Set Of Solutions Research Articles

Non-perturbative Lee-Wick gauge theory: Towards Confinement & RGE with strong couplings

We consider a non-Abelian Lee–Wick gauge theory and discuss Becchi-Rouet-Stora-Tyutin invariance. It contains fourth-order derivative as extensions of the kinetic term, leading to massive ghosts in the theory upon quantization. We particularly provide essential clues towards confinement conditions in strongly-coupled regimes, using the Kugo–Ojima approach, and obtain the functions in the non-perturbative regimes. This is achieved using a set of exact solutions of the corresponding local theory in terms of Jacobi elliptical functions. We obtain a similar function just as for the ordinary Yang-Mills theory but the main differences are that now, the cut-off arises naturally from the Lee–Wick heavy mass scales (M). We show that the fate of the ghosts are fixed in these regimes: they are no more the propagating degrees of freedom in the infrared-limit. As it also happens for the ordinary case, confinement is due to the non-Abelian nature of the theory. In the limit , one recovers the standard results for the local non-Abelian Yang-Mills theory.

Study on the Effect of Parameter Sensitivity on Engine Optimization Results

The effects of six control parameters, intake valve opening timing (IVO), exhaust valve opening timing (EVO), compression ratio (CR), engine speed, intake temperature, and intake pressure on engine output power, indicated specific fuel consumption (ISFC), and nitrogen oxides (NOx) emissions, are analyzed through engine simulation. The six parameters were categorized into two groups based on the degree of influence: high influence (EVO, speed and intake pressure) and low influence (CR, IVO and intake temperature). The relationship between these two groups of parameters and power, ISFC and NOx emissions was explored. Optimization was carried out for each of the two groups of parameters, and the optimization of the high impact parameters resulted in a higher diversity and wider distribution of the solution set. On the other hand, the optimization of the low-impact parameters resulted in a more concentrated distribution of the solution set, while better reflecting the trade-off between the optimization objectives. For the optimal solutions for both sets of parameters, the high-impact parameters provided significant optimization performance compared to the standard operating conditions. Although power and ISFC were optimized, the optimal solution for the low-impact parameter performed poorly with a significant increase in NOx emissions. Therefore, the parameters should be evaluated for optimization using high impact parameters to improve engine performance.

Multi-objective optimization design of anti-roll torsion bar using improved beluga whale optimization algorithm

PurposeThis study aims to reduce the redundant weight of the anti-roll torsion bar brought by the traditional empirical design and improving its strength and stiffness.Design/methodology/approachBased on the finite element approach coupled with the improved beluga whale optimization (IBWO) algorithm, a collaborative optimization method is suggested to optimize the design of the anti-roll torsion bar structure and weight. The dimensions and material properties of the torsion bar were defined as random variables, and the torsion bar's mass and strength were investigated using finite elements. Then, chaotic mapping and differential evolution (DE) operators are introduced to improve the beluga whale optimization (BWO) algorithm and run case studies.FindingsThe findings demonstrate that the IBWO has superior solution set distribution uniformity, convergence speed, solution correctness and stability than the BWO. The IBWO algorithm is used to optimize the anti-roll torsion bar design. The error between the optimization and finite element simulation results was less than 1%. The weight of the optimized anti-roll torsion bar was lessened by 4%, the maximum stress was reduced by 35% and the stiffness was increased by 1.9%.Originality/valueThe study provides a methodological reference for the simulation optimization process of the lateral anti-roll torsion bar.

LQG Graphon Mean Field Games: Analysis via Graphon-Invariant Subspaces

This paper studies approximate solutions to large-scale linear quadratic stochastic games with homogeneous nodal dynamics parameters and heterogeneous network couplings within the graphon mean field game framework in [2]-[4]. A graphon time-varying dynamical system model is first formulated to study the finite and then limit problems of linear quadratic Gaussian graphon mean field games (LQG-GMFG). The Nash equilibrium of the limit problem is then characterized by two coupled graphon time-varying dynamical systems. Sufficient conditions are established for the existence of a unique solution to the limit LQG-GMFG problem. For the computation of LQG-GMFG solutions, two methods are established and employed where one is based on fixed point iterations and the other on a decoupling operator Riccati equation; furthermore, two corresponding sets of solutions are established based on spectral decompositions. Finally, a set of numerical simulations on networks associated with different types of graphons are presented.

Quantum space-time marginal problem: global causal structure from local causal information

Spatial and temporal quantum correlations can be unified in the framework of the pseudo-density operators (PDOs), and quantum causality between the involved events in an experiment is encoded in the corresponding PDO. We study the relationship between local causal information and global causal structure. A space-time marginal problem is proposed to infer global causal structures from given marginal causal structures where causal structures are represented by the reduced PDOs; we show that there almost always exists a solution in this case. By imposing the corresponding constraints on this solution set, we could obtain the required solutions for special classes of marginal problems, like a positive semidefinite marginal problem, separable marginal problem, etc. We introduce a space-time entropy and propose a method to determine the global causal structure based on the maximum entropy principle. The notion of quantum pseudo-channel (QPC) is also introduced and we demonstrate that the QPC marginal problem can be solved by transforming it into a PDO marginal problem via the channel-state duality.

Regarding the Theory of Power Lines Emission Propagation to the Space

AbstractThe analytical theory is presented that describes the propagation of power lines emission (PLE) with frequency of 50/60 Hz in the heights range from the Earth surface to the magnetosphere. Validation of the theory is made by the comparison with earlier published results of numerical modeling. It is shown that the actual source of emission is a magnetic dipole formed by the power line current and by the secondary image current in the ground. The emission is propagating to the lower boundary of ionosphere, where its main part is reflected back, but some of the energy (a few percent) penetrates into the ionosphere. There it is transformed into a quasi‐flat whistler wave. The generation of current in ground and the reflection from the ionosphere are the main factors that reduce the emission into space. In the ionosphere wave fronts propagate approximately vertically, and the energy propagates in a certain direction that depends on the geomagnetic field inclination. Thus, the ionosphere acts as a focusing system that collects PLE into a unidirectional beam. The PLE intensity does not change with altitude within the total range of ionospheric heights. In the magnetosphere PLE is transformed to both magnetosonic and Alfvén waves and the emission splits into two rays: one propagates along the wave vector and the other one—along the geomagnetic field lines. A set of analytical solutions is presented allowing determining the change in PLE parameters with altitude depending on the source parameters and ionospheric conditions.

The theory of fifth-order Stokes waves in a linear shear current

In this study, a new set of fifth-order Stokes wave solutions, incorporating the effects of a linear shear current, is derived by using the perturbation method originally proposed for pure waves that was recently published. The present solutions are checked against the existing experimental data, the third-order stream function solutions, as well as the numerical results. The comparisons demonstrate that the present solutions are more accurate in describing the velocity distributions during wave propagation, especially in strong following currents and negative vorticity conditions. Subsequently, the present solutions are used to investigate the fluid particle trajectories for different wave–current interaction conditions. The results indicate that the background vorticity can alter the patterns of fluid particle trajectories and the direction of Stokes drifts.

κ-Exponential Inflation

We investigate a possible inflationary scenario where the expansion of the universe is driven by a slow evolution of a homogeneous single scalar field, whose potential V (φ) is given by an unusual κ-generalized power law. Within the slow-roll approximation we obtain several of the main predictions of the model, as the scalar spectral index, the tensor-to-scalar ratio, the number of e-folds, and the local non-Gaussianity. We also show that this model admits a much wider set of solutions than the usual exponential approach, and that their theoretical predictions are contemplated by the observational data.

Multi-objective optimization of fiber laser cutting quality characteristics of glass fiber reinforced plastic (GFRP) materials

Laser cutting can achieve ultra-precision cutting of materials by using appropriate parameters. In order to optimize processing parameters and obtain better processing quality, conducted experimental research on laser cutting of Glass fiber reinforced plastic (GFRP). In this study, the impact of four process parameters (laser power, cutting speed, assistant gas pressure and focus position) on quality characteristics (kerf width, kerf taper and kerf section roughness) was evaluated through analysis of variance (ANOVA), the regression relationship between laser processing parameters and quality characteristics was analyzed. And an integrative model for predicting and optimizing the quality characteristics of fiber laser cutting was constructed. In the proposed integrative model, Back-Propagation Neural Network (BPNN) was used to build a prediction model for quality characteristics. Through Non-dominated Sorting Genetic Algorithm (NSGAII) optimizes and outputs the complete optimal solution set of processing parameters, and finally realizes the nonlinear optimization of multi-objective parameters. The fitness value of BPNN model can reach 97.814%, and the maximum prediction relative error is 8.614%. And the set of suggested optimal solutions can be used as most of them are showing certain improvements in the quality characteristics. The results indicate that the integrative modeling strategy has the ability to predict and optimize laser cutting of composite materials.

Interindividual Correlation and Dimension-Based Dual Learning for Dynamic Multiobjective Optimization

Dynamic multiobjective optimization problems (DMOPs) are characterized by their multiple objectives, constraints, and parameters that may change over time. The challenge in solving DMOPs is how to track the varying Pareto optimal solution sets quickly and accurately. Therefore, an inter-individual correlation and dimension-based dual learning method is proposed in this paper. Two learning strategies, decomposition-based inter-individual correlation transfer learning (DICTL) and dimension-wise learning (DL), are developed to respectively generate one-half of the initial population in the new environment. More specifically, DICTL learns the inter-individual correlation from the final population of the adjacent environment and then transfers it to the new environment, aiming to maintain the diversity and distribution of the predicted population. While DL extracts the changing pattern of dynamic environments from the high-quality solutions of historical environments in the perspective of variable dimension, trying to improve the quality of the population and accelerate the convergence. The designed two learning strategies (DICTL&DL) work complementarily and collaboratively to make the algorithm adapt to dynamic environments better and faster. Comprehensive experiments have been conducted by comparing the proposed method with four state-of-the-art algorithms on 14 benchmark problems. The results demonstrate the superiority of the proposed method.

An Incremental Gradient Method for Optimization Problems With Variational Inequality Constraints

We consider minimizing a sum of agent-specific nondifferentiable merely convex functions over the solution set of a variational inequality (VI) problem in that each agent is associated with a local monotone mapping. This problem finds an application in computation of the best equilibrium in nonlinear complementarity problems arising in transportation networks. We develop an iteratively regularized incremental gradient method where at each iteration, agents communicate over a directed cycle graph to update their solution iterates using their local information about the objective and the mapping. The proposed method is single-timescale in the sense that it does not involve any excessive hard-to-project computation per iteration. We derive non-asymptotic agent-wise convergence rates for the suboptimality of the global objective function and infeasibility of the VI constraints measured by a suitably defined dual gap function. The proposed method appears to be the first fully iterative scheme equipped with iteration complexity that can address distributed optimization problems with VI constraints over cycle graphs.

On the Convergence Properties of a Distributed Projected Subgradient Algorithm

A weight-balanced network plays an important role in the exact convergence of distributed optimization algorithms, but is not always satisfied in practice. Different from most of existing works focusing on designing distributed algorithms, we analyze the convergence of a well-known distributed projected subgradient algorithm over time-varying general graph sequences, i.e., the weight matrices of the network are only required to be row stochastic instead of doubly stochastic. We first show that there may exist a graph sequence such that the algorithm is not convergent when the network switches freely within finitely many graphs. Then to guarantee its convergence under any uniformly jointly strongly connected graph sequence, we provide a necessary and sufficient condition on the cost functions, i.e., the intersection of optimal solution sets to all local optimization problems is not empty. Furthermore, we surprisingly find that the algorithm is convergent for any periodically switching graph sequence, but the converged solution minimizes a weighted sum of local cost functions, where the weights depend on the Perron vectors of some product matrices of the underlying switching graphs. Finally, we consider a slightly broader class of quasi-periodically switching graph sequences, and show that the algorithm is convergent for any quasi-periodic graph sequence if and only if the network switches between only two graphs. This work helps us understand impacts of communication networks on the convergence of distributed algorithms, and complements existing results from a different viewpoint.

Differential Stability in a Multi-Objective Optimal Control Problems with a Possibly Empty Solution Set

Differential Stability in a Multi-Objective Optimal Control Problems with a Possibly Empty Solution Set

The solution set to the nonlinear operator equation XAX = BX on Hilbert spaces

We present the representation of solution sets of the operator equation XAX = BX on Hilbert spaces by taking advantage of the invariant subspace of B, including solution sets of nonzero solutions, normal solutions and self-adjoint solutions. Moreover, necessary conditions and sufficient conditions are established for existence of nonzero solutions of the operator equation XAX = BX which commute with B.

Neural networks as an approximator for a family of optimization algorithm solutions for online applications

In this paper, we propose a sufficient condition at which a neural network can approximate a set of optimization algorithm solutions; we establish under which conditions a neural network can replace an optimization algorithm to solve a problem with the objective of safely deploying that network in a system where online solutions are necessary to simplify the hardware or allowing the processor to solve the optimization problem on time. To that end, first, we define the family of optimization problems to be addressed; then, we construct a vector with the parameters on which the solution depends, in order to propose a function based on the first-order Karush–Kuhn–Tucker conditions to find conditions under which the inverse of the proposed function maps the problem minimizer with respect to the constructed vector, we provide the sufficiency proof of, both, existence and feasibility of approximation by a neural network regarding the inverse function. Two case studies are proposed, one numerical case showing how a neural network can solve an optimization problem faster than popular solvers to illustrate how it can be implemented in applications where the computation time is tight, and the other case is a Model Predictive Control implementation with the optimization problem solver replaced by a neural network which allows a hardware downgrade; both cases are presented with time statistics comparisons.

Stability and weak KAM solutions of contact Hamilton-Jacobi equation

We are concerned with the stability of viscosity solutions to contact Hamilton-Jacobi equation H ( x , ∂ x u ( x ) , u ( x ) ) = 0 , x ∈ M , \begin{align*} H(x,\partial _x u(x),u(x))=0, \quad x\in M, \end{align*} where H = H ( x , p , u ) H=H(x,p,u) satisfies Tonelli conditions. We study the relationship between Lyapunov stability of viscosity solutions and the structure of the set of weak KAM solutions to the contact Hamilton-Jacobi equation.

Limit Directions of Julia Sets of Entire Functions and Complex Differential Equations

The limiting directions of Julia sets of infinite order entire functions are studied by combining the theory of complex dynamic system and the theory of complex differential equations, in which the lower bound of the measure of limiting direction of Julia set of entire solutions of complex differential equations is obtained.

Subgradient Extra-Gradient Algorithm for Pseudomonotone Equilibrium Problems and Fixed-Point Problems of Bregman Relatively Nonexpansive Mappings

In this article, we introduce a new subgradient extra-gradient algorithm to find the common element of a set of fixed points of a Bregman relatively nonexpansive mapping and the solution set of an equilibrium problem involving a Pseudomonotone and Bregman–Lipschitz-type bifunction in reflexive Banach spaces. The advantage of the algorithm is that it is run without prior knowledge of the Bregman–Lipschitz coefficients. Finally, two numerical experiments are reported to illustrate the efficiency of the proposed algorithm.

Improved production of Taxol® precursors in S. cerevisiae using combinatorial in silico design and metabolic engineering

BackgroundIntegrated metabolic engineering approaches that combine system and synthetic biology tools enable the efficient design of microbial cell factories for synthesizing high-value products. In this study, we utilized in silico design algorithms on the yeast genome-scale model to predict genomic modifications that could enhance the production of early-step Taxol® in engineered Saccharomyces cerevisiae cells.ResultsUsing constraint-based reconstruction and analysis (COBRA) methods, we narrowed down the solution set of genomic modification candidates. We screened 17 genomic modifications, including nine gene deletions and eight gene overexpressions, through wet-lab studies to determine their impact on taxadiene production, the first metabolite in the Taxol® biosynthetic pathway. Under different cultivation conditions, most single genomic modifications resulted in increased taxadiene production. The strain named KM32, which contained four overexpressed genes (ILV2, TRR1, ADE13, and ECM31) involved in branched-chain amino acid biosynthesis, the thioredoxin system, de novo purine synthesis, and the pantothenate pathway, respectively, exhibited the best performance. KM32 achieved a 50% increase in taxadiene production, reaching 215 mg/L. Furthermore, KM32 produced the highest reported yields of taxa-4(20),11-dien-5α-ol (T5α-ol) at 43.65 mg/L and taxa-4(20),11-dien-5-α-yl acetate (T5αAc) at 26.2 mg/L among early-step Taxol® metabolites in S. cerevisiae.ConclusionsThis study highlights the effectiveness of computational and integrated approaches in identifying promising genomic modifications that can enhance the performance of yeast cell factories. By employing in silico design algorithms and wet-lab screening, we successfully improved taxadiene production in engineered S. cerevisiae strains. The best-performing strain, KM32, achieved substantial increases in taxadiene as well as production of T5α-ol and T5αAc. These findings emphasize the importance of using systematic and integrated strategies to develop efficient yeast cell factories, providing potential implications for the industrial production of high-value isoprenoids like Taxol®.

A new tree-based approach to mine sequential patterns

Generic sequential pattern mining problem aims to mine the set of sequential patterns from a sequential database that satisfies a minimum support or occurrence threshold constraint. The main challenges that affect the efficiency of a solution lie in reducing the pattern search space, early detecting the infrequent patterns, representing the database in an efficient format, etc. Also, additional challenges get included when the problem environment transitions from static to incremental database leading to not to re-mine but efficiently tracking the effect of the incremental portion over the complete updated database. In this article, we introduce a new tree-based solution to the sequential pattern mining problem, including two sets of novel solutions for static and incremental sequential databases. We propose two new structures, SP-Tree and IncSP-Tree, and design two efficient algorithms, Tree-Miner and IncTree-Miner to mine the complete set of sequential patterns from static and incremental databases respectively. The proposed novel structures provide an efficient manner to store the complete sequential database maintaining “build-once-mine-many” property and giving scope to perform interactive mining. Additionally, we also design a new breath-first based support counting technique to efficiently identify the infrequent patterns at early stages and a new heuristic pruning strategy to reduce pattern search space. We also design a new pattern storage structure BPFSP-Tree to store the frequent patterns during successive iterations in incremental mining to reduce the number of database scans and to remove the infrequent patterns efficiently. A novel structure named Sequence Summarizer is also introduced to efficiently calculate and update the co-occurrence information of the items, especially in an incremental environment. Experimental results from various real-life and synthetic datasets demonstrate the efficiency of our work in comparison with the related state-of-the-art approaches.