stress, de lengte van de hoofdwortel en het aantal zijwortels was gereduceerd in alle genotypen. Uit kinematische analyses en morfologische parameters onder controle en abiotische stress condities gevonden dat het kortere wortelfenotype van rgir1-1 is geassocieerd met remming van de celstrekking en kleiner aantal cortexcellen in de overgangs- en strekkingszone in het wortelpuntje. Echter, de reductie in wortelgroei en -ontwikkeling van rgir1-1was meer uitgesproken bij hoge temperaturen, maar verdween wanneer de planten werden blootgesteld aan ACC, zout en koude. Dit duidt erop dat RGIR1 een positieve regulator is van het proces van wortelgroei en –ontwikkeling onder optimale omstandigheden. Het regulatiemechanisme waarmee RGIR1 de wortellengte beïnvloedt lijkt onafhankelijk van het mechanisme waarmee lage temperatuur, zout en ACC de wortellengte remmen.In the present study, we identified an Arabidopsis mutant with a short root phenotype of mutated in/at the At2g37050 locus. The gene was annotated as Root Growth Inhibition Receptor 1 (RGIR1), which encodes a leucine-rich repeat kinase belonging to the LRR-I RLK subfamily of Arabidopsis. Seedlings of the knock-out mutant rgir1-1 showed a significantly reduced root length and root surface area compared to the wild type when grown on agar while no difference was found in leaf phenotype both on agar plates and in soil. Thus, RGIR1 only function in root growth and root development. In the presence of the ethylene precursor ACC, salt or cold stress, all genotypes produced roots with a shorter main root length and less lateral roots. From the results of kinematic analysis and morphology parameters under control and abiotic stress conditions, the observed short root phenotype of rgir1-1 mutant root is associated with a lower cell elongation rate and decreased cortex cell number in the transition and elongation zone of the root tip. However, the reduction of root growth and development of rgir1-1 was more pronounced at high temperatures, but disappeared when exposed to ACC, high salinity or cold stress, indicating that RGIR1 is a positive regulator of root growth in Arabidopsis under optimal growth conditions and it seems not directly to interact with pathways of plants in response to cold and salinity stress, or ACC

A Novel Model of Atherosclerosis in Rabbits Using Injury to Arterial Walls Induced by Ferric Chloride as Evaluated by Optical Coherence Tomography as well as Intravascular Ultrasound and Histology

This study aim was to develop a new model of atherosclerosis by FeCl3-induced injury to right common carotid arteries (CCAs) of rabbits. Right CCAs were induced in male New Zealand White rabbits (n = 15) by combination of a cholesterol-rich diet and FeCl3-induced injury to arterial walls. The right and left CCAs were evaluated by histology and in vivo intravascular ultrasound (IVUS) and optical coherence tomography (OCT) examinations of 24 hours (n = 3), 8 weeks (n = 6), and 12 weeks (n = 6) after injury. Each right CCA of the rabbits showed extensive white-yellow plaques. At eight and 12 weeks after injury, IVUS, OCT, and histological findings demonstrated that the right CCAs had evident eccentric plaques. Six plaques (50%) with evident positive remodeling were observed. Marked progression was clearly observed in the same plaque at 12 weeks after injury when it underwent repeat OCT and IVUS. We demonstrated, for the first time, a novel model of atherosclerosis induced by FeCl3. The model is simple, fast, inexpensive, and reproducible and has a high success rate. The eccentric plaques and remodeling of plaques were common in this model. We successfully carried out IVUS and OCT examinations twice in the same lesion within a relatively long period of time

A novel S-sulfhydrated human serum albumin preparation suppresses melanin synthesis

Products of ultraviolet (UV) irradiation such as reactive oxygen species (ROS) and nitric oxide (NO) stimulate melanin synthesis. Reactive sulfur species (RSS) have been shown to have strong ROS and NO scavenging effects. However, the instability and low retention of RSS limit their use as inhibitors of melanin synthesis. The free thiol at Cys34 on human serum albumin (HSA) is highly stable, has a long retention and possess a high reactivity for RSS. We report herein on the development of an HSA based RSS delivery system. Sulfane sulfur derivatives released from sodium polysulfides (Na2Sn) react readily with HSA. An assay for estimating the elimination of sulfide from polysulfide showed that almost all of the sulfur released from Na2Sn bound to HSA. The Na2Sn-treated HSA was found to efficiently scavenge ROS and NO produced from chemical reagents. The Na2Sn-treated HSA was also found to inhibit melanin synthesis in B16 melanoma cells and this inhibition was independent of the number of added sulfur atoms. In B16 melanoma cells, the Na2Sn-treated HSA also inhibited the levels of ROS and NO induced by UV radiation. Finally, the Na2Sn-treated HSA inhibited melanin synthesis from L-DOPA and mushroom tyrosinase and suppressed the extent of aggregation of melanin pigments. These data suggest that Na2Sn-treated HSA inhibits tyrosinase activity for melanin synthesis via two pathways; by directly inhibiting ROS signaling and by scavenging NO. These findings indicate that Na2Sn-treated HSA has potential to be an attractive and effective candidate for use as a skin whitening agent