Classical Ensemble Research Articles

Understanding and Quantifying Molecular Flexibility: Torsion Angular Bin Strings.

Molecular flexibility is a commonly used, but not easily quantified term. It is at the core of understanding composition and size of a conformational ensemble and contributes to many molecular properties. For many computational workflows, it is necessary to reduce a conformational ensemble to meaningful representatives, however defining them and guaranteeing the ensemble's completeness is difficult. We introduce the concepts of torsion angular bin strings (TABS) as a discrete vector representation of a conformer's dihedral angles and the number of possible TABS (nTABS) as an estimation for the ensemble size of a molecule, respectively. Here, we show that nTABS corresponds to an upper limit for the size of the conformational space of small molecules and compare the classification of conformer ensembles by TABS with classifications by RMSD. Overcoming known drawbacks like the molecular size dependency and threshold picking of the RMSD measure, TABS is shown to meaningfully discretize the conformational space and hence allows e.g. for fast checks of the coverage of the conformational space. The current proof-of-concept implementation is based on the ETKDGv3 conformer generator as implemented in the RDKit and known torsion preferences extracted from small-molecule crystallographic data.

Classification of Logging Data Using Machine Learning Algorithms

A log data analysis plays an important role in the uranium mining process. Automating this analysis using machine learning methods improves the results and reduces the influence of the human factor. In particular, the identification of reservoir oxidation zones (ROZs) using machine learning allows a more accurate determination of ore reserves, and correct lithological classification allows the optimization of the mining process. However, training and tuning machine learning models requires labeled datasets, which are hardly available for uranium deposits. In addition, in problems of interpreting logging data using machine learning, data preprocessing is of great importance, in other words, a transformation of the original dataset that allows improving the classification or prediction result. This paper describes a uranium well log (UWL) dataset generated with the employment of floating data windows and designed to solve the problems of identifying ROZ and lithological classification (LC) on sandstone-type uranium deposits. Comparative results of the ways of solving these problems using classical machine learning methods and ensembles of machine learning algorithms are presented. It has been shown that an increase in the size of the floating data window can improve the quality of ROZ classification by 7–9% and LC by 6–12%. As a result, the best-quality indicators for solving these problems were obtained, f1_score_macro = 0.744 (ROZ) and accuracy = 0.694 (LC), using the light gradient boosting machine and extreme gradient boosting, respectively.

Nonsequential double ionization of Ar in two-color inhomogeneous laser fields

With the classical ensemble method, we investigate the correlated electron dynamics in nonsequential double ionization (NSDI) of Ar in parallel two-color inhomogeneous laser fields with different inhomogeneity parameter ϵ. Numerical results show that at low laser intensities, the probability of NSDI is higher for two-color laser fields with a higher inhomogeneity parameter ϵ. At high laser intensities, however, the probability of NSDI decreases as ϵ increases. It is also shown that under low laser intensities, the two-color inhomogeneous laser fields drives the NSDI predominantly dominated by the RII channel, and the ratio of the RII channel increases as ϵ increases. More interestingly, an arc-like structure is found in the correlated electron momentum distributions for the two-color inhomogeneous laser fields. The underlying dynamics are revealed by tracing back to classical trajectories.

Enhancement and suppression of nonsequential double ionization by spatially inhomogeneous fields

Using the three-dimensional classical ensemble approach, we theoretically investigate the nonsequential double ionization of argon atoms in an intense laser field enhanced by bowtie-nanotip. We observe an anomalous decrease in the double ionization yield as the laser intensity increases, along with a significant gap in the low momentum of photoelectrons. According to our theoretical analysis, the finite range of the induced field by the nanostructure is the fundamental cause of the decline in double ionization yield. Driven by the enhanced inhomogeneous field, energetic electrons can escape from the finite range of nanotips without returning. This reduces the possibility of re-scattering on the nucleus and imprints the finite size effect into the double ionization yield and momentum distribution of photoelectrons in the form of yield decline and a gap in the photoelectron-momentum distribution.

A fuzzy rough granular ensemble learning based on the feature selection with chi-square1

Neighborhood granulation is a classical granulation method. Although it is adequate for clustering and classification tasks, its granules are more complex, and the data representation is binary. This paper proposes a new granulation method based on the neighborhood granulation. Firstly, a detailed definition of the granular form is given with fuzzy rough set theory. Then, a modified fuzzy rough discriminant function is proposed based on neighborhood systems. The samples are globally granulated on single features to construct granules and on multiple features to construct granular vectors. Also, a feature selection technique based on the Chi-square, which strikingly reduces the complexity of the fuzzy rough granular vectors, is introduced to address the disadvantage of the fuzzy rough granular vectors. An ensemble model structure is also proposed in the paper for the mixed nature of fuzzy rough granular vectors. The paper makes a detailed comparison between the fuzzy rough granulation and the neighborhood granulation. The results show that fuzzy rough granulation has higher computational efficiency and classification performance. Finally, a detailed comparison is made between the fuzzy rough granular ensemble model and various classical ensemble algorithms. The final results show that the fuzzy rough granular ensemble model has better robustness and generalization.

Ensembles of quantum classifiers

In the current era, known as Noisy Intermediate-Scale Quantum (NISQ), encoding large amounts of data in the quantum devices is challenging and the impact of noise significantly affects the quality of the obtained results. A viable approach for the execution of quantum classification algorithms is the introduction of a well-known machine learning paradigm, namely, the ensemble methods. Indeed, the ensembles combine multiple internal classifiers, which are characterized by compact sizes due to the smaller data subsets used for training, to achieve more accurate and robust prediction performance. In this way, it is possible to reduce the qubit requirements with respect to a single larger classifier while achieving comparable or improved performance. In this work, we present an implementation and an extensive empirical evaluation of ensembles of quantum instance-based classifiers for binary classification, with the purpose of providing insights into their effectiveness, limitations, and potential for enhancing the performance of basic quantum models. In particular, three classical ensemble methods and three quantum instance-based classifiers have been taken into account here. Hence, the scheme that has been implemented (in Python) has a hybrid nature. The results (obtained on real-world datasets) have shown an accuracy advantage for the ensemble techniques with respect to the single quantum classifiers, and also an improvement in robustness. In fact, ensembles have proven effective not only in mitigating unsuitable data normalizations but also in reducing the impact of noise on quantum classifiers, enhancing their stability.

An efficient quantum algorithm for ensemble classification using bagging

AbstractEnsemble methods aggregate predictions from multiple models, typically demonstrating improved accuracy and reduced variance compared to individual classifiers. However, they often come with significant memory usage and computational time requirements. A novel quantum algorithm that leverages quantum superposition, entanglement, and interference to construct an ensemble of classification models using bagging as an aggregation strategy is introduced. Through the generation of numerous quantum trajectories in superposition, the authors achieve B transformations of the training set with only operations, allowing an exponential enlargement of the ensemble size while linearly increasing the depth of the corresponding circuit. Moreover, when assessing the algorithm's overall cost, the authors demonstrate that the training of a single weak classifier contributes additively to the overall time complexity, as opposed to the multiplicative impact commonly observed in classical ensemble methods. To illustrate the efficacy of the authors’ approach, experiments on reduced real‐world datasets utilising the IBM qiskit environment to demonstrate the functionality and performance of the proposed algorithm are introduced.

On the thermodynamic entropy in the microcanonical ensemble of classical systems

We demonstrate that the surface entropy given by the volume of an energy shell in the phase space can be the thermodynamically consistent entropy in a classical microcanonical ensemble if the thickness of the energy shell is not an arbitrary constant but a non-extensive function satisfying a specific differential equation. A particular form of the energy shell thickness as a possible solution to the differential equation converts the surface entropy into the volume entropy given by the phase-space volume bounded by a constant energy surface. However, such a form bears a problem: The temperature derived accordingly becomes extensive when the density of states is a non-monotonic function of energy. Based on the adiabatic invariance of the degeneracy of a quantum system and the Weyl correspondence, we propose an alternative solution: the energy shell thickness given by the energy level spacing in the quantum counterpart of the classical ensemble considered, which is illustrated by a few simple examples.

Extreme gradient boosting-enhanced molecularly imprinted fluorescence nanosensor for rapid identification and visual detection of deltamethrin in seawater and aquatic products

Deltamethrin (DEL), a synthetic pyrethroid insecticide, may have long-term adverse effects on the aquatic environment. Extreme Gradient Boosting (XGBoost) is a classic ensemble boosting algorithm framework known for its high training efficiency, strong prediction performance, and versatile applications. In this study, we successfully developed a highly sensitive molecularly imprinted fluorescence nanosensor (MF-sensor) for DEL determination, enhanced by the XGBoost algorithm. The MF-sensor was fabricated by grafting blue and red CdSe/ZnS quantum dots onto a molecularly imprinted silica layer. The MF-sensor consisted of blue-molecularly imprinted polymer (MIP)-quantum dots (QDs) and r-MIP-QDs, which selectively detected DEL, and unmodified green CdSe QDs, which were not selective for DEL. Under optimized conditions, we observed an excellent linear relationship between the I526/(I450 +I630) ratio and DEL concentration ranging from 0.01 mg/L to 40.0 mg/L (R2 = 0.9944). The limit of detection was determined to be 1.34 µg/L. The recoveries in actual samples ranged from 98.5% to 109.0%, with a relative standard deviation (RSD) below 7.5%. Additionally, we utilized the XGBoost algorithm to establish a DEL prediction model, achieving an accuracy of 95.7%. The recoveries ranged from 96.0% to 102.4%, with a RSD below 5.5%. Overall, the proposed MF-sensor, enhanced by the XGBoost algorithm, was successfully utilized for the detection of DEL in environmental and aquatic products.

Playing music together: Exploring the impact of a classical music ensemble on adolescent's life skills self-perception.

This paper explored the effectiveness of ensemble performance on the development of adolescent's life skills. An explorative qualitative study investigated young musicians' self-perception about the benefits and challenges of learning and playing music together. A convenience sampling technique was adopted for interviewing 15 adolescents (12-18 years old) who participated in a long-term music education programme led by a charity in the North-West of England. The data were analysed using NVivo, employing a thematic analysis approach. Two main themes emerged from the analyses: (1) the main benefits of playing and learning in an ensemble: the development of music and life skills; (2) the challenges experienced by the musicians learning in the ensemble. The findings suggest that participants were conscious of the positive effects of playing in an ensemble on their lives. This extended beyond merely learning a musical instrument, i.e. acquiring music skills. In particular, young musicians recognised they had developed greater self-confidence and cognitive skills such as critical thinking and self-awareness. Primarily, they developed effective communication and interpersonal skills. At the same time, these young musicians recognised they had to face challenges related to the process of learning music in an ensemble, such as managing emotions of frustration and adapting to different music learning styles and techniques. Finally, suggestions are made for the implementation and evaluation of future projects to explore the impact and effectiveness of classical music programmes, with a particular emphasis on ensemble-based initiatives and their influence on life skills.

Financial sentiment analysis: Classic methods vs. deep learning models

Sentiment Analysis, also known as Opinion Mining, gained prominence in the early 2000s alongside the emergence of internet forums, blogs, and social media platforms. Researchers and businesses recognized the imperative to automate the extraction of valuable insights from the vast pool of textual data generated online. Its utility in the business domain is undeniable, offering actionable insights into customer opinions and attitudes, empowering data-driven decisions that enhance products, services, and customer satisfaction. The expansion of Sentiment Analysis into the financial sector came as a direct consequence, prompting the adaptation of powerful Natural Language Processing models to these contexts. In this study, we rigorously test numerous classical Machine Learning classification algorithms and ensembles against five contemporary Deep Learning Pre-Trained models, like BERT, RoBERTa, and three variants of FinBERT. However, its aim extends beyond evaluating the performance of modern methods, especially those designed for financial tasks, to a comparison of them with classical ones. We also explore how different text representation and data augmentation techniques impact classification outcomes when classical methods are employed. The study yields a wealth of intriguing results, which are thoroughly discussed.

Discrimination and Representation in Classical Music Ensembles

Discrimination and Representation in Classical Music Ensembles

Newtonian approximation to estimate the current temperature of the universe

Based on supernovae data, we built a potential for the observable universe. Using classical mechanics, we built a classical Lagrangian and a Hamiltonian to describe the evolution of the universe as a three-dimensional sphere. We then considered the universe as a classical statistical ensemble and determined the partition function of the universe and thus estimated its current temperature. This analysis is classical, quantum approximation was never used.

Physics-informed Bayesian inference of external potentials in classical density-functional theory.

The swift progression and expansion of machine learning (ML) have not gone unnoticed within the realm of statistical mechanics. In particular, ML techniques have attracted attention by the classical density-functional theory (DFT) community, as they enable automatic discovery of free-energy functionals to determine the equilibrium-density profile of a many-particle system. Within classical DFT, the external potential accounts for the interaction of the many-particle system with an external field, thus, affecting the density distribution. In this context, we introduce a statistical-learning framework to infer the external potential exerted on a classical many-particle system. We combine a Bayesian inference approach with the classical DFT apparatus to reconstruct the external potential, yielding a probabilistic description of the external-potential functional form with inherent uncertainty quantification. Our framework is exemplified with a grand-canonical one-dimensional classical particle ensemble with excluded volume interactions in a confined geometry. The required training dataset is generated using a Monte Carlo (MC) simulation where the external potential is applied to the grand-canonical ensemble. The resulting particle coordinates from the MC simulation are fed into the learning framework to uncover the external potential. This eventually allows us to characterize the equilibrium density profile of the system by using the tools of DFT. Our approach benchmarks the inferred density against the exact one calculated through the DFT formulation with the true external potential. The proposed Bayesian procedure accurately infers the external potential and the density profile. We also highlight the external-potential uncertainty quantification conditioned on the amount of available simulated data. The seemingly simple case study introduced in this work might serve as a prototype for studying a wide variety of applications, including adsorption, wetting, and capillarity, to name a few.

Exact Solution of Interacting Particle Systems Related to Random Matrices

We consider one-dimensional diffusions, with polynomial drift and diffusion coefficients, so that in particular the motion can be space-inhomogeneous, interacting via one-sided reflections. The prototypical example is the well-known model of Brownian motions with one-sided collisions, also known as Brownian TASEP, which is equivalent to Brownian last passage percolation. We obtain a formula for the finite dimensional distributions of these particle systems, starting from arbitrary initial condition, in terms of a Fredholm determinant of an explicit kernel. As far as we can tell, in the space-inhomogeneous setting and for general initial condition this is the first time such a result has been proven. We moreover consider the model of non-colliding diffusions, again with polynomial drift and diffusion coefficients, which includes the ones associated to all the classical ensembles of random matrices. We prove that starting from arbitrary initial condition the induced point process has determinantal correlation functions in space and time with an explicit correlation kernel. A key ingredient in our general method of exact solution for both models is the application of the backward in time diffusion flow on certain families of polynomials constructed from the initial condition.

Finite Reservoirs Corrections to Hamiltonian Systems Statistics and Time Symmetry Breaking

We consider several Hamiltonian systems perturbed by external agents that preserve their Hamiltonian structure. We investigate the corrections to the canonical statistics resulting from coupling such systems with possibly large but finite reservoirs and from the onset of processes breaking the time-reversal symmetry. We analyze exactly solvable oscillator systems and perform simulations of relatively more complex ones. This indicates that the standard statistical mechanical formalism needs to be adjusted in the ever more investigated nano-scale science and technology. In particular, the hypothesis that heat reservoirs be considered infinite and be described by the classical ensembles is found to be critical when exponential quantities are considered since the large size limit may not coincide with the infinite size canonical result. Furthermore, process-dependent emergent irreversibility affects ensemble averages, effectively frustrating, on a statistical level, the time reversal invariance of Hamiltonian dynamics that are used to obtain numerous results.

Electron dynamics of molecular frustrated double ionization driven by strong laser fields* *Supported by the National Natural Science Foundation of China (Grant Nos. 12004323, 12074329, 12104389, 1174131 and 91850114), National Key R&D Program of China (2022YFE0134200) and Nanhu Scholars Program for Young Scholars of Xinyang Normal University, Natural Science Foundation of Jilin Province, China (Grant No. 20220101016JC), and the Open

We theoretically investigate the frustrated double ionization (FDI) of molecules with different alignment-dependence using a three-dimensional classical ensemble method. The numerical results show that the FDI probability decreases with increasing wavelength, which is similar to the wavelength dependence of the FDI probability of atoms. Tracing the classical trajectories reveals that the contributions to molecular FDI from single-recollision and multiple-recollision mechanisms are equal in the short wavelength regime. In the long wavelength regime, the single-recollision FDI channel dominates in FDI. The nature in which molecular FDI occurs is identified and explained.

Scattering and transport properties of the three classical Wigner-Dyson ensembles at the Anderson transition.

An extensive numerical analysis of the scattering and transport properties of the power-law banded random matrix model (PBRM) at criticality in the presence of orthogonal, unitary, and symplectic symmetries is presented. Our results show a good agreement with existing analytical expressions in the metallic regime and with heuristic relations widely used in studies of the PBRM model in the presence of orthogonal and unitary symmetries. Moreover, our results confirm that the multifractal behavior of disordered systems at criticality can be probed by measuring scattering and transport properties, which is of paramount importance from the experimental point of view. Thus, a full picture of the scattering and transport properties of the PBRM model at criticality corresponding to the three classical Wigner-Dyson ensembles is provided.

Discovery of potential biomarkers for lung cancer classification based on human proteome microarrays using Stochastic Gradient Boosting approach.

Early identification of lung cancer (LC) will considerably facilitate the intervention and prevention of LC. The human proteome micro-arrays approach can be used as a "liquid biopsy" to diagnose LC to complement conventional diagnosis, which needs advanced bioinformatics methods such as feature selection (FS) and refined machine learning models. A two-stage FS methodology by infusing Pearson's Correlation (PC) with a univariate filter (SBF) or recursive feature elimination (RFE) was used to reduce the redundancy of the original dataset. The Stochastic Gradient Boosting (SGB), Random Forest (RF), and Support Vector Machine (SVM) techniques were applied to build ensemble classifiers based on four subsets. The synthetic minority oversampling technique (SMOTE) was used in the preprocessing of imbalanced data. FS approach with SBF and RFE extracted 25 and 55 features, respectively, with 14 overlapped ones. All three ensemble models demonstrate superior accuracy (ranging from 0.867 to 0.967) and sensitivity (0.917to 1.00) in the test datasets with SGB of SBF subset outperforming others. The SMOTE technique has improved the model performance in the training process. Three of the top selected candidate biomarkers (LGR4, CDC34, and GHRHR) were highly suggested to play a role in lung tumorigenesis. A novel hybrid FS method with classical ensemble machine learning algorithms was first used in the classification of protein microarray data. The parsimony model constructed by the SGB algorithm with the appropriate FS and SMOTE approach performs well in the classification task with higher sensitivity and specificity. Standardization and innovation of bioinformatics approach for protein microarray analysis need further exploration and validation.

Robust and accurate performance anomaly detection and prediction for cloud applications: a novel ensemble learning-based framework

Effectively detecting run-time performance anomalies is crucial for clouds to identify abnormal performance behavior and forestall future incidents. To be used for real-world applications, an effective anomaly detection framework should meet three main challenging requirements: high accuracy for identifying anomalies, good robustness when application patterns change, and prediction ability for upcoming anomalies. Unfortunately, existing research about performance anomaly detection usually focuses on improving detection accuracy, while little research tackles the three challenges simultaneously. We conduct experiments for existing detection methods on multiple application monitoring data, and results show that existing detection methods usually focus on different features in data, which will lead to their diverse performance on different data patterns. Therefore, existing anomaly detection methods have difficulty improving detection accuracy and robustness and predicting anomalies. To address the three requirements, we propose an Ensemble Learning-Based Detection (ELBD) framework which integrates existing well-selected detection methods. The framework includes three classic linear ensemble methods (maximum, average, and weighted average) and a novel deep ensemble method. Our experiments show that the ELBD framework realizes better detection accuracy and robustness, where the deep ensemble method can achieve the most accurate and robust detection for cloud applications. In addition, it can predict anomalies in the next four minutes with an F1 score higher than 0.8. The paper also proposes a new indicator ARP_score to measure detection accuracy, robustness, and multi-step prediction ability. The ARP_score of the deep ensemble method is 5.1821, which is much higher than other detection methods.