Solution Of Problem Research Articles

Экология техносферы человеческого сообщества

In the 19th century, the sphere of interest of the science of “ecology” was formulated. Over the course of a century and a half, the semantics of its tasks has undergone significant changes. However, the original definition of ecology given by E.G. Haeckel, as a science about the interaction of living and inanimate nature, has again become relevant with the technological development of mankind. This development led to the emergence of an alternative habitat - the technosphere. The technosphere, within the framework of environmental ideas, is considered as a formation deeply hostile to nature in its essence. Nature is considered as a certain ideal that creates favorable conditions for the existence of living organisms in it. The experience of natural disasters and cataclysms, accompanied by the mass death of living organisms, indicates that this is an idealized idea. The existence of modern man outside the technosphere is practically impossible. The techno-sphere takes on the task of providing humanity with protection from pathogens. An example of such control is the use of DDT against vectors of malaria and other diseases. The technosphere solves problems in relation to humanity that are similar to providing the body with food, solving the problems of energy supply and movement over various distances – both people and cargo. The technosphere is evolving, using the achievements of developing sciences and technologies, reducing the specific impact on the natural environment while meeting the needs of the individual. For the further development of human ecology at the intersection of natural and artificial, the solution of traditional management problems is required: strict control of raw materials, technologies and products used, and their rational distribution. This is important since the human population is steadily growing and a significant part of the planet’s population finds itself in conditions of food and energy shortages, while the other part has an abundance of resources.

An integrated binary metaheuristic approach in dynamic unit commitment and economic emission dispatch for hybrid energy systems

The current generation portfolio is obligated to incorporate zero-emissions energy sources, predominantly wind and solar, due to the depletion of fossil fuels and the alarming rate of global warming. In the current scenario, power engineers must devise a compromised solution that not only advocates for the adoption of renewable energy sources (RES) but also efficiently schedules all conventional power generation units to balance the increasing load demand while simultaneously minimizing fuel costs and harmful emissions that are currently addressed by Unit Commitment (UC) and Combined Economic Emission Dispatch (CEED) problem solutions. However, the integration of renewable energy resources (RES) further complicates the UC-CEED problem due to their intermittent nature. Recently, metaheuristic algorithms are acquiring momentum in resolving constrained UC-CEED problems due to their improved global solution ability, adaptability, and derivative-free construction. In this research, a computationally efficient binary hybrid version of crow search algorithm and improvised grey wolf optimization is proposed, namely Crow Search Improved Binary Grey Wolf Optimization Algorithm (CS-BIGWO) by inclusion of nonlinear control parameter, weight-based position updating, and mutation approach. Statistical results on standard mathematical functions prove the supremacy of the proposed algorithm over conventional algorithms. Further, a novel optimization strategy is devised by integrating enhanced lambda iteration with the CS-BIGWO algorithm (CS-BIGWO-λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda$$\\end{document}) to solve a day-ahead UC-CEED problem of the hybrid energy system incorporating cost functions of RES. For the model, a day-ahead forecast of wind power and solar photovoltaic power is obtained by using the Levy-Flight Chaotic Whale Optimization Algorithm optimized Extreme Learning Machines(LCWOA-ELM). The proposed algorithm is tested for the UC-CEED solution of an IEEE-39 bus system with two distinct cases: (1) without RES integration and (2) with RES integration. Several independent trial runs are executed, and the performance of the algorithms is assessed based on optimal UC schedules, fuel cost, emission quantization, convergence curve, and computational time. For case 1, the proposed algorithm resulted in a percentage reduction of 0.1021% in fuel cost and 0.7995% in emission. In contrast, for test case 2, it resulted in a percentage reduction of 0.12896% in fuel cost and 0.772% in emission with the proposed algorithm. The results validate the dominance of the proposed methodology over existing methods in terms of lower fuel costs and emissions.

Radial Kernels Collocation Method for the Solution of Volterra Integro-Differential Equations

Radial kernel interpolation is an advanced method in approximation theory for the construction of higher order accurate interpolants for scattered data up to higher dimensional spaces. In this manuscript, we formulate a radial kernel collocation approach for solving problems involving the Volterra integro-differential equations using two radial kernels: The Generalized Multi-quadrics and the linear Laguerre-Gaussians. This was achieved by simplifying the Volterra integral problem's solution to an algebraic system of equations. The impact of the shape parameter present in every kernel on the method's accuracy is examined and found to be significant. Two examples were used to illustrate the process; the numerical results are shown as tables and graphs. MATLAB 2018a was employed in the process.

Asymptotic analysis of sign-changing transmission problems with rapidly oscillating interface

We study the asymptotic behavior of a sign-changing transmission problem, stated in a symmetric oscillating domain obtained by gluing together a positive and a negative material, separated by an imperfect and rapidly oscillating interface. The interface separating the two heterogeneous materials has a periodic microstructure and is a small perturbation of a flat interface. The solution of the transmission problem is continuous and its flux has a jump on the oscillating interface. Under certain conditions on the properties of the two materials, we derive the limit problem and we prove the convergence result. The T-coercivity method is used to handle the lack of coercivity for both the microscopic and the macroscopic limit problems. For more information see https://ejde.math.txstate.edu/Volumes/2024/60/abstr.html

Osprey optimization algorithm for MPPT of PV system with forward DC to DC converter under partial shading conditions

Abstract Electric power is required anywhere for multiple purposes to do various tasks. Production of electricity from renewable sources such solar energy is feasible solution for many problems. Photovoltaic modules are generally used to produce electricity through solar irradiance. However, a maximum power point tracking device (MPPTD) must be incorporated to Photovoltaic system to ensure its maximum utilization or best efficiency. A forward DC to DC circuit is selected to work as MPPTD in this paper. Many conventional algorithms including incremental conductance, perturb & observe are available to work effectively for MPPTD under uniform solar irradiances. However, non-uniform irradiances will be received by Photovoltaic modules where many are connected to form a power generation system due to trees, shading, dust, birds, clouds, etc Such phenomenon drags the system into Partial Shading Condition (PSC). Under PSC, conventional algorithms cannot identify the best location to harvest more energy. Hence, an optimization technique is required to operate Photovoltaic system at its outfit utilization during PSC. An optimization technique namely ‘Osprey Optimization Algorithm (OOA)’ is developed in this paper on MPPTD to harvest more energy during PSC. The comparison among OOA, Grey Wolf Optimization (GWO), Modified Invasive Weed Optimization (MIWO) and Whale Optimization Algorithm (WOA) is also included in this paper. The Hardware—in the—Loop is establish by using OPAL-RT technology to collect various results for presenting analysis under different operating conditions.

Numerical solutions of boundary value problems via fixed point iteration

Numerical solutions of boundary value problems via fixed point iteration

Recursive utility optimization problem described by forward–backward stochastic differential inclusions

The main result of the paper deals with the existence of a solution of a recursive utility optimization problem described by systems of the forward–backward stochastic differential inclusion of the form: X t − X s ∈ ∫ s t F ( τ , X τ ) d τ + ∫ s t ( G ∘ X ) d B τ and Y t ∈ E [ H ( X T ) + ∫ t T Φ ( τ , X τ , Y τ ) d τ | F t ] , considered in the author paper [Kisielewicz. Weak compactness of weak solutions to forward–backward stochastic differential inclusions. Stoch Anal Appl. 2024;42(2):306–326], where the existence of weak solutions and weak compactness in distribution of the set W ( F , H , Φ , G , μ ) of all its weak solutions have been proved.

A nonlinear least-squares convexity enforcing 𝐶⁰ interior penalty method for the Monge–Ampère equation on strictly convex smooth planar domains

We construct a nonlinear least-squares finite element method for computing the smooth convex solutions of the Dirichlet boundary value problem of the Monge-Ampère equation on strictly convex smooth domains in R 2 {\mathbb {R}}^2 . It is based on an isoparametric C 0 C^0 finite element space with exotic degrees of freedom that can enforce the convexity of the approximate solutions. A priori and a posteriori error estimates together with corroborating numerical results are presented.

Design of reliable and fast Schmitt trigger 10T SRAM cells using in-memory computing

Abstract Microprocessors, integrated data storage systems, and cache memories are just a few applications that can benefit from Static random access memory (SRAM). Computing In memory provides a solution for the von Neumann bottleneck problems. Simultaneously, it removes needless repeated data transmission between CPU and memory. Schmitt trigger was utilized for energy-efficient operation to get high reading and writing capacity. Two cross-coupled inverters with a transistor in between increase the design writing process. Furthermore, voltage boost logic is prioritized to maximize the node capacity. Using two dummy columns and dummy rows in RAM, the Replica technique controls the flow of signals via the core. The simulated results are compared to the designs that already exist. The simulation results show that the leakage power of the proposed design is 0.75 nw at 0.6 volts. The write static noise margin (WSNM) of the proposed cell is twice that of SEDF10T, which can be helpful for high-performance computing applications.

Oracle-Net for Nonlinear Compressed Sensing in Electrical Impedance Tomography Reconstruction Problems

Sparse recovery principles play an important role in solving many nonlinear ill-posed inverse problems. We investigate a variational framework with learned support estimation for compressed sensing sparse reconstructions, where the available measurements are nonlinear and possibly corrupted by noise. A graph neural network, named Oracle-Net, is proposed to predict the support from the nonlinear measurements and is integrated into a regularized recovery model to enforce sparsity. The derived nonsmooth optimization problem is then efficiently solved through a constrained proximal gradient method. Error bounds on the approximate solution of the proposed Oracle-based optimization are provided in the context of the ill-posed Electrical Impedance Tomography problem (EIT). Numerical solutions of the EIT nonlinear inverse reconstruction problem confirm the potential of the proposed method which improves the reconstruction quality from undersampled measurements, under sparsity assumptions.

Joint Approach for Vehicle Routing Problems Based on Genetic Algorithm and Graph Convolutional Network

The logistics demands of industries represented by e-commerce have experienced explosive growth in recent years. Vehicle path-planning plays a crucial role in optimization systems for logistics and distribution. A path-planning scheme suitable for an actual scenario is the key to reducing costs and improving service efficiency in logistics industries. In complex application scenarios, however, it is difficult for conventional heuristic algorithms to ensure the quality of solutions for vehicle routing problems. This study proposes a joint approach based on the genetic algorithm and graph convolutional network for solving the capacitated vehicle routing problem with multiple distribution centers. First, we use the heuristic method to modularize the complex environment and encode each module based on the constraint conditions. Next, the graph convolutional network is adopted for feature embedding for the graph representation of the vehicle routing problem, and multiple decoders are used to increase the diversity of the solution space. Meanwhile, the REINFORCE algorithm with a baseline is employed to train the model, ensuring quick returns of high-quality solutions. Moreover, the fitness function is calculated based on the solution to each module, and the genetic algorithm is employed to seek the optimal solution on a global scale. Finally, the effectiveness of the proposed framework is validated through experiments at different scales and comparisons with other algorithms. The experimental results show that, compared to the single decoder GCN-based solving method, the method proposed in this paper improves the solving success rate to 100% across 15 generated instances. The average path length obtained is only 11% of the optimal solution produced by the GCN-based multi-decoder method.

A Modified Bubnov-Galerkin Method for Solving Boundary Value Problems with Linear Ordinary Differential Equations

Introduction. The paper considers the solution of boundary value problems on an interval for linear ordinary differential equations, in which the coefficients and the right-hand side are continuous functions. The conditions for the orthogonality of the residual equation to the coordinate functions are supplemented by a system of linearly independent boundary conditions. The number of coordinate functions m must exceed the order n of the differential equation. Materials and Methods. To numerically solve the boundary value problem, a system of linearly independent coordinate functions is proposed on a symmetric interval [−1,1], where each function has a unit Chebyshev’s norm. A modified Petrov-Galerkin method is applied, incorporating linearly independent boundary conditions from the original problem into the system of linear algebraic equations. An integral quadrature formula with twelfth-order error is used to compute the scalar product of two functions. Results. A criterion for the existence and uniqueness of a solution to the boundary value problem is obtained, provided that n linearly independent solutions of the homogeneous differential equation are known. Formulas are derived for the matrix coefficients and the coefficients of the right-hand side in the system of linear algebraic equations for the vector expansion of the solution in terms of the coordinate function system. These formulas are obtained for second- and third-order linear differential equations. The modified Bubnov-Galerkin method is formulated for differential equations of arbitrary order. Discussion and Conclusions. The derived formulas for the generalized Bubnov-Galerkin method may be useful for solving boundary value problems involving linear ordinary differential equations. Three boundary value problems with second- and third-order differential equations are numerically solved, with the uniform norm of the residual not exceeding 10–11.

Mathematical Modelling of Spatially Inhomogeneous Non-Stationary Interaction of Pests with Transgenic and Non-Modified Crops Considering Taxis

Introduction. This paper addresses a unified spatially inhomogeneous, non-stationary model of interaction between genetically modified crop resources (corn) and the corn borer pest, which is also present on a relatively small section of non-modified corn. The model assumes that insect pests influence both types of crops and are capable of independent movement (taxis) towards the gradient of plant resources. It also considers diffusion processes in the dynamics of all components of the unified model, biomass growth, genetic characteristics of both types of plant resources, processes of crop consumption, phenomena of growth and degradation, diffusion, and mutation of pests. The model allows for predictive calculations aimed at reducing crop losses and increasing the resistance of transgenic crops to pests by slowing down the natural mutation rate of the pest. Materials and Methods. The mathematical model is an extension of Kostitsin’s model and is formulated as an initial-boundary value problem for a nonlinear system of convection-diffusion equations. These equations describe the spatiotemporal dynamics of biomass density changes in two types of crops — transgenic and non-modified — as well as the specific populations (densities) of three genotypes of pests (the corn borer) resulting from mutations. The authors linearized the convection-diffusion equations by applying a time-lag method on the time grid, with nonlinear terms from eachequation taken from the previous time layer. The terms describing taxis are presented in a symmetric form, ensuring the skew-symmetry of the corresponding continuous operator and, in the case of spatial grid approximation, the finite-difference operator. Results. A stable monotonic finite-difference scheme is developed, approximating the original problem with second-order accuracy on a uniform 2D spatial grid. Numerical solutions of model problems are provided, qualitatively corresponding to observed processes. Solutions are obtained for various ratios of modified and non-modified sections of the field. Discussion and Conclusion. The obtained results regarding pest behavior, depending on the type of taxis, could significantly extend the time for pests to acquire Bt resistance. The concentration dynamics of pests moving in the direction of the food gradient differs markedly from the concentration of pests moving towards a mate for reproduction.

Optimising seismic imaging design parameters via bilevel learning

Abstract Full waveform inversion (FWI) is a standard algorithm in seismic imaging. It solves the inverse problem of computing a model of the physical properties of the earth’s subsurface by minimising the misfit between actual measurements of scattered seismic waves and numerical predictions of these, with the latter obtained by solving the (forward) wave equation. The implementation of FWI requires the a priori choice of a number of ‘design parameters’, such as the positions of sensors for the actual measurements and one (or more) regularisation weights. In this paper we describe a novel algorithm for determining these design parameters automatically from a set of training images, using a (supervised) bilevel learning approach. In our algorithm, the upper level objective function measures the quality of the reconstructions of the training images, where the reconstructions are obtained by solving the lower level optimisation problem—in this case FWI. Our algorithm employs (variants of) the BFGS quasi-Newton method to perform the optimisation at each level, and thus requires the repeated solution of the forward problem—here taken to be the Helmholtz equation. This paper focuses on the implementation of the algorithm. The novel contributions are: (i) an adjoint-state method for the efficient computation of the upper-level gradient; (ii) a complexity analysis for the bilevel algorithm, which counts the number of Helmholtz solves needed and shows this number is independent of the number of design parameters optimised; (iii) an effective preconditioning strategy for iteratively solving the linear systems required at each step of the bilevel algorithm; (iv) a smoothed extraction process for point values of the discretised wavefield, necessary for ensuring a smooth upper level objective function. The algorithm also uses an extension to the bilevel setting of classical frequency-continuation strategies, helping avoid convergence to spurious stationary points. The advantage of our algorithm is demonstrated on a problem derived from the standard Marmousi test problem.

A Fractional Order Derivative Newton-Raphson Method for the Computation of the Power Flow Problem Solution in Energy Systems

A Fractional Order Derivative Newton-Raphson Method for the Computation of the Power Flow Problem Solution in Energy Systems

Source localization of mu-rhythm event related desynchronization in EEG during tactile imagery

Tactile imagery remains a relatively understudied phenomenon in the field of mental imagery research. However, alongside motor imagery, this technique holds promise as an effective tool for sensorimotor rehabilitation following stroke and spinal cord injuries. In this study, conducted with 22 healthy volunteers, we investigated the source localization of mu-rhythm event related desynchronization (Event-Related Desynchronization, ERD) using multi-channel electroencephalogram recordings and subsequent inverse problem solution with the sLORETA method. All participants exhibited ERD during tactile imagery task, as well as under vibrotactile stimulation. It was demonstrated that mu-rhythm ERD during vibrotactile stimulation, as well as tactile imagery, was localized in the sensorimotor areas of the contralateral hemisphere. Within the source space, ERD in the postcentral gyrus was significantly stronger compared to the precentral gyrus. These findings indicate that tactile imagery, akin to the perception of real tactile stimuli, leads to prominent activation of sensorimotor cortical areas, consistent with the general understanding of the shared neural substrate during mental imagery and perception.

Determinant- and derivative-free quantum Monte Carlo within the stochastic representation of wavefunctions

Abstract Describing the ground states of continuous, real-space quantum many-body systems, like atoms and molecules, is a significant computational challenge with applications throughout the physical sciences. Recent progress was made by variational methods based on machine learning (ML) ansatzes. However, since these approaches are based on energy minimization, ansatzes must be twice differentiable. This (a) precludes the use of many powerful classes of ML models; and (b) makes the enforcement of bosonic, fermionic, and other symmetries costly. Furthermore, (c) the optimization procedure is often unstable unless it is done by imaginary time propagation, which is often impractically expensive in modern ML models with many parameters. The stochastic representation of wavefunctions (SRW), introduced in (Atanasova et al 2023 Nat. Commun. 14 3601), is a recent approach to overcoming (c). SRW enables imaginary time propagation at scale, and makes some headway towards the solution of problem (b), but remains limited by problem (a). Here, we argue that combining SRW with path integral techniques leads to a new formulation that overcomes all three problems simultaneously. As a demonstration, we apply the approach to generalized ‘Hooke’s atoms’: interacting particles in harmonic wells. We benchmark our results against state-of-the-art data where possible, and use it to investigate the crossover between the Fermi liquid and the Wigner molecule within closed-shell systems. Our results shed new light on the competition between interaction-driven symmetry breaking and kinetic-energy-driven delocalization.

Quantum Procedures for Nested Search Problems

In this paper we study search problems that arise very often in cryptanalysis: nested search problems, where each search layer has known degrees of freedom and/or constraints. A generic quantum solution for such problems consists of nesting Grover's quantum search algorithm or amplitude amplification (QAA) by Brassard et al., obtaining up to a square-root speedup on classical algorithms. However, the analysis of nested Grover or QAA is complex and introduces technicalities that in previous works are handled in a case-by-case manner. Moreover, straightforward nesting of l layers multiplies the complexity by a constant factor (pi/2)^l. In this paper, we aim to remedy both these issues and introduce a generic framework and tools to transform a classical nested search into a quantum procedure. It improves the state-of-the-art in three ways: 1) our framework results in quantum procedures that are significantly simpler to describe and analyze; 2) it reduces the overhead factor from (pi/2)^l to sqrt(l); 3) it is simpler to apply and optimize, without needing manual quantum analysis. We give generic complexity formulas and show that for concrete instances, numerical optimizations enable further improvements, reducing even more the gap to an exact quadratic speedup. We demonstrate our framework by giving a tighter analysis of quantum attacks on reduced-round AES.

Design optimization of automotive carbon fiber composite material floor laminate based on PSO-BFO algorithm

In response to the current challenges of low precision and efficiency in the optimization of composite material layups, the insufficient lightweight of automotive body floors, and the high cost of carbon fiber composites, this study introduces an optimized design method for carbon fiber composite flooring layups. Based on implicit parametric technology, a hybrid PSO-BFO (Particle Swarm Optimization-Bacterial Foraging Optimization) algorithm is employed. This approach achieves an integrated optimization of materials, processes, and structures, thereby balancing and reducing costs. The SFE-CONCEPT is utilized to establish an implicit parameterization model for the body floor, which is validated through experiments and finite element simulation analysis. Concept design and modeling of the carbon fiber composite material floor laminate are performed. Continuous variable optimization is employed to determine the thickness, tile shape, and number of layers for the front, middle, and rear floors. A continuous variable discretization rounding strategy is used to obtain the discrete layer numbers for each laminate orientation of the composite material floor. The continuous fiber lamination strategy is applied to create different shared lamination regions. The PSO-BFO hybrid optimization method is proposed to optimize the lamination sequence as a multi-objective optimization, addressing the challenges of discrete lamination sequence, explosive combinations, and multiple variables in the optimization design of carbon fiber composite material floor laminates. The optimization results demonstrate improvements of 34.4% in floor quality M, 6.0% in static bending stiffness BS, and 5.3% in lightweight coefficient QLX using the proposed PSO-BFO method. PSO-BFO and PSO-GA (Particle Swarm Optimization-Genetic Algorithm) methods are more capable of obtaining global optimal solutions for complex optimization problems than single optimization algorithms. Still, the results obtained by the PSO-BFO method are more balanced.

Design and Improvement of Bone Adhesive in response to Clinical Needs.

Fracture represents one of the most common diagnoses in contemporary medical practice, with the majority of cases traditionally addressed through metallic device fixation. However, this approach is marred by several drawbacks, including prolonged operative durations, considerable expenses, suboptimal applicability to comminuted fractures, increased infection risks, and the inevitable requirement for secondary surgery. The inherent advantages of bone adhesives in these fields have garnered the attention of orthopedic surgeons, who have commenced utilizing biocompatible and biodegradable bone adhesives to bond and stabilize bone fragments. Regrettably, the current bone adhesives generally exhibit insufficient adhesive strength in vivo environments, and it is desirable for them to possess effective osteogenesis to facilitate fracture healing. Consequently, aligning bone adhesives with practical clinical demands remains a significant hurdle, which has catalyzed a surge in research endeavors. Within this review, the conceptual framework, characteristics, and design ideas of bone adhesives based on clinical needs are delineated. Recent advancements in this domain, specifically focusing on the enhancement of two pivotal characteristics-adhesive strength and osteogenic potential are also reviewed. Finally, a prospective analysis of the future advancements in bone adhesives, offering new insights into solutions for diverse clinical problems is presented.