Minimization Scheme Research Articles

Solvent-Environment Dependence of the Excess Chemical Potential and Its Computation Scheme Formulated through Error Minimization.

Solvent environment may significantly affect the equilibria involving flexible solute species, such as proteins and polymers. In the present work, a computation scheme is formulated for the change in the excess chemical potential of a flexible solute molecule upon variation of the solvent condition. The formulation adopts the scheme of error minimization in parallel to the method of Bennett acceptance ratio, and an exact expression is presented that provides the change in the excess chemical potential from solvation free energies computed in two solvent conditions of interest. The formulated scheme is applied to n-hexanol as the solute in water and n-octanol as the two solvent systems and to an oligomer of ethylene glycol as the solute in water with urea or NaCl added as a cosolvent. It is demonstrated that the change in the excess chemical potential of the solute due to the variation of the solvent condition (composition) can be obtained from the solvation free energies calculated over ∼10 to ∼102 solute configurations, without referring to any intermediate states between the two solvent conditions concerned. The connection to the solvent-condition dependence of the solute structure is further discussed for the systems of the ethylene-glycol oligomer, and the role is addressed for the probability distribution functions of the cosolvent-induced changes in the solvation free energies.

The simplest minimal subtraction for massive scalar field theory

The simplest minimal subtraction method for massive λϕ4 scalar field theory is presented. We utilize the one-particle irreducible vertex parts framework to deal only with the primitive divergent ones that can be renormalized multiplicatively. We give a unified description for spacetime metric tensor with either Minkowski or Euclidean signature. The partial-p operation in the remaining diagrams of the two-point vertex part eliminates its overlapping divergences. We show how the parametric dissociation transform effectively removes the external momentum dependence of the coefficient of the squared bare mass after performing the partial-p operation in the two-point vertex part diagrams. The resemblance of this method with a minimal subtraction scheme in the massless theory is pointed out. We derive the Callan-Symanzik equations using minimal subtraction arguments and discuss the scaling limit in the ultraviolet region. We apply the method to determine critical exponents for an O(N) internal symmetry at least up to two-loop order with a flat Euclidean metric and find perfect agreement with all previous results in the literature.

A novel property to modify weighted [formula omitted] minimization for improved compressed sensing

Weighted l1 minimization schemes are common methods to achieve compressed sensing (CS). However, they fail in the presence of inaccurate prior knowledge or improper scaling of weights due to inappropriately assigned large weights causing large and destructive errors in signal recovery. This paper proposes a theory-based algorithm to identify and correct such destructive weights for each signal entry. The enhancement is achieved through a novel sparsity-inducing property (SIP) which establishes a necessary condition for successful signal recovery. SIP outperforms existing properties such as coherence, restricted isometry property, and nullspace property by indicating which signal entries fail to be recovered. This unique advantage enables us to correct destructive weights that do not satisfy the SIP condition, making signal recovery successful where it previously failed. Results from many numerical experiments demonstrate that our proposed method can improve the signal recovery capability, robustness, and stability of the weighted l1 minimization for a wide range of applications, including sparse and compressive signal recovery, noise-aware recovery, sparse error correction, fast image acquisition, and sub-Nyquist sampling.

Mathematical modeling of the vortices couple dynamics in a stratified fluid

Abstract The problem of the dynamics of the vortex couple in stratified fluid is considered. The couple is two vortexes, arranged symmetrically relative to the vertical axis, but with the opposite direction of rotation, so that it begins to rise upwards. The mathematical model of a couple of vortices in a viscous stratified medium was studied. Salinity is chosen as a stratifying component, just as it can be implemented in the laboratory. The task is described by the Navier-Stokes equations in the Boussinesq approximation. To solve the problem, the SMIF method is used, of course, the finite different scheme of which has such properties as the second order of approximation on spatial variables, minimal scheme dissipation and dispersion, performance in wide range of Reynolds and Froude numbers and, most importantly, when solving wave processes are a property of monotony. The dynamics of such a couple are studied depending on its geometric sizes, the intensity of the vortexes and the depth of their initial immersion.

Weakly nonlinear analysis of minimal models for Turing patterns

The simplest particle-based mass-action models for Turing instability – i.e. those with only two component species undergoing instantaneous interactions of at most two particles, with the smallest number of distinct interactions – fall into a surprisingly small number of classes of reaction schemes. In previous work we have computed this classification, with different schemes distinguished by the structure of the interactions. Within a given class the reaction stoichiometry and rates remain as parameters that determine the linear and nonlinear evolution of the system.Adopting the usual weakly nonlinear scalings and analysis reveals that, under suitable choices of reaction stoichiometry, and in nine of the 11 classes of minimal scheme exhibiting a spatially in-phase (“true activator-inhibitor”) Turing instability, stable patterns are indeed generated in open regions of parameter space via a generically supercritical bifurcation from the spatially uniform state. In three of these classes the instability is always supercritical while in six there is an open region in which it is subcritical. Intriguingly, however, in the remaining two classes of minimal scheme we require different weakly nonlinear scalings, since the coefficient in the usual cubic normal form unexpectedly vanishes identically. In these cases, a different set of asymptotic scalings is required.We present a complete analysis through deriving the normal form for these two cases also, which involves quintic terms. This fifth-order normal form also captures the behaviour along the boundaries between the supercritical and subcritical cases of the cubic normal form. The details of these calculations reveal the distinct roles played by reaction rate parameters as compared to stoichiometric parameters.We quantitatively validate our analysis via numerical simulations and confirm the two different scalings for the amplitude of predicted stable patterned states.

Implementation of Solar PV Protection System in Indonesia: A Review

Conventional energy sources will run out if used continuously and damage the environment. Therefore, it is necessary to develop other energy sources that are safe, environmentally friendly, and inexhaustible known as renewable energy sources to meet energy needs in Indonesia. This article presents a review that discusses the protection of solar panels and PLTS. Solar panels are vulnerable to lightning strikes and other electrical disturbances, so an effective protection system is needed. This study uses a qualitative method through a literature study, reviewing various protection methods such as conventional and electrostatic lightning rods, good grounding systems, and overcurrent detection devices such as Solar Charge Controller (SCC) and Maximum Power Point Tracking (MPPT). In addition, battery protection with Automatic Transfer Switch (ATS) and Low Voltage Disconnected (LVD) is also discussed. Using Arduino Uno, ESP 32, and PLC, automation approaches offer real-time monitoring and control solutions for solar power plant performance. Innovations in the lightning protection zone concept and minimal quantity measurement schemes enable more cost-effective design of protection systems without reducing the level of protection. The results show that these various protection methods can provide effective and efficient protection for solar power plants, enabling optimization of system function and safety. In conclusion, the protection systems reviewed in this study offer a sustainable solution to Indonesia's energy challenges by utilizing the maximum potential of solar energy. The potential for further research is presented in this article to develop more efficient and effective protection methods.

Gauge-invariant renormalization of four-quark operators

We study the renormalization of four-quark operators in one-loop perturbation theory. We employ a coordinate-space gauge-invariant renormalization scheme (GIRS), which can be advantageous compared to other schemes, especially in nonperturbative lattice investigations. From our perturbative calculations, we extract the conversion factors between GIRS and the modified minimal subtraction scheme (MS¯) at the next-to-leading order. As a by-product, we also obtain the relevant anomalous dimensions in the GIRS scheme. A formidable issue in the study of the four-quark operators is that operators with different Dirac matrices mix among themselves upon renormalization. We focus on both parity-conserving and parity-violating four-quark operators, which change flavor numbers by two units (ΔF=2). The extraction of the conversion factors entails the calculation of two-point Green’s functions involving products of two four-quark operators, as well as three-point Green’s functions with one four-quark and two bilinear operators. The significance of our results lies in their potential to refine our understanding of QCD phenomena, offering insights into the precision of Cabibbo-Kobayashi-Maskawa (CKM) matrix elements and shedding light on the nonperturbative treatment of complex mixing patterns associated with four-quark operators. Published by the American Physical Society 2024

Modulation and control scheme for DC-link current minimization of an improved current source inverter

The traditional three-phase current source inverter (CSI) cannot maintain a constant DC-link current, the charging and discharging process under different operating modes will lead to the DC-link current being discontinuous or continuously increasing. To address this issue, the topology of CSI is improved, and a modulation scheme without additional losses is proposed in this paper to control the DC-link current. Then, based on the analysis of the DC-link ripple under all switching states, the calculation expression for the optimal reference of the DC-link current is derived, under the premise of meeting the current demand for the AC load, the minimum loss and harmonic distortion can be obtained by reducing the DC-link current. Finally, the math model of the AC-side is established, and the closed-loop control system including the voltage outer loop and the current inner loop is designed. The feasibility and correctness of the proposed modulation strategy and control method are validated by the simulation and experimental results, the minimum and stable DC-link current with the ripple below ± 1 A is obtained, and the high steady-state and dynamic control performances are achieved. The total harmonic distortion of the load current is less than 4 %, and the dynamic response time is 0.3 s.

Robust estimation of structural orientation parameters and 2D/3D local anisotropic Tikhonov regularization

Understanding the orientation of geologic structures is crucial for analyzing the complexity of the earths’ subsurface. For instance, information about geologic structure orientation can be incorporated into local anisotropic regularization methods as a valuable tool to stabilize the solution of inverse problems and produce geologically plausible solutions. We introduce a new variational method that uses the alternating direction method of multipliers within an alternating minimization scheme to jointly estimate orientation and model parameters in 2D and 3D inverse problems. Specifically, our approach adaptively integrates recovered information about structural orientation, enhancing the effectiveness of anisotropic Tikhonov regularization in recovering geophysical parameters. The paper also discusses the automatic tuning of algorithmic parameters to maximize the new method’s performance. Our algorithm is tested across diverse 2D and 3D examples, including structure-oriented denoising and trace interpolation. The results indicate that the algorithm is robust in solving the considered large and challenging problems, alongside efficiently estimating the associated tilt field in 2D cases and the dip, strike, and tilt fields in 3D cases. Synthetic and field examples show that our anisotropic regularization method produces a model with enhanced resolution and provides a more accurate representation of the true structures.

Distributed Optimal Power Control Scheme for Structural Loads Minimization in Wind Farms via a Consensus Approach

Distributed Optimal Power Control Scheme for Structural Loads Minimization in Wind Farms via a Consensus Approach

Forecasting Urban Traffic States with Sparse Data Using Hankel Temporal Matrix Factorization

Forecasting urban traffic states is crucial to transportation network monitoring and management, playing an important role in the decision-making process. Despite the substantial progress that has been made in developing accurate, efficient, and reliable algorithms for traffic forecasting, most existing approaches fail to handle sparsity, high-dimensionality, and nonstationarity in traffic time series and seldom consider the temporal dependence between traffic states. To address these issues, this work presents a Hankel temporal matrix factorization (HTMF) model using the Hankel matrix in the lower dimensional spaces under a matrix factorization framework. In particular, we consider an alternating minimization scheme to optimize the factor matrices in matrix factorization and the Hankel matrix in the lower dimensional spaces simultaneously. To perform traffic state forecasting, we introduce two efficient estimation processes on real-time incremental data, including an online imputation (i.e., reconstruct missing values) and an online forecasting (i.e., estimate future data points). Through extensive experiments on the real-world Uber movement speed data set in Seattle, Washington, we empirically demonstrate the superior forecasting performance of HTMF over several baseline models and highlight the advantages of HTMF for addressing sparsity, nonstationarity, and short time series. History: Accepted by Ram Ramesh, Area Editor for Data Science & Machine Learning. Funding: This research was supported by the Institute for Data Valorisation, the Interuniversity Research Centre on Enterprise Networks, Logistics and Transportation, the National Natural Science Foundation of China [Grants 12371456, 72101049, 72232001], the Sichuan Science and Technology Program [Grant 2024NSFJQ0038], and the Fundamental Research Funds for the Central Universities [Grant DUT23RC(3)045].

Fuzzy clustering with capacity constraints: Algorithm, convergence analysis and numerical experiments

In this paper we study the fuzzy clustering problem with capacity constraints. Despite of the fact that the fuzzy clustering approach is widely encountered in the literature, the inclusion of capacity constraints is recent and has several practical applications. We propose a general formulation of the clustering problem, where each point has an associated weight and the sum of the weights of the points that compose each group is established a priori. We discuss existence of solutions of the involved problems, providing a mathematical foundation for the established formulas. Besides, we propose a practical algorithm for solving this problem and present its convergence analysis. This algorithm follows an alternate minimization scheme, wherein a given iteration addresses the problem first in terms of the probabilities of each point xj belonging to each cluster i, denoted as uij, finding subsequently the position of the centroids, ci,i=1,…,g,j=1,…,n. This procedure is K-means-like, with the distinction that, as a point does not exclusively belong to a group, the computation of uij requires optimization techniques. In our case, this involves solving a linear system derived from the Karush–Kuhn–Tucker (KKT) conditions. With the aim of validating our algorithm, we present numerical tests with synthetic and real-world data to demonstrate its performance for the given problems. Since the proposal successfully solved these numerical tests within a reasonable computational time, it can be considered a valuable resource for addressing real-world applications.

Imprints of dark matter on the structural properties of minimally deformed compact stars

In this manuscript, we investigate the possibility of constructing anisotropic dark matter compact stars motivated by the Einasto density profile. This work develops analytical solutions for an anisotropic fluid sphere within the framework of the well-known Adler–Finch–Skea metric. This toy model incorporates an anisotropic fluid distribution that includes a dark matter component. We use the minimal geometric deformation scheme within the framework of gravitational decoupling to incorporate anisotropy into the pressure profile of the stellar system. In this context, we model the temporal constituent of the Θ-field sector to characterize the contribution of dark matter within the gravitational matter source. We present an alternative approach to studying anisotropic self-gravitating structures. This approach incorporates additional field sources arising from gravitational decoupling, which act as the dark component. We explicitly verify whether the proposed model satisfies all the requirements for describing realistic compact structures in detail. We conclude that the modeling of the Einasto density model with the Adler–Finch–Skea metric gives rise to the formation of well-behaved and viable astrophysical results that can be employed to model the dark matter stellar configurations.

The single tax in Ukraine: reform or repeal

The institution of a simplified taxation system provided for in the tax system of Ukraine is characterized by permanent variability, which is always aimed at achieving an optimal balance between national interests (reduction of the shadow economy sector; attracting funds to budgets; reducing the level of tax administration costs; preventing the use of simplified taxation system in minimization schemes; etc.) and individual interests of taxpayers (reducing the tax burden; promoting the competitiveness of taxpayers; improving the convenience of paying taxes; minimizing the amount of tax reporting; etc.). Since the introduction of the simplified taxation system, it has been significantly transformed and, compared to 1998, is qualitatively better. Despite this, discussions in political and scientific circles about the need to take steps to further modify this special tax regime, up to its complete abolition, do not stop. The article considers the National Revenue Strategy until 2030 approved by the supreme executive body of Ukraine, which defines a medium-term roadmap for reforming tax policy and tax administration in Ukraine. The article outlines the main principles that should be followed in modernizing the national simplified taxation system and considers the goals that the state seeks to achieve through the practical implementation of the approved strategy. The author describes in detail the key measures envisaged by this national strategy for reforming the simplified taxation system, including in the context of Europeanization of the tax system of Ukraine, and points out the uncertainty of certain elements of these measures, which leads to complications in the tax planning process for entities. The author concludes that the approved national strategy, which is aimed at approximating the national tax policy and tax legislation of Ukraine to the provisions of the European Union legislation, provides for depriving legal entities (including agricultural producers) of the right to tax their income with a single tax, and defines measures to tighten the requirements for single tax payers (individual entrepreneurs) and increase their tax burden.

Role of complexity on the minimal deformation of black holes

Abstract We investigate spherically symmetric classes of anisotropic solutions within the realm of a schematic gravitational decoupling scheme, primarily decoupling through minimal geometric deformation, applied to non-rotating, ultra-compact, self-gravitational fluid distributions. In this respect, we employ the minimal complexity factor scheme to generate physically realistic models for anisotropic matter distributions, using a well-behaved model. The zero-complexity factor condition enables us to determine the deformation function for solving the decoupled system. We explore all the structure-defining scalar variables, such as density inhomogeneity, strong energy condition, density homogeneity, and the complexity factor (an alloy of density inhomogeneity and pressure anisotropy) for the decoupling constant ranging between 0 and 1. We observe that the anisotropy vanishes when the coupling constant is set to unity. This finding holds significance as it implies that, in the context of a zero-complexity factor approach, an anisotropic matter distribution becomes perfect without requiring any isotropy requirements. This work effectively explored the impact of complexity on the composition of self-gravitational stellar distributions. This effective approach enables the development of new, physically realistic isotropic stellar models for anisotropic matter distributions. Additionally, our findings indicate that the complexity factor in static, spherically symmetric self-gravitational objects can significantly affect the nature of the matter distribution within these systems. It is concluded that the minimally deformed Durgapal-IV model features an increasing pressure profile, and the local anisotropy of pressure vanishes throughout the model under complexity-free conditions.

QCD equation of state and thermodynamic observables from computationally minimal Dyson-Schwinger equations

We study the QCD equation of state and other thermodynamic observables including the isentropic trajectories and the speed of sound. These observables are of eminent importance for the understanding of experimental results in heavy ion collisions and also provide a QCD input for studies of the timeline of heavy-ion-collisions with hydrodynamical simulations. They can be derived from the quark propagator whose gap equation is solved within a minimal approximation to the Dyson-Schwinger equations (DSEs) of QCD at finite temperature and density. This minimal approximation aims at a combination of computational efficiency and simplification of the truncation scheme while maintaining quantitative precision. This minimal DSE scheme is confronted and benchmarked with results for correlation functions and observables from lattice QCD at vanishing density and quantitative functional approaches at finite density. Published by the American Physical Society 2024

Perturbative versus non-perturbative renormalization

Approximated functional renormalization group (FRG) equations lead to regulator-dependent β-functions, in analogy to the scheme-dependence of the perturbative renormalization group (pRG) approach. A scheme transformation redefines the couplings to relate the β-functions of the FRG method with an arbitrary regulator function to the pRG ones obtained in a given scheme. Here, we consider a periodic sine-Gordon scalar field theory in d = 2 dimensions and show that the relation of the FRG and pRG approaches is intricate. Although both the FRG and the pRG methods are known to be sufficient to obtain the critical frequency βc2=8π of the model independently of the choice of the regulator and the renormalization scheme, we show that one has to go beyond the standard pRG method (e.g. using an auxiliary mass term) or the Coulomb-gas representation in order to obtain the β-function of the wave function renormalization. This aspect makes the scheme transformation non-trivial. Comparing flow equations of the two-dimensional sine-Gordon theory without any scheme-transformation, i.e. redefinition of couplings, we find that the auxiliary mass pRG β-functions of the minimal subtraction scheme can be recovered within the FRG approach with the choice of the power-law regulator with b = 2, which therefore constitutes a preferred choice for the comparison of FRG and pRG flows.

Transverse momentum moments

We establish robust relations between Transverse Momentum Dependent distributions (TMDs) and collinear distributions. We define weighted integrals of TMDs that we call Transverse Momentum Moments (TMMs) and prove that TMMs are equal to collinear distributions evaluated in some minimal subtraction scheme. The conversion to the modified minimal subtraction (MS¯) scheme can be done by a calculable factor, which we derive up to three loops for some cases. We discuss in detail the zeroth, the first, and the second TMMs and provide phenomenological results for them based on the current extractions of TMDs. The results of this paper open new avenues for theoretical and phenomenological investigation of the three-dimensional and collinear hadron structures. Published by the American Physical Society 2024

Thermoelectric response in zigzag chains: Impact of irradiation-induced conformational changes

This study explores the enhancement of thermoelectric response in a zigzag chain through irradiation with arbitrarily polarized light. The irradiation induces changes in hopping strengths, creating an asymmetric transmission profile around the Fermi energy, which is a crucial factor for achieving a higher figure of merit (FOM). Specific light configurations result in an FOM exceeding unity. We employ the Floquet–Bloch ansatz and minimal coupling scheme to model the irradiation effect, with transport properties evaluated using Green’s function technique within the Landauer–Büttiker formalism. The investigation covers electrical conductance, thermopower, and thermal conductance due to electrons and phonons. Our research deepens understanding and opens avenues for tailoring nanostructures to fine-tune thermoelectric properties, advancing highly efficient energy conversion devices exploiting irradiation effects.

SYNTACTIC ARRANGEMENT OF THE TEXTS OF THE STATE ANTHEM: ENGLISH-GERMAN PARALLELS

The work is devoted to the study of the syntactic arrangement of ESA/GSA texts within the opposition “simple sentence vs. complex sentence”, the number of which in these texts turns out to be very close to the golden ratio. The subject of the analysis is the structural-semantic understanding of the form and content of syntactic constructions in the chain “simple sentence — parataxis — hypotaxis — period” against the background of syncretization processes. It was found that a simple sentence in ADH/NDH texts rarely conforms to the canon of the minimal structural scheme, deviating from it either towards lacunarity or complexity. Lacunarity is associated with predicate ellipsis and inversion, and complexity is associated with right-sided branching typical for Germanic languages, which is caused by the desire for full informativeness of the spoken message and is regulated by two factors — proximity to the canon and distance from it. Each of them is, as a rule, a carrier of linguistic expression, which is created by the contrast of form and content. Instead, in para- and hypotaxis, a function is also connected to the creation of contrast. Of all the variety of common meanings in the texts of ESA/GSA, only copulative, adversative and causal are realized with the absolute preference of the first. Their use is limited by the absolute predominance of attributive and conditional sentences (for German) and attributive and explanatory (for English). The rest of the subjunctive syntaxemes are not implemented at all in anthems. An even less used syntactic form in the texts of ESA/GSA is the period, which is connected with its inconsistency with the postulate of maximum cognitive and emotional accessibility for consumers of this intellectual product. The period faces an important task: avoiding cognitive and logical overload and achieving maximum informativeness of the construction. It is proven that the laws of the genre and the requirements of the customers, giving preference to simple sentence formations and imposing restrictions on the use of complex ones, cause a close interweaving of orderliness, subordination and homogeneity in the brevity of the form. Relationships of causality, opposition, concessivety, finality, temporality, etc. are foreign to the anthem, because they are not attributes of political discourse, and therefore are not suitable for artistically expressive, ad vertising concise and convincing depiction of the image of the state and the idea of national unity.