A Herglotz wavefunction method for solving the inverse Cauchy problem connected with the Helmholtz equation

AbstractThis paper is concerned with the Cauchy problem connected with the Helmholtz equation. On the basis of the denseness of Herglotz wavefunctions, we propose a numerical method for obtaining an approximate solution to the problem. We analyze the convergence and stability with a suitable choice of regularization method. Numerical experiments are also presented to show the effectiveness of our method

A Solution to the Ambiguity Problem in Depth Contouring

Depth contours on a chart are important for safe navigation. The ambiguity problem can appear when points of equal depth are joined in contouring. Unreasonable solutions may mistake a shallow area for a deep one, which could result in a potential danger for navigation. A solution is presented to solve the ambiguity problem using constrained lines formed by two shallow depths. The constrained lines are used to limit the joining of the points with equal depth. Experimental results demonstrate that the proposed solution can reduce the dangers of producing non-existent deep areas in bathymetric contouring.Las isobatas en una carta son importantes para la seguridad de la navegaciôn. El problema de ambiguedad puede aparecer cuando puntos de igual profundidad se unen en el trazado de la isobata. Soluciones no razonadas pueden confundir un area somera por una profunda, lo que podria resultar en un peligro potencial a la navegaciôn. Una soluciôn se présenta para resolver el problema de ambigüedad utilizando lineas forzadas formadas por dos profundidades s orneras. Las lineas forzadas se ut Uizan para limitar la union de puntos con igual profundidad. Los resultados expérimentales demuestran que la soluciôn propuesta puede reducir los peligros de producir areas profundas no existentes en los contornos batimétricos.Sur une carte, les isobathes sont importantes en ce qui concerne la sécurité de la navigation. Le problème de l'ambiguïté peut apparaître lorsque des points de profondeur égale se rejoignent sur le tracé de l'isobathe. Certaines solutions non fondées rationnellement peuvent prendre par erreur une zone peu profonde pour une zone profonde, ce qui peut entraîner un danger potentiel pour la navigation. Une solution est présentée pour résoudre le problème de l’ambiguïté en utilisant des lignes contraintes formées par deux faibles profondeurs. Les lignes contraintes sont utilisées pour limiter la réunion de points d’une égale profondeur. Des résultats expérimentaux ont montré que la solution proposée peut réduire les dangers liés à la création de zones profondes non existantes dans le tracé bathymétrique

Improving fatty acids production by engineering dynamic pathway regulation and metabolic control

Global energy demand and environmental concerns have stimulated increasing efforts to produce carbon-neutral fuels directly from renewable resources. Microbially derived aliphatic hydrocarbons, the petroleum-replica fuels, have emerged as promising alternatives to meet this goal. However, engineering metabolic pathways with high productivity and yield requires dynamic redistribution of cellular resources and optimal control of pathway expression. Here we report a genetically encoded metabolic switch that enables dynamic regulation of fatty acids (FA) biosynthesis in Escherichia coli. The engineered strains were able to dynamically compensate the critical enzymes involved in the supply and consumption of malonyl-CoA and efficiently redirect carbon flux toward FA biosynthesis. Implementation of this metabolic control resulted in an oscillatory malonyl-CoA pattern and a balanced metabolism between cell growth and product formation, yielding 15.7- and 2.1-fold improvement in FA titer compared with the wild-type strain and the strain carrying the uncontrolled metabolic pathway. This study provides a new paradigm in metabolic engineering to control and optimize metabolic pathways facilitating the high-yield production of other malonyl-CoA–derived compounds.National Science Foundation (U.S.) (Award CBET1144226)National Science Foundation (U.S.) (Award CBET0836513)Rensselaer Polytechnic Institute. Biocatalysis and Metabolic Engineering Constellatio

Fractionation of sulfated galactan from the red alga Botryocladia occidentalis separates its anticoagulant and anti-SARS-CoV-2 properties

Sulfation pattern and molecular weight (MW) play a key role in the biological actions of sulfated glycans. Besides anticoagulant effects, certain sulfated glycans can also exhibit anti-SARS-CoV-2 properties. To develop a more selective antiviral carbohydrate, an efficient strategy to separate these two actions is required. In this work, low MW fractions derived from the red alga Botryocladia occidentalis sulfated galactan (BoSG) were generated, structurally characterized, and tested for activity against SARS-CoV-2 and blood coagulation. The lowest MW fraction was found to be primarily composed of octasaccharides of monosulfated monosaccharides. Unlike heparin or native BoSG, we found that hydrolyzed BoSG products had weak anticoagulant activities as seen by aPTT and inhibitory assays using purified cofactors. In contrast, lower MW BoSG-derivatives retained anti-SARS-CoV-2 activity using SARS-CoV-2 spike (S)-protein pseudotyped lentivirus vector in HEK-293T-hACE2 cells monitored by GFP. Surface plasmon resonance confirmed that longer chains are necessary for BoSG to interact with coagulation cofactors but is not required for interactions with certain S-protein variants. We observed distinct affinities of BoSG derivatives for the S-proteins of different SARS-CoV-2 strains, including WT, N501Y (Alpha), K417T/E484K/N501Y (Gamma), and L542R (Delta) mutants, and stronger affinity for the N501Y-containing variants. Docking of the four possible monosulfated BoSG disaccharides in interactions with the N501Y mutant S-protein predicted potential binding poses of the BoSG constructs and favorable binding in close proximity to the 501Y residue. Our results demonstrate that depolymerization and fractionation of BoSG are an effective strategy to segregate its anticoagulant property from its anti-SARS-CoV-2 action

Enhancement of shot noise due to the fluctuation of Coulomb interaction

We have developed a theoretical formalism to investigate the contribution of fluctuation of Coulomb interaction to the shot noise based on Keldysh non-equilibrium Green's function method. We have applied our theory to study the behavior of dc shot noise of atomic junctions using the method of nonequilibrium Green's function combined with the density functional theory (NEGF-DFT). In particular, for atomic carbon wire consisting 4 carbon atoms in contact with two Al(100) electrodes, first principles calculation within NEGF-DFT formalism shows a negative differential resistance (NDR) region in I-V curve at finite bias due to the effective band bottom of the Al lead. We have calculated the shot noise spectrum using the conventional gauge invariant transport theory with Coulomb interaction considered explicitly on the Hartree level along with exchange and correlation effect. Although the Fano factor is enhanced from 0.6 to 0.8 in the NDR region, the expected super-Poissonian behavior in the NDR regionis not observed. When the fluctuation of Coulomb interaction is included in the shot noise, our numerical results show that the Fano factor is greater than one in the NDR region indicating a super-Poissonian behavior

Unified framework of the microscopic Landau-Lifshitz-Gilbert equation and its application to Skyrmion dynamics

The Landau-Lifshitz-Gilbert (LLG) equation is widely used to describe magnetization dynamics. We develop a unified framework of the microscopic LLG equation based on the nonequilibrium Green's function formalism. We present a unified treatment for expressing the microscopic LLG equation in several limiting cases, including the adiabatic, inertial, and nonadiabatic limits with respect to the precession frequency for a magnetization with fixed magnitude, as well as the spatial adiabatic limit for the magnetization with slow variation in both its magnitude and direction. The coefficients of those terms in the microscopic LLG equation are explicitly expressed in terms of nonequilibrium Green's functions. As a concrete example, this microscopic theory is applied to simulate the dynamics of a magnetic Skyrmion driven by quantum parametric pumping. Our work provides a practical formalism of the microscopic LLG equation for exploring magnetization dynamics