Exact Method Research Articles

Toward a Correct Description of Initial Electronic Coherence in Nonadiabatic Dynamics Simulations.

The recent improvement in experimental capabilities for interrogating and controlling molecular systems with ultrafast coherent light sources calls for the development of theoretical approaches that can accurately and efficiently treat electronic coherence. However, the most popular and practical nonadiabatic molecular dynamics techniques, Tully's fewest-switches surface hopping and Ehrenfest mean-field dynamics, are unable to describe the dynamics proceeding from an initial electronic coherence. While such issues are not encountered with the analogous coupled-trajectory algorithms or numerically exact quantum dynamics methods, applying such techniques necessarily comes with a higher computational cost. Here we show that a correct description of initial electronic coherence can indeed be achieved using independent-trajectory methods derived from the semiclassical mapping formalism. The key is the introduction of an initial sampling over the electronic phase space and a means of incorporating phase interference between trajectories, both of which are naturally achieved when working within the semiclassical mapping framework.

An alternating minimization algorithm with trajectory for direct exoplanet detection. The AMAT algorithm

Effective image post-processing algorithms are vital for the successful direct imaging of exoplanets. Standard point spread function (PSF) subtraction methods use techniques based on a low-rank approximation to separate the rotating planet signal from the quasi-static speckles and rely on signal-to-noise ratio maps to detect the planet. These steps do not interact or feed each other, leading to potential limitations in the accuracy and efficiency of exoplanet detection. We aim to develop a novel approach that iteratively finds the flux of the planet and the low-rank approximation of quasi-static signals in an attempt to improve upon current PSF subtraction techniques. In this study, we extend the standard L2 norm minimization paradigm to an L1 norm minimization framework in order to better account for noise statistics in the high contrast images. Then, we propose a new method, referred to as the alternating minimization algorithm with trajectory (AMAT), that makes more advanced use of estimating the low-rank approximation of the speckle field and the planet flux by alternating between them and utilizing both L1 and L2 norms. For the L1 norm minimization, we propose using L1 norm low-rank approximation (L1-LRA), a low-rank approximation computed using an exact block-cyclic coordinate descent method, while we use randomized singular value decomposition for the L2 norm minimization. Additionally, we enhance the visibility of the planet signal using a likelihood ratio as a post-processing step. Numerical experiments performed on a VLT/SPHERE-IRDIS dataset show the potential of AMAT to improve upon the existing approaches in terms of higher S/N, sensitivity limits (contrast curves), and receiver operating characteristic curves. Moreover, for a systematic comparison, we used datasets from the exoplanet data challenge to compare our algorithm with other algorithms in the challenge, and we find AMAT with a likelihood ratio map performs better than most algorithms tested on the exoplanet data challenge.

ON INEXACT NEWTON METHODS FOR SOLVING TWO NONLINEAR MATRIX EQUATIONS

In this paper we consider inexact Newton methods for finding the largest positive definite solutions of two nonlinear matrix equations X+ A∗X−1A = Q and X − A∗X−1A = Q, respectively. Using Newton’s method for considered equations requires solving a Stein’s equation at each iteration. For solving the Stein’s equation, we use Smith type iterations instead of exact methods. Nonlocal convergence of the process is shown. Numerical experiments are included to illustrate the theory.

Seeking the first phylogenetic method–Edvard A. Vainio (1853–1929) and his troubled endeavour towards a natural lichen classification in the late nineteenth century Finland

Edvard August Vainio was a world-renowned Finnish lichenologist. In Finland, however, he was a controversial person due to his strong pro-Finnish political views. Equally disputed was his opinion that systematics should be based on evolutionary theory and phylogenetic thinking. Vainio was familiar with the ideas of the early German phylogeneticists—especially those of Carl Wilhelm von Nägeli – and, applying them, aimed to create an exact method for building a natural classification of lichens already at the end of the nineteenth century. In this respect, Vainio was a true pioneer, as no actual phylogenetic method had yet been developed. In the general spirit of the time, Vainio focused on finding the ancestors of species and other taxa by comparing primitive and derived features of homologous characters. However, Vainio already understood the concept of sister groups in 1880, the identification of which is the basis of all modern phylogenetic research. Nevertheless, the distinctive method developed by Vainio was not so much focused on the construction of a phylogenetic tree, but on revealing the origin of species through the differentiation and fixation of their polymorphic variation. Indeed, Vainio’s species concept is surprisingly similar to the phylogenetic species concepts presented a hundred years later. Although in many ways progressive, Vainio’s views did not influence the development of phylogenetics more widely, but his discussions are nevertheless a valuable source to understanding the early development of phylogenetic theory.

Solving blockage problem of the 5G mmWaves Wireless Communications using Jellyfish Search Optimizer

The 5G technologies are aimed to support a variety of vertically connected applications with heterogeneous devices and machines with significant improvements in terms of higher quality of service, increased network capacity and improved system throughput. However, 5G systems still face a number of challenges mentioned by researchers and organizations, and among these challenges, we highlight that millimeter wave links are very susceptible to blockage. If the line-of-sight communication path is blocked, reflexive path communication can help maintain communication. The shortest route was to take an alternate route when the first route was blocked. Among the proposed solutions to the blocking problem is an algorithm to distribute the power between different mmWave communication paths in order to overcome the masses of links under randomly distributed obstacles. The problem has been resolved with an exact method. In this article, we have optimized all the results of this exact method by applying a powerful metaheuristic technique called jellyfish search optimizer to maximize the overall capacity of the path between two nodes. The results showed that our approach procures an improvements exceed 100% over the results of the exact method.

Genomic complexity and clinical significance of the RCCX locus.

Nearly identical, repetitive elements in the genome contribute to the variability in genetic inheritance patterns, particularly in regions like the RCCX locus, where such repeats can lead to structural variations. In addition, during the formation of gametes as a result of meiosis, variants of loci with repetitive elements that do not code for the required proteins may occur. As a result, an individual with certain genetic rearrangements in this region may have an increased risk of developing a congenital disorder, particularly in cases where the non-functional allele is inherited dominantly. At the same time, there is still no routine or generally recognized diagnostic method to determine the sequence of the repetitive fragments. The functionally important RCCX locus consists of such repetitive fragments. The available knowledge about the genomic variants of the RCCX locus is fragmented, as there is no standardized method to determine its structure. It should be noted that in some structural variants of the RCCX locus, the sequence of protein-coding genes is disrupted, leading to the development of diseases such as congenital adrenal hyperplasia (CAH). Although genetic testing is generally accepted as a gold standard for CAH diagnosis, there are a myriad of strategies on which exact methods to use and in which order. The reason for this inconsistency lies in the complexity of the RCCX locus and the fact that each patient or carrier may have a highly individualized mutation or combination thereof. In this review, we have discussed all known methods that can be used to study the structure of the RCCX locus. As a result, optimal approaches are proposed for the diagnosis of the most common disease caused by lesions in the RCCX-CAH due to CYP21A2 deficiency.

Lateral deflections of slender RC columns under eccentric compression loading with different end conditions

AbstractIn the literature, several methods have focused mostly on determining the lateral deflection of columns with pinned end conditions. This paper presents a powerful method that allows the calculation of lateral deflection for columns of different end conditions, with particular attention to reinforced concrete (RC) columns. By utilizing the moment–curvature relations, a numerical procedure to compute slopes and deflections of pin‐ended columns is proposed, in which the slopes and deflections are corrected via an efficient and fast technique. Accordingly, slopes and deflections of columns with different end conditions are determined via procedures that rely on a simple searching technique. The second‐order analysis is individually included in the calculations; therefore, the complexity arising from the direct impact of the axial load on the lateral deflection is averted. Therefore, the method has the potential for inclusion in many numerical models for different structural members. The equations derived via the developed method have identical responses to the expressions obtained via the exact methods. A series of numerical examples are presented to illustrate the applicability of the proposed method to RC columns with different loadings and end conditions. Finally, the proposed method is evaluated, and its accuracy is demonstrated via parametric verification. As the axial load increased, the lateral displacement increased somewhat. The greater the eccentricity is, the greater the lateral displacement. As the eccentricity increased, the failure mode of the RC column changed from compression failure to bending failure.

Exact results on the dynamics of the stochastic Floquet-East model

Abstract We introduce a stochastic generalisation of the classical deterministic Floquet-East model, a discrete circuit with the same kinetic constraint as the East model of glasses. We prove exactly that, in the limit of long time and large size, this model has a large deviation phase transition between active and inactive dynamical phases. We also compute the finite time and size scaling of general space-time fluctuations, which for the case of inactive regions gives rise to dynamical hydrophobicity. We also discuss how, through the Trotter limit, these exact results also hold for the continuous-time East model, thus proving long-standing observations in kinetically constrained models. Our results here illustrate the applicability of exact tensor network methods for solving problems in many-body stochastic systems.

Exact solution methods for the Resource Constrained Project Scheduling Problem with a flexible Project Structure

Exact solution methods for the Resource Constrained Project Scheduling Problem with a flexible Project Structure

A goodness-of-fit measure for logistic regression under separation

Logistic regression models have a severe problem called separation. The maximum likelihood estimator does not exist in logistic regression models for data structures under separation. Under separation, the forcibly estimated maximum likelihood estimate may have an extremely large value. Separation often occurs when the size of dataset is small. Consequently, goodness-of-fit measures based on the likelihood ratio and those based on covariance functions using the maximum likelihood estimate indicate that the model is excessively good regardless of the cause of the separation. The Firth and exact logistic regression methods are valid estimation methods for separation problems. Therefore, we propose methods to reasonably evaluate the goodness-of-fit measures of statistical models under separation with dataset of a small sample size with the abovementioned methods. The goodness-of-fit measures based on covariance functions which are a generalization of the multiple correlation coefficient, referred to as the regression correlation coefficient and the entropy coefficient of determination are then used combined with the abovementioned methods for the separation data. In addition, we conducted a data analysis using the definition of the non separation ratio based on the regression depth.

Chemical thermodynamics of biomass, cellulose, and cellulose derivatives: A review

This article provides a review of the research on the chemical thermodynamics and thermochemistry of biomass, cellulose, and its derivatives such as ethers, esters, and oxycelluloses. For diverse biomass types, gross and net heating values were studied. It has been established that these energetical characteristics of biomass can be calculated using a superposition of the energetical characteristics of the main components of biomass such as cellulose, hemicelluloses, lignin, lipids, proteins, etc. The pelletization of biomass improves its fuel performance. It was shown that, if the ultimate goal is to generate the maximum amount of thermal energy, then it is more profitable to directly burn the initial biomass in the form of pellets than to burn the amount of solid or liquid biofuel that can be extracted from this biomass. After the cellulose study, the direct and exact thermochemical method for determining the crystallinity degree of this biopolymer was proposed. In addition, the standard combustion and formation enthalpies of various cellulose samples were studied. As a result, the thermodynamic characteristics of four crystalline allomorphs of cellulose, CI, CII, CIII, and CIV, were obtained and their thermodynamic stability was evaluated. The thermochemistry of enzymatic hydrolysis of cellulose was studied. In addition. The thermodynamical characteristics of various cellulose derivatives were determined, and the thermochemistry of the reactions of cellulose alkalization, etherification, esterification, and oxidation was studied.

Political Districting to Minimize County Splits

Political Districting to Minimize County Splits When dividing a state into districts for elections, one traditional criterion is that political subdivisions like counties and cities should not be divided unnecessarily. Some states go as far as to say that the number of county splits should be minimized, but previously there was no scalable exact method for determining this. With new integer programming techniques, Shahmizad and Buchanan exactly compute this minimum number for all states and district types (congressional, state senate, state house) across the USA.

Determining of gully erosion susceptibility based on UAV and machine learning in Loess Plateau

In order to determine the susceptibility of gully erosion at a small watershed scale on the Loess Plateau of China, three hybrid models were developed. These models were based on the Multi-Attributive Border Approximation Area Comparison (MABAC), frequency ratio (FR), CatBoost (CB), LightGBM (LG), and extremely-randomized tree (ET). Based on the Unmanned Aerial Vehicles (UAV) photos, a total of 83 gullies with 12,150 gully pixels and 8 conditioning variables were extracted and used to create the gully inventory database. The correlations between the conditioning parameters and the pixels of gullies were then determined using FR, and the relative importance of these conditioning factors was quantified using machine learning. Then, for gully erosion susceptibility mapping (GESM), three hybrid gully erosion susceptibility models called MABAC-FR-CB, MABAC-FR-LG, and MABAC-FR-ET were developed. The performance of three hybrid models was assessed using the receiver operating characteristic curve (ROC) and the Kappa coefficient. The results claimed that slope steepness greatly influenced the erosion of the gully. The MABAC-FR-ET performed the most precisely, with area under curvature (AUC) of 0.998 and a Kappa of 0.952. As a result, it was determined that MABAC-FR-ET is the most exact and accurate method for predicting the susceptibility to gully erosion in the study watershed.

Electric-field-induced enhancement of exciton binding energy in one-dimensional phosphorene atomic chain

An electric field normally increases the separation between the electron and hole in an exciton without intrinsic polarization and suppresses their Coulombic interaction, resulting in the reduction of its binding energy. Our study of one-dimensional (1D) excitons in phosphorene atomic chains, by using the exact diagonalization method, however, reveals that an electric field applied along the chain axis actually increases the exciton binding energies. Further analysis shows that the electric field tends to enhance the long-range interaction between the electron and hole while suppressing their short-range interaction by inducing an alternating charge distribution along the atomic chain. The zigzag symmetry is believed to account for this unique excitonic phenomenon in the 1D system.

Scheduling a single machine with multiple due dates per job

AbstractIn this paper, we consider single-machine scheduling with multiple due dates per job. This is motivated by several industrial applications, where it is not important by how much we miss a due date. Instead the relevant objective is to minimize the number of missed due dates. Typically, this situation emerges whenever fixed delivery appointments are chosen in advance, such as in the production of individualized pharmaceuticals or when customers can only receive goods at certain days in the week, due to constraints in their warehouse operation. We compare this previously unexplored problem with classical due date scheduling, for which it is a generalization. We show that single-machine scheduling with multiple due dates is NP-hard in the strong sense if processing times are job dependent. If processing times are equal for all jobs, then single-machine scheduling with multiple due dates is at least as hard as the long-standing open problem of weighted tardiness with equal processing times and release dates $$1 \mid r_j, p_j = p \mid \sum w_j T_j$$ 1 ∣ r j , p j = p ∣ ∑ w j T j . Finally, we focus on the case of equal processing times and provide several polynomially solvable special cases as well as an exact branch-and-bound algorithm and heuristics for the general case. Experiments show that our branch-and-bound algorithm compares well to modern exact methods to solve problem $$1 \mid r_j, p_j = p \mid \sum w_{j} T_{j}$$ 1 ∣ r j , p j = p ∣ ∑ w j T j .

Sequential and Parallel Algorithms to Compute Turbulent Coherent Structures

The behavior of turbulent flows remains a significant unsolved problem in physics. Recently, a large quantity of effort has been directed toward understanding the non-linear interactions of the different flow structures in order to address this challenge. In this paper, different implementations of one exact method for identifying these structures are analyzed. This includes two sequential algorithms and a parallelizable one, developed to handle large-scale data efficiently. The new parallel algorithm offers significant advantages in handling the computational demands of large simulations, providing a more scalable solution for future research.

Towards quantum gravity with neural networks: solving the quantum Hamilton constraint of U(1) BF theory

Abstract In the canonical approach of loop quantum gravity, arguably the most important outstanding problem is finding and interpreting solutions to the Hamiltonian constraint. In this work, we demonstrate that methods of machine learning are in principle applicable to this problem. We consider U(1) BF theory in three dimensions, quantised with loop quantum gravity methods. In particular, we formulate a master constraint corresponding to Hamilton and Gauß constraints using loop quantum gravity methods. To make the problem amenable for numerical simulation we fix a graph and introduce a cutoff on the kinematical degrees of freedom, effectively considering U q ( 1 ) BF theory at a root of unity. We show that the neural network quantum state ansatz can be used to numerically solve the constraints efficiently and accurately. We compute expectation values and fluctuations of certain observables and compare them with exact results or exact numerical methods where possible. We also study the dependence on the cutoff.

Prospects for the economy and foreign trade of Ethiopia: fore cast estimates based on mathematical modeling

The article presents a forecast assessment of the development of the national economy and foreign trade of Ethiopia until 2030, calculated by the authors on the basis of a mathematical and systematic analysis of macroeconomic processes and methods of modeling these processes usingthe Box-Jenkins model (ARIMA). Estimation method: the exact maximum likelihood method. The topic seems relevant due to Ethiopia's accession to the BRICS alliance from 2024. Therefore, it is important to predict possible trends in Ethiopia's economic and foreign trade development, their significance for the country itself, as well as their impact on the economic dynamics of other BRICS countries and the association as a whole. The study is updated taking into account the continued increase in global volatility and the emergence of new threats, including in Africa. The subject is trends in the economic development of Ethiopia as a member of the BRICS. The purpose of the article is to develop a scientifically based forecast of the development of the economy and foreign trade of Ethiopia in the medium term. The article identifies potential threats to the development of the Ethiopian economy. The statistical basis of the study was mainly data from the United Nations Conference on Trade and Development (UNCTAD). The results of the study can be used to understand the trends of socio-economic and foreign trade development of the country, adjust this development, as well as expand and enrich the theoretical concepts of the world economy. The research and author's calculations are based solely on the current circumstances and current realities, without taking into account any fundamental changes in the politics and economy of the country under study. The author's calculations and conclusions can be useful to economists, entrepreneurs, and researchers as a basis for their further practical and scientific activities.

An Exact Stochastic Simulation Method for Fractional Order Compartment Models

An Exact Stochastic Simulation Method for Fractional Order Compartment Models

Demographic characteristics, clinical manifestations, and treatment outcomes of May-Thurner Syndrome: a five-year retrospective analysis using computed tomography venography in a Chinese population

Objective This study aimed to analyze the demographic characteristics, symptoms, and treatment outcomes of patients diagnosed with May-Thurner syndrome (MTS) using computed tomography venography (CTV). Methods Medical records of patients diagnosed with MTS through CTV at Hebei General Hospital of China between April 1, 2017, and May 31, 2022, were reviewed. The data collected included: (1) gender, age, body mass index (BMI), and smoking and drinking habits; (2) time of onset and symptoms of MTS, as well as other accompanying symptoms; (3) additional diagnoses, length of hospital stay (days), treatment methods, treatment success, and the occurrence of post-treatment bleeding or recurrence. Descriptive statistics were used, with mean ± standard deviation and median values reported. The t-test/u-test and Chi-square test (including the exact probability method) were used to compare means and rates, respectively, with a significance level set at α = 0.05. Results Out of 402 patients (233 males, 169 females), 118 (29.4%) were diagnosed with MTS, with 47 (21.1%) males and 71 (39.7%) females. The incidence of MTS was significantly higher in females than males (χ2 proportion = 16.545, χ2 composition = 9.763, P < 0.05). The average ages of male and female MTS patients were 56.4 and 59.9 years, respectively, with mean BMIs of 27.05 and 27.09 kg/m2. Among male patients, 27.7% (13) were smokers, and 17.0% (8) consumed alcohol. Inferior vena cava (IVC) thrombosis was notable in 59.3% of MTS patients, with a significantly higher proportion in females (70.4%) than in males (42.6%) (χ2 = 9.102, P < 0.05). Lower limb swelling without pain was reported by 70.3% of patients, with 53.4% (44.7% male, 59.2% female) experiencing swelling on the left side only, which was significantly more common than swelling on the right side only or both sides (χ2 = 44.554, P < 0.05). Additionally, 12.7% of patients reported both swelling and pain, with left-side symptoms being more prevalent than right-side or both sides. The average ages at symptom onset were 51.3 ± 17.1 years in males and 57.1 ± 13.2 years in females. All treatments for MTS were successful without bleeding or recurrence. The most common treatment method was balloon dilation combined with stent placement (57.6%). Conclusion CTV is highly effective in detecting and facilitating the successful treatment of MTS. It should be fully utilized to promote early diagnosis and treatment of MTS. Female MTS patients need more medical resources for diagnosis and treatment.