Small Solutes Research Articles

Hybrid Parallel Ant Colony Optimization for Application to Quantum Computing to Solve Large-Scale Combinatorial Optimization Problems

Quantum computing is a promising technology that may provide breakthrough solutions to today’s difficult problems such as breaking encryption and solving large-scale combinatorial optimization problems. An algorithm referred to as Quantum Approximate Optimization Algorithm (QAOA) has been recently proposed to approximately solve hard problems using a protocol know as bang–bang. The technique is based on unitary evolution using a Hamiltonian encoding of the objective function of the combinatorial optimization problem. The QAOA was explored in the context of several optimization problems such as the Max-Cut problem and the Traveling Salesman Problem (TSP). Due to the relatively small node-size solution capability of the available quantum computers and simulators, we developed a hybrid approach where sub-graphs of a TSP tour can be executed on a quantum computer, and the results from the quantum optimization are combined for a further optimization of the whole tour. Since the local optimization of a sub-graph is prone to becoming trapped in a local minimum, we overcame this problem by using a parallel Ant Colony Optimization (ACO) algorithm with periodic pheromone exchange between colonies. Our method exceeds existing approaches which have attempted partitioning a graph for small problems (less than 48 nodes) with sub-optimal results. We obtained optimum results for benchmarks with less than 150 nodes and results usually within 1% of the known optimal solution for benchmarks with around 2000 nodes.

Atomistic simulations reveal strength reductions due to short-range order in alloys

A theory for strengthening for multicomponent non-dilute alloys possessing short-range order (SRO) has recently been developed. The theory predicts that, in addition to a well-known athermal strengthening, there is a notable effect of SRO on the solute–dislocation interactions that can decrease or increase the strength relative to a random alloy. Here, carefully designed atomistic simulations in a model binary NbW alloy are used to demonstrate that alloy strength due to solute–dislocation interactions can be increased or decreased, depending on the SRO and consistent with theoretical predictions. Specifically, SRO is introduced using fictitious solute–solute interactions in an alloy system with very small true solute–solute interactions, and the Nudged Elastic Band (NEB) method is then used to compute the energy barriers for edge dislocation motion for various levels of SRO. Energy barriers, and hence alloy strengths, can be decreased when the Warren-Cowley SRO parameters are negative (attraction of unlike solutes). The theoretical predictions for the same system are in reasonable quantitative agreement with the simulation results. These findings demonstrate the unexpected possibility of reduced strength due to SRO and also further validate the analytical theory as a tool to guide alloy design.

Genome-wide identification and characterisation of Aquaporins in Rosa chinensis

ABSTRACT Aquaporins (AQPs) are small integral membrane proteins that facilitate the efficient transport of small solutes like water, metalloids, urea, and CO2 across the membrane. Plant aquaporins are known to be involved in vital physiological processes like seed germination, stomatal movement, cell elongation, and reproductive growth. In the present study, 36 AQPs were identified through genome-wide computational analysis performed in the rose genome. Subsequent phylogenetic analysis classified the AQPs into five subfamilies, including 10 Plasma membrane intrinsic proteins (PIPs), 8 Tonoplast intrinsic proteins (TIPs), 9 Nodulin intrinsic proteins (NIPs), 3 Small intrinsic proteins (SIPs), and 6 uncharacterised intrinsic proteins (XIPs). Based on the prediction of silicon solute specificity, one of the NIPs is predicted to be a silicon transporter. Structural analysis revealed the characteristic six trans-membrane domains and two-half alpha helix harbouring two conserved NPA motifs in the majority of the predicted AQPs. The protein tertiary structures predicted with homology-based modelling were used to study the pore lining remains and to predict the solute transport activity of the AQPs. Expression profiling of the rose AQPs showed tissue-specific expression of many members. The data provided here will help in understanding the AQP-based solute transport system in roses and other related species.

On the planar Gaussian-Minkowski problem

The current work focuses on the Gaussian-Minkowski problem in dimension 2. In particular, we show that if the Gaussian surface area measure is proportional to the spherical Lebesgue measure, then the corresponding convex body has to be a centered disk. As an application, this “uniqueness” result is used to prove the existence of smooth small solutions to the Gaussian-Minkowski problem via a degree-theoretic approach.

Global small solutions to the 3D compressible viscous non-resistive MHD system

Whether or not smooth solutions to the 3D compressible magnetohydrodynamic (MHD) equations without magnetic diffusion are always global in time remains an extremely challenging open problem. No global well-posedness or stability result is currently available for this 3D MHD system in the whole space [Formula: see text] or the periodic box [Formula: see text] even when the initial data is small or near a steady-state solution. This paper presents a global existence and stability result for smooth solutions to this 3D MHD system near any background magnetic field satisfying a Diophantine condition.

Assisted PD throughout Europe: advantages, inequities, and solution proposals

BackgroundPeritoneal dialysis provides several benefits for patients and should be offered as first line kidney replacement therapy, particularly for fragile patients. Limitation to self-care drove assisted peritoneal dialysis to evolve from family-based care to institutional programs, with specialized care givers. Some European countries have mastered this, while others are still bound by the availability of a volunteer to become responsible for treatment.MethodsA group of leading nephrologists from 13 European countries integrated real-life application of such therapy, highlighting barriers, lessons learned and practical solutions. The objective of this work is to share and summarize several different approaches, with their intrinsic difficulties and solutions, which might helpperitoneal dialysis units to develop and offer assisted peritoneal dialysis.ResultsAssisted peritoneal dialysis does not mean 4 continuous ambulatory peritoneal dialysis exchanges, 7 days/week, nor does it exclude cycler. Many different prescriptions might work for our patients. Tailoring PD prescription to residual kidney function, thereby maintaining small solute clearance, reduces dialysis burden and is associated with higher technique survival. Assisted peritoneal dialysis does not mean assistance will be needed permanently, it can be a transitional stage towards individual or caregiver autonomy. Private care agencies can be used to provide assistance; other options may involve implementing PD training programs for the staff of nursing homes or convalescence units. Social partners may be interested in participating in smaller initiatives or for limited time periods.ConclusionAssisted peritoneal dialysis is a valid technique, which should be expanded. In countries without structural models of assisted peritoneal dialysis, active involvement by the nephrologist is needed in order for it to become a reality.Graphical abstract

Global behavior of small data solutions for the 2D Dirac–Klein-Gordon system

In this paper, we are interested in the two-dimensional Dirac–Klein-Gordon system, which is a basic model in particle physics. We investigate the global behavior of small data solutions to this system in the case of a massive scalar field and a massless Dirac field. More precisely, our main result is twofold: (1) we show sharp time decay for the pointwise estimates of the solutions, which implies the asymptotic stability of this system; (2) we show the linear scattering result of this system which is a fundamental problem when it is viewed as dispersive equations. Our result is valid for general small, high-regular initial data, and in particular, there is no restriction on the support of the initial data.

Global Existence of Small Amplitude Solutions for a Model Quadratic Quasilinear Coupled Wave-Klein-Gordon System in Two Space Dimension, with Mildly Decaying Cauchy Data

The aim of this monograph is to study the global existence of solutions to a coupled wave-Klein-Gordon system in space dimension two when initial data are small smooth and mildly decaying at infinity. Some physical models strictly related to general relativity have shown the importance of studying such systems but very few results are known at present in low space dimension. We study here a model two-dimensional system, in which the nonlinearity writes in terms of “null forms”, and show the global existence of small solutions. Our goal is to prove some energy estimates on the solution when a certain number of Klainerman vector fields is acting on it, and some optimal uniform estimates. The former ones are obtained using systematically quasilinear normal forms, in their para-differential version; the latter ones are recovered by deducing a new coupled system of a transport equation and an ordinary differential equation from the starting PDE system by means of a semiclassical micro-local analysis of the problem. We expect the strategy developed here to be robust enough to enable us, in the future, to treat the case of the most general nonlinearities.

Advanced optical imaging reveals preferred spatial orientation of podocyte processes along the axis of glomerular capillaries

Mammalian kidneys filter enormous volumes of water and small solutes, a filtration driven by the hydrostatic pressure in glomerular capillaries, which is considerably higher than in most other tissues. Interdigitating cellular processes of podocytes form the slits for fluid filtration connected by the membrane-like slit diaphragm cell junction containing a mechanosensitive ion channel complex and allow filtration while counteracting hydrostatic pressure. Several previous publications speculated that podocyte processes may display a preferable orientation on glomerular capillaries instead of a random distribution. However, for decades, the controversy over spatially oriented filtration slits could not be resolved due to technical limitations of imaging technologies. Here, we used advanced high-resolution, three-dimensional microscopy with high data throughput to assess spatial orientation of podocyte processes and filtration slits quantitatively. Filtration-slit-generating secondary processes preferentially align along the capillaries' longitudinal axis while primary processes are preferably perpendicular to the longitudinal direction. This preferential orientation required maturation in development of the mice but was lost in mice with kidney disease due to treatment with nephrotoxic serum or with underlying heterologous mutations in the podocyte foot process protein podocin. Thus, the observation that podocytes maintain a preferred spatial orientation of their processes on glomerular capillaries goes well in line with the role of podocyte foot processes as mechanical buttresses to counteract mechanical forces resulting from pressurized capillaries. Future studies are needed to establish how podocytes establish and maintain their orientation and why orientation is lost under pathological conditions.

Infinitely Many Solutions for a Perturbed Partial Discrete Dirichlet Problem Involving ϕc-Laplacian

In this paper, by using critical point theory, the existence of infinitely many small solutions for a perturbed partial discrete Dirichlet problems including the mean curvature operator is investigated. Moreover, the present study first attempts to address discrete Dirichlet problems with ϕc-Laplacian operator in relative to some relative existing references. Based on our knowledge, this is the research of perturbed partial discrete bvp with ϕc-Laplacian operator for the first time. At last, two examples are used to examplify the results.

On an incompressible inertial nematic electrolyte model of liquid crystal flow

ABSTRACT We study the Cauchy problem of the new model of the three dimensional inertial nematic electrolyte, which models the N-species charged particles diffuse and advect in the nematic liquid crystalline matrix. This new model was proposed by [Calderer MC, Golovaty D, Lavrentovich O, et al. Modeling of nematic electrolytes and nonlinear electroosmosis. SIAM J Appl Math. 2016;76:2260–2285. doi: 10.1137/16M1056225]. The inertial effect is such that the system involves a hyperbolic feature. We first derive the local existence in large initial data when the flow is isotropy, i.e. λ = 1 . For the anisotropy case ( λ > 0 , λ ≠ 1 ), we obtain small data local solutions. Then, by seeking some further dissipative mechanisms from the elliptic structures, the local solution can be extended globally near the constant states with electro-neutrality condition.

Analysis of Financing Difficulties for Small and Medium-sized Businesses and Solutions

Small and medium-sized businesses in China have grown quickly in recent years, making them the largest and most dynamic group of businesses there. They play a significant role in the country's overall economy. However, small and medium-sized businesses are facing financing difficulties. Businesses financing is necessary for the future operation and development of a company, and it is also a necessary guarantee for the sustainable operation of the businesses. The method used in this paper is literature analysis. Therefore, this paper mainly analyzes the reasons for the financing difficulties faced by small and medium-sized businesses from three aspects: the financing difficulties of small and medium-sized businesses are mainly caused by their own characteristics, financial institutions such as banks, and imperfect laws and regulations. And then gives corresponding solutions. Small and medium-sized businesses have improved their comprehensive strength, improved the construction of banking and other financial systems, and the state has revised and improved laws and regulations.

Nonlinear fractional damped wave equation on compact Lie groups

In this paper, we deal with the initial value fractional damped wave equation on G, a compact Lie group, with power-type nonlinearity. The aim of this manuscript is twofold. First, using the Fourier analysis on compact Lie groups, we prove a local in-time existence result in the energy space for the fractional damped wave equation on G. Moreover, a finite time blow-up result is established under certain conditions on the initial data. In the next part of the paper, we consider fractional wave equation with lower order terms, i.e., damping and mass with the same power type nonlinearity on compact Lie groups, and prove the global in-time existence of small data solutions in the energy evolution space.

Center point prediction using Gaussian elliptic and size component regression using small solution space for object detection

Center point prediction using Gaussian elliptic and size component regression using small solution space for object detection

Multiple Solutions to a Non-Local Problem of Schrödinger–Kirchhoff Type in ℝN

The main purpose of this paper is to show the existence of a sequence of infinitely many small energy solutions to the nonlinear elliptic equations of Kirchhoff–Schrödinger type involving the fractional p-Laplacian by employing the dual fountain theorem as a key tool. Because of the presence of a non-local Kirchhoff coefficient, under conditions on the nonlinear term given in the present paper, we cannot obtain the same results concerning the existence of solutions in similar ways as in the previous related works. For this reason, we consider a class of Kirchhoff coefficients that are different from before to provide our multiplicity result. In addition, the behavior of nonlinear terms near zero is slightly different from previous studies.

MCPAP: A MSIS-based conditional privacy-preserving authentication protocol for smart grids

The smart grid is considered a promising second-generation power grid because electricity service companies can use it to store energy more securely and deliver energy more efficiently. To protect the reliability of power consumption information and the privacy of users’ identity information in a smart grid, many conditional privacy-preserving authentication protocols have been proposed in the last decade. However, these protocols are vulnerable to attacks from the quantum computer because of the large integer factorization problem or the discrete logarithm problem embedded in these protocols. To solve this problem, a security-enhanced conditional privacy-preserving authentication protocol is designed in this paper by using the module small integer solution problem. Besides, we show that our protocol has superior security in the random oracle model. The potential utility of this protocol in the smart grid is also demonstrated through our detailed performance analysis. Moreover, our protocol can use the batch verification method to improve its efficiency significantly.

The σ$$ \sigma $$‐evolution equations with friction and unbounded coefficients

We present in this article the study on the decay estimates for solutions of the Cauchy problem for a class of linear ‐evolution equations with unbounded coefficients with in space dimension , where the coefficient is continuous and unbounded satisfying the asymptotic behavior as , with the parameter , and is a positive and bounded continuous function. By investigating the diffusion phenomenon, we obtain new results that generalize our previous study for the damped wave models with constant and nearly constant coefficients. Using the decay estimates for the solution of the linear problem, we establish a result on the global (in time) existence of the small data solution for the corresponding semilinear Cauchy problem with the nonlinearity of power type.

A Heteronuclear NMR Study of Aqueous Lithium Salt Solutions of l-Alanine: Revealing Solute Hydrophobic Association through the NMR B' Coefficient.

In the present study, a set of heteronuclear NMR approaches has been adopted to investigate the solution behavior of a small hydrophobic solute l-alanine in the presence of lithium (Li) salts. The presence of salts plays a major role in determining the structure and solvation of biomolecules. It therefore evokes interest to understand the effect of Li salts on amino acids (alanine), the building block of biomolecules. The ionic solute dynamics in the present case has been probed using 1H, 7Li, and 13C nuclei available in the aqueous Li salt solution of l-alanine. Nuclear longitudinal spin relaxation of alanine protons was examined at a variable concentration range of three lithium salts, i.e., LiCl, Li2SO4 and LiClO4, to introduce the NMR B' coefficient for each salt defining ionic solute/solvent interaction in the solution. Analysis of the active relaxation mechanism of 7Li spin-lattice relaxation further revealed the presence of alanine in the solvation shell of Li ion depending on the anionic counterpart.

Blow-up solutions of damped Klein–Gordon equation on the Heisenberg group

We prove the blow-up of solutions of the semilinear damped Klein–Gordon equation in a finite time for arbitrary positive initial energy on the Heisenberg group. This work complements the paper Ruzhansky and Tokmagambetov (J Differ Equ 265(10):5212–5236, 2018), where the global in time well-posedness was proved for the small energy solutions.

Analytical solutions and mathematical simulation of traveling wave solutions to fractional order nonlinear equations

We investigate the tanh–coth method’s usefulness in understanding space–time fractional nonlinear evolution problems. To use this method and then examine their plots, we take into consideration three significant equations: the space–time fractional Burgers equation, the space–time fractional regularized long wave equation, and the space–time fractional Boussinesq equation. The modified Riemann–Liouville derivatives are used to define the fractional derivative. The approach provides a linearization- or small perturbation-free analytical solution in the form of a convergent series with easily calculable components. For the aforementioned nonlinear fractional equations, we have discovered their precise solutions. We utilize a generalized fractional complex transform to translate these to ordinary differential equations which subsequently resulted into number of exact solutions. The method provides us abundant analytical traveling wave solutions containing fewer number parameters with the aid of Mathematica and MATLAB.