Local Minima Research Articles

Implementation of the Global Minimum Tax in Italy and EU Directive Proposals: Does This Approach Effectively Pave the Way for the Establishment of a More Sustainable Tax System?

This contribution describes the implementation of a global minimum tax in Italy and provides an initial assessment of its anticipated impact, both financially and in respect of the sustainable evolution of the tax system in economic, social and environmental terms, considering the latest directive proposals, i.e. the directives on Business in Europe: Framework for Income Taxation, transfer pricing and Head Office Tax system for micro, small and medium-sized enterprises.

Implementation of the Global Minimum Tax in Italy and EU Directive Proposals: Does this Approach Effectively Pave the Way for the Establishment of a More Sustainable Tax System?

This contribution describes the implementation of a global minimum tax in Italy and provides an initial assessment of its anticipated impact, both financially and in respect of the sustainable evolution of the tax system in economic, social and environmental terms, considering the latest directive proposals, i.e. the directives on Business in Europe: Framework for Income Taxation, transfer pricing and Head Office Tax system for micro, small and medium-sized enterprises.

Endergonic synthesis driven by chemical fuelling

AbstractSpontaneous chemical reactions proceed energetically downhill to either a local or global minimum, limiting possible transformations to those that are exergonic. Endergonic reactions do not proceed spontaneously and require an input of energy. Light has been used to drive a number of deracemizations and thermodynamically unfavourable bond-forming reactions, but is restricted to substrates that can absorb, directly or indirectly, energy provided by photons. In contrast, anabolism involves energetically uphill transformations powered by chemical fuels. Here we report on the transduction of energy from an artificial chemical fuel to drive a thermodynamically unfavourable Diels–Alder reaction. Carboxylic acid catalysed carbodiimide-to-urea formation is chemically orthogonal to the reaction of the diene and dienophile, but transiently brings the functional groups into close proximity, causing the otherwise prohibited cycloaddition to proceed in modest yield (15% after two fuelling cycles) and with high levels of regio- (>99%) and stereoselectivity (92:8 exo:endo). Kinetic asymmetry in the fuelling cycle ratchets the Diels–Alder reaction away from the equilibrium distribution of the Diels–Alder:retro-Diels–Alder products. The driving of the endergonic reaction occurs through a ratchet mechanism (an energy or information ratchet, depending on the synthetic protocol), reminiscent of how molecular machines directionally bias motion. Ratcheting synthesis has the potential to expand the synthetic chemistry toolbox in terms of reactivity, complexity and control.

An adaptative differential evolution with enhanced diversity and restart mechanism

Differential Evolution (DE) stands out as an exceptional intelligent evolutionary algorithm, acclaimed for its simplicity in implementation and the ability to optimize without necessitating differentiable conditions. However, a significant pitfall of DE lies in its susceptibility to getting trapped in local minima, leading to algorithmic stagnation and substantial performance impairments. To counteract the shortcoming, the Adaptative Differential Evolution with Diversity Maintenance and Restart Mechanism (ADE-DMRM) is proposed. This approach integrates three primary innovations. Firstly, the algorithm controls the number of generations that individuals stay in the external archive based on the successful evolution rate, thereby optimizing the mutation strategy to effectively maintain population diversity. Secondly, ADE-DMRM proposes a novel restart mechanism in which the current stagnant individuals are identified by combining a stagnation tracker and a diversity assessment indicator and then regenerated using a dimension-learning-based approach. Thirdly, wavelet basis functions and Cauchy distributions are employed for scaling factor implementation across different stages, while the dimension change information of successfully evolved individuals is harnessed to refine the adaptive parameter control scheme. Finally, comprehensive experiments were undertaken on the CEC2013, CEC2014, and CEC2017 test sets, assessing accuracy, convergence speed, the efficacy of each module, and time complexity. The results confirm that ADE-DMRM is an efficient single-objective optimization algorithm that outperforms current advanced variants.

Tunneling Effect of Fermions in Silicene Through Potential Barrier

AbstractThe influence of a a rectangular potential barrier on the quantum transport of fermions in silicene is explored. Specifically, analytical solutions are presented to derive transmission and reflection probabilities together with conductance. It is shown that the transmission is highly sensitive to both the barrier height and incident energy. As a result, the occurrence of Klein and resonant tunnelings is observed, with a significant dependence on the barrier width. Notably, it is found that perfect transmission extends beyond normal incidence, occurring at various oblique angles. Moreover, the transmission pattern exhibits a more fragmented structure with increasing barrier width, reminiscent of Fabry‐Pérot resonances. In contrast, the conductance displays a non‐monotonic dependence on incident energy and features rapid oscillations with a rising barrier height. However, at a constant barrier height, there is a minimal disparity among conductance profiles for high incident energy values. When incident energy equals the barrier height, the conductance experiences a local minimum. For a thin barrier, a substantial reduction in conductance is observed, unlike the oscillatory behavior seen with a thicker barrier. These findings underscore the progress in silicene research and offer a fresh perspective on the relativistic applications of tunneling in this material.

Satellite fault tolerant attitude control based on expert guided exploration of reinforcement learning agent

ABSTRACT This research provides a method that accelerates learning and avoids local minima to improve the policy gradient algorithm’s learning process. Reinforcement learning has the advantage of not requiring a model. Consequently, it can improve control performance, mainly when a model is generally unavailable, such as when an error occurs. The proposed method efficiently and expeditiously investigates the action space. First, it quantifies the resemblance between agents’ and traditional controllers’ actions. Then, the principal reward function is modified to reflect this similarity. This reward-shaping mechanism guides the agent to maximize its return via an attractive force during the gradient ascent. To validate our concept, we establish a satellite attitude control environment with a similarity subsystem. The outcomes demonstrate the effectiveness and robustness of our method.

Tunnel resistivity deep learning inversion method based on physics‐driven and signal interpretability

AbstractData‐driven deep learning technology has a strong non‐linear mapping ability and has good development potential in geophysical inversion problems. Traditional inversion techniques offer broad generality, but they can remain trapped in local minima, particularly for three‐dimensional tunnelling resistivity inversion. In this work, we present an inversion methodology that combines traditional physics‐driven and deep learning data‐driven inversion approaches. To further support deep neural networks' dependability on unseen data, the interpretability of their working mechanism is explored. We execute migration learning based on small sample data after identifying the critical parameters that restrict the effectiveness of inversion by analysing the feature maps of various model data. We demonstrate, using both synthetic examples and field data, that the proposed method can improve the accuracy in detecting water‐bearing anomalies (caves and faults), which are typically encountered during tunnel excavation.

Variational techniques for a one-dimensional energy balance model

Abstract. A one-dimensional climate energy balance model (1D EBM) is a simplified climate model for the zonally averaged global temperature profile, based on the Earth's energy budget. We examine a class of 1D EBMs which emerges as the parabolic equation corresponding to the Euler–Lagrange equations of an associated variational problem, covering spatially inhomogeneous models such as with latitude-dependent albedo. Sufficient conditions are provided for the existence of at least three steady-state solutions in the form of two local minima and one saddle, that is, of coexisting “cold”, “warm” and unstable “intermediate” climates. We also give an interpretation of minimizers as “typical” or “likely” solutions of time-dependent and stochastic 1D EBMs. We then examine connections between the value function, which represents the minimum value (across all temperature profiles) of the objective functional, regarded as a function of greenhouse gas concentration, and the global mean temperature (also as a function of greenhouse gas concentration, i.e. the bifurcation diagram). Specifically, the global mean temperature varies continuously as long as there is a unique minimizing temperature profile, but coexisting minimizers must have different global mean temperatures. Furthermore, global mean temperature is non-decreasing with respect to greenhouse gas concentration, and its jumps must necessarily be upward. Applicability of our findings to more general spatially heterogeneous reaction–diffusion models is also discussed, as are physical interpretations of our results.

Robust Transceiver Design for Correlated MIMO Interference Channels in the Presence of CSI Errors under General Power Constraints

In this paper, we consider a new design problem of optimizing a linear transceiver for correlated multiple-input multiple-output (MIMO) interference channels in the presence of channel state information (CSI) errors, which is a more realistic and practical scenario than those considered in the previous studies on uncorrelated MIMO interference channels. By taking CSI errors into account, the optimization problem is initially formulated to minimize the average mean square error (MSE) under the general power constraints. Since the objective function is not jointly convex in precoders and receive filters, we split the original problem into two convex subproblems, and then linear precoders and receive filters are obtained by solving two subproblems iteratively. It is shown that the proposed algorithm is guaranteed to converge to a local minimum. The numerical results show that the proposed algorithm can significantly reduce the sensitivity to CSI errors compared with the existing robust schemes in the correlated MIMO interference channel.

Bio-Inspired Jumping Spider Optimization for Controller Tuning/ Parameter Estimation of an Uncertain Aerodynamic MIMO System

The practical near impossibility of empirical attempts in estimating optimal controller gains makes the use of metaheuristics strategies inevitable to automatically obtain these gains by an iterative, heuristic simulation procedure. The convergence of the gains values to the local or global solutions occur with ease. In designing controllers for the Twin-Rotor MIMO System (TRMS), Jumping Spider Optimization Algorithm (JSOA), a novel neoteric population-based bio-inspired metaheuristic approach is used to obtain optimum values for the Proportional, Integral and Derivative (PID) controllers. With the k,p,i controller gains as the decision variables, the JSOA solution to a nonlinear multi-objective optimization problem subject to some intrinsic constraints spawned optimal values for the controllers’ variables. Counter to other algorithms (deterministic and stochastic) that get caught in local minima, JSOA evolved a solution after searchingly rummaging the entire solution search space in a vectorized fashion for an optimal value. Compared with several other versatile controllers (using GA, PSO, Pattern Search and Simulated Annealing), statistical results obtained showed JSOA technique provided a unique solution and found the gains of the PID controllers, marginally in relation to the others (optimization methods).

Current study on PID control method with optimized BP neural network based on particle swarm optimization

At present, robots show great application value in various industries, and the progress of the industry constantly puts forward higher requirements for the performance of robots, and robot control is an important part of robot application. It is difficult for the traditional PID controller to implement online tuning when it is faced with actual objects. Consequently, the neural network algorithm has been included into robot control methods in recent years; the PID controller based on BP neural network is the subject of this research. This study presents the current state of research, the basic concept behind BP neural networks, how they are used in controller design, and how to optimize the PID parameters of BP neural networks using a particle swarm optimization method. To increase system stability, the neural network is coupled with a PID controller. The adaptive learning capability of the neural network is utilized to modify PID control parameters online in real time. Targeting the trouble that it slips into a local minimum easily during the BP-PID self-learning process and the refined PSO algorithm is used to improve it. It makes sure that the BP-PID system converges to the global optimal solution. The proposed method can effectively improve the system control accuracy and control stability.

Improved Collision Avoidance Algorithm of Autonomous Rice Transplanter Based on Virtual Goal Point

To ensure the operation safety and efficiency of an autonomous rice transplanter, a path planning method of obstacle avoidance based on the improved artificial potential field is proposed. Firstly, the obstacles are divided into circular or elliptic obstacles according to the difference between the length and width of an obstacle as well as the angle between the vehicle’s forward direction and the length direction of the obstacle. Secondly, improved repulsive fields for circular and elliptic models are developed. To escape the local minimum and goal inaccessibility of the traditional artificial potential field as well as meet the requirements of agronomy and vehicle kinematics constraints, the adaptive setting and adjusting strategy for virtual goal points is proposed according to relative azimuth between obstacle and vehicle. The path smoothing method based on the B-spline interpolation method is presented. Finally, the intelligent obstacle avoidance algorithm is designed, and the path evaluation rule is given to obtain the low-cost, non-collision, smooth and shortest obstacle avoidance path. To verify the effectiveness of the proposed obstacle avoidance algorithm, simulation and field experiments are conducted. Simulation and experimental results demonstrate that the proposed improved collision avoidance algorithm is highly effective and realizable.

Supplier Evaluation in Supply Chain Environment Based on Radial Basis Function Neural Network

The comprehensive evaluation and selection of suppliers under the environment of supply chain management has become a key factor affecting the success of supply chain. How to select suppliers and the strategic partnership between suppliers under the environment of supply chain management has become an important challenge. To solve this problem, this paper takes the supplier evaluation and selection of Guangzhou Automobile Toyota Company as the research object, constructs the index system of supplier comprehensive evaluation and selection, uses the RBF neural network algorithm to establish the supplier evaluation and selection model, and makes an experimental study. The results show that radial basis function neural network is a local approximation network, which has a unique and definite solution to the problem, and there is no local minimum problem in BP network. It is a method that enables enterprises and suppliers to have a clear understanding and seek further promotion together. The research provides theoretical data support for enterprise managers to make decisions.

Studying GPR's direct and reflected waves

AbstractAs the transmitter and receiver (Tx and Rx, respectively) are located in close proximity during a typical ground‐penetrating radar (GPR) survey, the powerful signal generated by the Tx and which is then recorded by the Rx at various time delays, can be saturated at early times (i.e., this is the direct wave (DW) signal reaching the Rx). This often causes the masking of shallow targets, complicating data interpretation. In this study, our aim is to examine the spatial distribution of the electromagnetic signals around the Tx, attempting to locate areas where the DW becomes minimum, whereas the signal strength from subsurface targets (i.e., reflected wave – RW) remains ideally unchanged. The position of these local minima in the DW signal could give rise to advantageous Tx–Rx configurations, where clear reflections from subsurface targets lying at shallow depths can be obtained with the least possible involvement of the DW. To perform such a study, we carried out static field measurements over a flat lying reflector as well as numerical simulations in a reflection, common‐offset mode around a transmitting antenna. In the field, we also collected wide‐angle reflection–refraction data to determine the GPR wave velocity in the uppermost layer. GPR signals were recorded by the Rx around the Tx in three concentric circles of various radii (i.e., varying the Tx/Rx separation), using a specific angular step and varying the Tx/Rx polarization each time. The synthetic data were produced using a three‐dimensional finite‐difference time‐domain modelling tool. Field and numerically simulated data were analysed and compared to study the behaviour of both the DW and RW events around the Tx when changing the Tx/Rx distance, their respective angular position, as well as their relative polarization/orientation.

Deep Learning Enabled Whale Optimization Algorithm for Accurate Prediction of RA Disease

Whale Optimization Algorithm (WOA) is an optimization technique and based on food foraging behavior of whales. It has been applied in many domain including processing of images, framework controls, and ML (machine learning). WOA assists in choosing the right parameters required for Deep Neural Networks. This work uses DNN to examine metacarpophalangeal (MCP) rheumatoid joint discomforts in patients from diagnostic medical images including X-rays or Magnetic Resource images. The use of WOA enhances resultant outcomes of DNN as it searched for optimal solutions within search spaces, instead of getting trapped in local minima found by gradient descent. The combination of WOA and DNN for grading MCP rheumatoid arthritis can provide an efficient and accurate solution for medical practitioners and researchers

A first principle investigation of the CO gas adsorption property of pristine, cobalt (Co), and phosphorus (P) doped BN nanosheets

There has been an investigation into the sensing abilities of pristine as well as Co-doped and P-doped boron nitride nanosheets (BNNSs) in the detection of toxic carbon monoxide (CO) gas. We found the calculated adsorption energies are 0.06eV, 0.63eV, and 0.12eV for more stable structures with global minima. The physisorption of CO on BN nanosheets results in the formation of complex structures. We found Co-BNNS to be the most stable and promising nanostructure for detecting CO gas among the three complex configurations. A decrease of roughly 20.42 percent in the HOMO-LUMO gap (Eg) was observed for the same structure, which has greater adsorption energy in forming complex structures. The lowest nonbonding adsorption length is seen in Co-doped BN nanosheets, which also promote the adsorption energy and shift in the HOMO-LUMO energy gap. In addition, we have investigated the HOMO-LUMO, DOS, MEP, and absorption spectra into reveal quantum mechanical insight of the detection processes, which supports our study of BNNS as a CO gas detector.

GMM weighting matrices in cross-sectional asset pricing tests

When estimating misspecified linear factor models for the cross-section of expected returns using GMM, the explanatory power of these models can be spuriously high when the estimated factor means are allowed to deviate substantially from the sample averages. In fact, by shifting the weights on the moment conditions, any level of cross-sectional fit can be attained. The mathematically correct global minimum of the GMM objective function can be obtained at a parameter vector that is far from the true parameters of the data-generating process. This property is not restricted to small samples, but rather holds in population. It is a feature of the GMM estimation design and applies to both strong and weak factors, as well as to all types of test assets.

Quantum approximate optimization via learning-based adaptive optimization

Combinatorial optimization problems are ubiquitous and computationally hard to solve in general. Quantum approximate optimization algorithm (QAOA), one of the most representative quantum-classical hybrid algorithms, is designed to solve combinatorial optimization problems by transforming the discrete optimization problem into a classical optimization problem over continuous circuit parameters. QAOA objective landscape is notorious for pervasive local minima, and its viability significantly relies on the efficacy of the classical optimizer. In this work, we design double adaptive-region Bayesian optimization (DARBO) for QAOA. Our numerical results demonstrate that the algorithm greatly outperforms conventional optimizers in terms of speed, accuracy, and stability. We also address the issues of measurement efficiency and the suppression of quantum noise by conducting the full optimization loop on a superconducting quantum processor as a proof of concept. This work helps to unlock the full power of QAOA and paves the way toward achieving quantum advantage in practical classical tasks.

Energy variation and stress fields of spherical inclusions with eigenstrain in three-dimensional anisotropic bi-materials

In this study, expressions for the interior stress fields of a spherical inclusion with uniform eigenstrain embedded in an anisotropic bi-material featuring a planar interface are derived. These expressions involve surface integrals of the imaginary term of the first derivative of the Green tensor in an anisotropic bi-material which are well-suited for standard numerical integrations. Specific formulations are provided for cases where the inclusion belongs to either the same material or both materials. Additionally, expressions are presented for the equivalent Eshelby tensor. The interior stress fields and variations in elastic strain energy are computed using cubic elastic constants of Cu. Various inclusion positions relative to the interface, eigenstrain forms, and crystallographic orientations are considered. For instances involving dilatational eigenstrain, the elastic strain energy variation with the inclusion’s position may exhibit multiple extrema. The global minimum and maximum consistently occur when the inclusion spans both materials. In the context of symmetrical tilt boundaries, energy variations are perfectly symmetric, with a global minimum on the interface that decreases with the tilt angle. The significance of the observed energy variations for defects segregation is quantitatively assessed by comparing them with the interaction energy between an eigenstrain and a grain boundary stress field.

Time-discrete momentum consensus-based optimization algorithm and its application to Lyapunov function approximation

In this paper, we study a discrete momentum consensus-based optimization (Momentum-CBO) algorithm which corresponds to a second-order generalization of the discrete first-order CBO [S.-Y. Ha, S. Jin and D. Kim, Convergence of a first-order consensus-based global optimization algorithm, Math. Models Methods Appl. Sci. 30 (2020) 2417–2444]. The proposed algorithm can be understood as the modification of ADAM-CBO, replacing the normalization term by unity. For the proposed Momentum-CBO, we provide a sufficient framework which guarantees the convergence of algorithm toward a global minimum of the objective function. Moreover, we present several experimental results showing that Momentum-CBO has an improved success rate of finding the global minimum compared to vanilla-CBO and show the stability of Momentum-CBO under different initialization schemes. We also show that Momentum-CBO can be used as the alternative of ADAM-CBO which does not have a proper convergence analysis. Finally, we give an application of Momentum-CBO for Lyapunov function approximation using symbolic regression techniques.