Functional Forms Research Articles

Information-entropy-driven generation of material-agnostic datasets for machine-learning interatomic potentials

In contrast to their empirical counterparts, machine-learning interatomic potentials (MLIAPs) promise to deliver near-quantum accuracy over broad regions of configuration space. However, due to their generic functional forms and extreme flexibility, they can catastrophically fail to capture the properties of novel, out-of-sample configurations, making the quality of the training set a determining factor, especially when investigating materials under extreme conditions. We propose a novel automated dataset generation method based on the maximization of the information entropy of the feature distribution, aiming at an extremely broad coverage of the configuration space in a way that is agnostic to the properties of specific target materials. The ability of the dataset to capture unique material properties is demonstrated on a range of unary materials, including elements with the FCC (Al), BCC (W), HCP (Be, Re and Os), graphite (C), and trigonal (Sb, Te) ground states. MLIAPs trained to this dataset are shown to be accurate over a range of application-relevant metrics, as well as extremely robust over very broad swaths of configurations space, even without dataset fine-tuning or hyper-parameter optimization, making the approach extremely attractive to rapidly and autonomously develop general-purpose MLIAPs suitable for simulations in extreme conditions.

SymbolFit: Automatic Parametric Modeling with Symbolic Regression

We introduce SymbolFit (API: https://github.com/hftsoi/symbolfit), a framework that automates parametric modeling by using symbolic regression to perform a machine-search for functions that fit the data while simultaneously providing uncertainty estimates in a single run. Traditionally, constructing a parametric model to accurately describe binned data has been a manual and iterative process, requiring an adequate functional form to be determined before the fit can be performed. The main challenge arises when the appropriate functional forms cannot be derived from first principles, especially when there is no underlying true closed-form function for the distribution. In this work, we develop a framework that automates and streamlines the process by utilizing symbolic regression, a machine learning technique that explores a vast space of candidate functions without requiring a predefined functional form because the functional form itself is treated as a trainable parameter, making the process far more efficient and effortless than traditional regression methods. We demonstrate the framework in high-energy physics experiments at the CERN Large Hadron Collider (LHC) using five real proton-proton collision datasets from new physics searches, including background modeling in resonance searches for high-mass dijet, trijet, paired-dijet, diphoton, and dimuon events. We show that our framework can flexibly and efficiently generate a wide range of candidate functions that fit a nontrivial distribution well using a simple fit configuration that varies only by random seed, and that the same fit configuration, which defines a vast function space, can also be applied to distributions of different shapes, whereas achieving a comparable result with traditional methods would have required extensive manual effort.

Novel constructed dynamical analytical solutions and conserved quantities of the new (2+1)-dimensional KdV model describing acoustic wave propagation

Abstract In this study, we delve into the exploration of the new (2+1)-dimensional KdV model, a mathematical model essential to the understanding of various nonlinear phenomena such as ion acoustic waves and harmonic crystals. The primary objective of this study is to conduct a comprehensive symmetry analysis of the model, a method that has not been previously applied to the model. This approach aims to uncover new exact solutions, which will not only enrich the existing literature but also provide valuable insights for researchers specializing in symmetry analysis and the broader scientific community. To achieve this goal, we employ a comprehensive analytical methodology that combines Lie symmetry analysis technique with Kudryashov’s method, the simplest equation technique, direct integration, Jacobi elliptic expansion technique, and the power series method. Through the utilization of these diverse analytical approaches, we successfully derive solutions for the model in various functional forms, including exponential, trigonometric, hyperbolic, Jacobi elliptic, and rational functions. These solutions exhibit broad applicability across diverse disciplines within nonlinear science and engineering. To provide a deeper understanding of the obtained solutions, we present our findings through visual representations, utilizing three-dimensional, two-dimensional, and density plots. By selecting appropriate ranges for the involved arbitrary constants, we effectively illustrate the dynamical wave behaviours inherent in the solutions. Notably, our visual representations reveal discernible patterns characterized by periodic and kink-shaped structures, shedding light on the intricate dynamics encapsulated within the solutions. Furthermore, we endeavour to identify conserved vectors associated with the model under investigation. To achieve this, we employ the multiplier method and Ibragimov’s theorem. The results are expected to enhance our understanding of the model’s physical implications and contribute to advancing the field.

A Review on Visible-Light-Mediated Aziridine Synthesis: Mechanisms and Recent Advances

Aziridines are highly valued in synthetic chemistry due to their substantial ring strain and reactive C-N bonds, making them remarkably reactive and essential for various transformations in organic synthesis. Their ring-opening ability reactions is crucial for synthesizing complex molecules, including natural products and pharmaceuticals. Over 130 biologically active aziridine-containing compounds exhibit pharmacological activities, including antitumor, antimicrobial and antibacterial effects, making aziridines key sources for drug prototypes and potential leads for drug discovery. In recent decades, numerous innovative and practical methodologies have been developed in the chemistry of aziridines, focusing on their synthesis and transformation into diverse functional forms. Traditional methods typically involve the use of precious transition metals, oxidants and strong acids or bases under harsh reaction conditions. In contrast, photochemistry has emerged as an intriguing approach, enabling the construction of aziridine derivatives from diverse substrates under milder conditions. Consequently, numerous light-driven synthetic approaches featuring high efficiency and mild conditions have been developed. This review focuses on environment-friendly and benign synthetic methods for preparing aziridine compounds, along with mechanistic insights into their formation under photocatalytic conditions.

Checking the Cox Proportional Hazards Model with Interval-Censored Data

This paper presents a general framework for checking the adequacy of the Cox proportional hazards model with interval-censored data, which arise when the event of interest is known only to occur over a random time interval. Specifically, we construct certain stochastic processes that are informative about various aspects of the model, i.e., the functional forms of covariates, the exponential link function and the proportional hazards assumption. We establish their weak convergence to zero-mean Gaussian processes under the assumed model through empirical process theory. We then approximate the limiting distributions by Monte Carlo simulation and develop graphical and numerical procedures to check model assumptions and improve goodness of fit. We evaluate the performance of the proposed methods through extensive simulation studies and provide an application to the Atherosclerosis Risk in Communities Study.

Chaperone Dependency during Primary Protein Biogenesis Does Not Correlate with Chaperone Dependency during in vitro Refolding

Many proteins require molecular chaperones to fold into their functional native forms. Previously we used limited proteolysis mass-spectrometry (LiP-MS) to find that ca. 40% of the E. coli proteome do not efficiently refold spontaneously following dilution from denaturation, a frequency that drops to ca. 15% once molecular chaperones like DnaK or GroEL are provided. However, the roles of chaperones during primary biogenesis in vivo can differ from the functions they play during in vitro refolding experiments. Here, we used LiP-MS to probe structural changes incurred by the E. coli proteome when two key chaperones, trigger factor and DnaKJ, are deleted. While knocking out DnaKJ induces pervasive structural perturbations across the soluble E. coli proteome, trigger factor deletion only impacts a small number of proteins’ structures. Overall, proteins which cannot spontaneously refold (or require chaperones to refold in vitro) are not more likely to be dependent on chaperones to fold in vivo. For instance, the glycolytic enzyme, phosphoglycerate kinase (PGK), cannot refold to its native form in vitro following denaturation (even with chaperones), but by LiP-MS we find that its structure is unperturbed upon DnaKJ or Tig deletion, which is further supported with biochemical and biophysical assays. Thus, PGK folds to its native structure most efficiently during co-translational folding and does so without chaperone assistance. This behaviour is generally found among chaperone-nonrefolders (proteins that cannot refold even with chaperone assistance), strengthening the view that chaperone-nonrefolders are obligate co-translational folders. Hence, for some E. coli proteins, the vectorial nature of co-translational folding is the most important “chaperone.”

The Curve Estimation Nonparametric Regression Multiresponse Mixed with Truncated Spline, Fourier Series, and Kernel

This study formulates a nonparametric regression model for multiresponse data by combining three estimators: truncated spline, Fourier series, and kernel function. Each estimator captures specific characteristics. Truncated spline capture local traits with knot points, while fourier series capture periodic patterns and kernel estimators provide flexible smoothing for unknown functional forms. The model proposed is under an additive assumption where each predictor contributes independently to each response. Estimation is done with Weighted Least Squares (WLS) method which is efficient in managing the correlations between the multiresponse variables. The final multiresponse nonparametric regression curve estimator combining truncated spline, Fourier series, and kernel is given by \\hat{\mu} = \hat{f} + \hat{g} + \hat{h}\] obtained by solving the WLS optimization problem: [\min_{\boldsymbol{\beta}, \boldsymbol{\alpha}} \{ \boldsymbol{\varepsilon}' W \boldsymbol{\varepsilon} \} =\min_{\boldsymbol{\beta}, \boldsymbol{\alpha}} \left\{ (\mathbf{y}^* - U \boldsymbol{\beta} - Z \boldsymbol{\alpha})' W (\mathbf{y}^* - U \boldsymbol{\beta} - Z \boldsymbol{\alpha}) \right\}.\]. The solution to this problem results in the mixed estimator, which can be expressed as: \[\hat{\boldsymbol{\mu}} = E \mathbf{y} \quad \text{with} \quad E = UB + ZA + T.\]

Strategi Pondok Pesantren dalam Meningkatkan Kedisiplinan Santri: Studi Deskriptif di Pondok Pesantren Perkampungan Minangkabau

Student discipline is a key factor in the success of education and character development in pesantren; however, violations disrupting order still frequently occur. This study aims to identify the strategies implemented at Pondok Pesantren Perkampungan Minangkabau to improve student discipline. A descriptive qualitative method was employed, involving observation, interviews, and document collection from the pesantren administrators, kyai, and students. The findings reveal that the pesantren applies the IQOB strategy, a form of punishment or penalty functioning as a means of self-evaluation and self-improvement, thereby fostering the growth of independent, disciplined, ethical, and responsible individuals. These findings provide a concrete depiction of disciplinary challenges in pesantren and demonstrate the effectiveness of the IQOB strategy in creating a more conducive learning environment. The study also opens opportunities for further research on unresolved issues related to discipline.

AABA Types in Rock/Pop Music

ABSTRACTThis article presents a methodology for understanding large‐scale form in rock/pop music, focusing on the much‐discussed AABA form. Though previous authors on rock/pop form differ on what situations should be classified as AABA, this article argues that there are four essential patterns with which AABA songs might engage: AA–BA–BA, AAB–AB–(A), AA–B–A and AA–B/A. These four types are differentiated by their highest‐level manifestation of form, whereby the A and B sections are grouped into distinct patterns. Building on previous research, the analysis focuses on the surface‐level aspects that generate these larger patterns, which encompass harmony, melody, texture, dynamics, lyrics and clock time. The structure and function of the B section is particularly crucial in articulating each pattern. In presenting a wider notion of what might constitute B music, I explain how different options for constructing a B section can produce distinct trajectories within the larger umbrella of the given AABA type. Additionally, this methodology exploits the concepts of formal functionality and rotational form to illuminate the dynamic relations within AABA forms, demonstrating how the tonal layout of a B section affects its grouping potential and how larger cycles that reference the thematic components of the A sections can occur in the latter portions of certain AABA types.

Nonparametric estimation of R = P(X > Y)

In this study, we propose a nonparametric kernel-based approach to estimate the stress-strength reliability coefficient R = P ( X > Y ) when the distributions of X and Y are unknown. Previous research has primarily focused on parametric methods, which assume specific functional forms for the distributions while estimating their unknown parameters. Given the wide range of potential distributions for data modeling, this topic has attracted significant attention over the past three decades. The use of a nonparametric method makes the proposed approach applicable to any pair of continuous distributions. It leads to three new estimators, all based on the nonparametric estimation of the cumulative distribution functions of the underlying random variables. We establish the consistency of these estimators and evaluate their performance through a simulation study for finite sample sizes. The numerical results demonstrate that the proposed estimators perform favorably compared to existing methods, highlighting their strong potential for practical applications.

Toward Chemical Accuracy in Biomolecular Simulations through Data-Driven Many-Body Potentials: I. Polyalanine in the Gas Phase.

A predictive understanding of how proteins fold, misfold, and stabilize requires accurate molecular-level insights into the thermodynamic and kinetic forces shaping their backbones. While empirical force fields remain the workhorse of biomolecular simulations, their limited functional forms often fall short in capturing the complex many-body interactions that govern protein dynamics. Quantum-mechanical methods, on the other hand, offer high accuracy but are prohibitively expensive for large biomolecules. In this work, we introduce a generalized, intramolecular formulation of the data-driven many-body MB-nrg formalism that approaches "gold standard" coupled cluster accuracy in simulating polyalanine chains in the gas phase. By decomposing polyalanines into chemically intuitive building blocks, we develop modular and transferable potential energy functions that accurately reproduce reference energies, normal-mode harmonic frequencies, and conformational free-energy landscapes. Compared to empirical force fields commonly used in biosimulations, the MB-nrg potential energy function yields a smoother and more physically grounded free-energy surface, captures transient structural motifs under-represented by empirical force fields, and enables flexible sampling of secondary structure transitions in longer peptides. This work establishes a foundation for extending coupled-cluster-level modeling to larger biomolecular systems under physiologically relevant conditions, while highlighting the methodological challenges that remain in achieving consistent accuracy at scale.

Formation of Motivated Adaptive Artificial Intelligence for Digital Generation of Information and Technological Actions

Motivated artificial intelligence plays a relevant role in digital generation of information. Motivated artificial intelligence activates the generation of meanings and technological action. Its motivational functionality and motivation goals are determined by developers and users of technologies, which in turn helps to form AI motivation in the context of digital transformation. Formation of artificial intelligence motivation in digital generation of information is complex and multifaceted task that includes both theoretical and practical aspects of AI motivation in technological thinking and actions. Artificial motivated intelligence must have clearly defined goals that it must achieve. The goal of motivation can be set in the form of functionality (ontology, erudition, reflection, usefulness, preference), which will guide the motivation of AI. The use of reinforcement learning methods will allow AI to independently find optimal strategies for achieving its goals. It receives positive or negative reinforcement depending on how successfully it performs information transformation tasks. To form motivation of AI, it is necessary to ensure its ability to adapt to changing conditions and tasks. This includes learning from new data, knowledge and experiences. In some cases, it is useful to implement elements of emotional intelligence so that AI can better understand and respond to human emotions and actions. This improves the digital generation of information. It is important to consider ethical aspects and security. It is necessary to ensure that the digital generation of information does not lead to undesirable consequences or harm. Artificial intelligence must be able to effectively interact with users and other systems to receive feedback and adjust its actions in accordance with changing conditions. Research and implementation of motivation models, such as the hierarchy of needs or self-determination, can be useful in international digital generation of information. Formation of AI motivation requires an interdisciplinary approach that includes psychology, computer science and ethics. Motivation of AI to advance scientific and technological achievements is relevant in digital generation of information in various fields of activity. The motivation of hybrid intelligent systems is realized on the basis of knowledge engineering through synergetic communication.

On Exact Non-Traveling Wave Solutions to the Generalized Nonlinear Kadomtsev–Petviashvili Equation in Plasma Physics and Fluid Mechanics

The Kadomtsev–Petviashvili (KP) equation serves as a powerful model for investigating various nonlinear wave phenomena in fluid dynamics, plasma physics, optics, and engineering. In this paper, by combining the method of separation of variables with the modified generalized exponential rational function method (mGERFM), abundant explicit exact non-traveling wave solutions for a (3+1)-dimensional generalized form of the equation are constructed. The proposed method utilizes a transformation approach to reduce the original equation to a simpler form. The derived solutions include several arbitrary functions, which enable the construction of a wide variety of exact solutions to the model. These solutions are expressed through diverse functional forms, such as exponential, trigonometric, and Jacobi elliptic functions. To the best of the author’s knowledge, these results are novel and have not been documented in prior studies. This study enhances understanding of wave dynamics in the equation and provides a practical method applicable to other related equations.

Characterizations and In Vitro Gut Microbiome Modulatory Effects of Gluco-Oligosaccharides Synthesized by the Acceptor Reactions of Glucansucrase 53

The production of novel oligosaccharides with potential prebiotic effects is of interest to expand the current market and explore the effectiveness of new functional carbohydrate forms. The utilization of glucansucrases is a cost-effective and environmentally friendly biotechnological strategy for producing novel gluco-oligosaccharides through acceptor reactions. In this study, an active glucansucrase (GS53) was used to produce gluco-oligosaccharides via its acceptor reactions with glucose, maltose, and maltotriose, and these oligosaccharides were tested in terms of structure and their gut microbiome modulatory effects. The formations of oligosaccharides were monitored by TLC analysis, and GS53 was active for the three acceptors but not for the other sugars tested. The structural characterization of the gluco-oligosaccharides by 1H NMR analysis revealed the glycosylation of each acceptor with α-(1 → 3) and α-(1 → 6) linkages, whereas LC-MS analysis demonstrated the formations of DP 8, DP 7, and DP 6 oligosaccharides with acceptors maltose, maltotriose, and glucose, respectively. In vitro fecal fermentation analysis, in which microbial short-chain fatty acids (SCFAs) and microbial compositional changes were assessed using gas chromatography and 16S rRNA sequencing, respectively, demonstrated that the gluco-oligosaccharides formed SCFAs—particularly propionate and butyrate—at levels comparable to those observed with inulin, a well-established prebiotic. Additionally, the gluco-oligosaccharides were found to promote the growth of Bifidobacterium adolescentis and Blautia OTUs, which are known to have important physiological functions beneficial to human health. Overall, these results demonstrate that gluco-oligosaccharides synthesized using GS53 through acceptor reactions exhibit prebiotic potentials and could be utilized in the future as dietary supplements as well as in the development of functional foods targeting colonic health.

Особенности аналитических форм глагола в аспекте эргативности ингушского языка

The aim of the study is to identify the features of the use of analytical verb forms as predicates in ergative, nominative, and affective syntactic constructions in the Ingush language. The article examines various models of constructing these types of sentences from the perspective of the realization of subject-object relations determined by the semantics of the main and auxiliary verbs of the analytical form in the predicative function. The scientific novelty of the research lies in presenting, based on texts of literary works and spoken language in Ingush, the functioning of analytical verb forms serving as complex verbal predicates in ergative, nominative, and affective sentences. As a result of the study, it was established that in the Ingush language, the choice of the auxiliary verb in the analytical form depends on the transitive or intransitive semantics of the main verb, as well as on the case of the subject of the sentence ‒ nominative, affective, or ergative. Different combinations of subject-predicate components actualize meanings of the qualificativity of the agent and the bearer of the action, repetitiveness, distancing and localization, obviousness, and evidentiality of the action.

Parameterization of Surface Layer Processes in Extreme Weather Conditions over Mountainous Region

Abstract A major uncertainty in parameterization of surface-atmosphere turbulent processes in the weather and climate models is due to various empirical functional forms which are utilized for incorporating the near-surface atmospheric stability in the convective conditions. Based on the study of Srivastava et al. (2021), Namdev et al. (2024) have carried out an extensive analysis and argued that functions suggested by Kader and Yaglom (1990) outperforms when utilized in the Weather Research and Forecasting model (WRFv4.2.2) for simulating the fair-weather condition over Indian land surface. In this study, an attempt has been made to evaluate the suitability of the updated surface layer module in the WRFv4.2.2 model over the Indian Himalayan region. For this purpose two extreme weather conditions, the Uttarakhand floods of (a) June 2013, (b) July 2023, and one fair weather conditions of November 2024 are analyzed. The analysis is based on very high-resolution (1 km) WRF model simulations, reanalysis data, observational rainfall data, and high-frequency turbulent data from the micrometeorological tower installed in Ranichauri (30.309°N, 78.408°E), Uttarakhand. The results indicate that the performance of different similarity functions varied across locations, atmospheric conditions, and variables. The similarity functions suggested by Kader and Yaglom (1990) outperformed others for sensible heat and momentum flux under fair weather conditions over Ranichauri, Uttarakhand. Fairall et al. (1996) functions have shown good spatial agreement for SHF, LHF, U10, and T2 in terms of statistical measures, despite some overestimation tendencies. The study recommends steps further to improve the surface-atmosphere turbulent processes over complex environments.

Implicit Function Method for Solving Difference Equations

An alternative new method to solve difference equations is outlined in this work. The method is named as implicit function method. The method relies on implicit functional forms that enable transformation of the difference equation into a more solvable simple form. First order variable coefficient difference equations are treated first. A second order variable coefficient difference equation is solved next. Perturbed first and second order difference equations are solved by the combination of the method and perturbation techniques. Some nonlinear equations are treated finally. Exact and approximate analytical solutions are constructed using the new method. The advantage of the method is that it can be applicable to any type of difference equation. The equations treated may be of arbitrary order, linear, nonlinear, constant coefficient or variable coefficient. The disadvantage of the method is that the transformation of the equation to a simpler form is not straightforward and requires some experience.

Reversible molecular simulation for training classical and machine-learning force fields

The next generation of force fields for molecular dynamics will be developed using a wealth of data. Training systematically with experimental data remains a challenge, however, especially for machine-learning potentials. Differentiable molecular simulation calculates gradients of observables with respect to parameters through molecular dynamics trajectories. Here, we improve this approach by explicitly calculating gradients using a reverse-time simulation with effectively constant memory cost and a computation count similar to the forward simulation. The method is applied to learn all-atom water and gas diffusion models with different functional forms and to train a machine-learning potential for diamond from scratch. Comparison to ensemble reweighting indicates that reversible simulation can provide more accurate gradients and train to match time-dependent observables.

Cleavage of the Meckel-Gruber syndrome protein TMEM67 by ADAMTS9 uncouples Wnt signaling and ciliogenesis

TMEM67 mutations cause Meckel-Gruber syndrome and other related ciliopathies. TMEM67 is involved in both ciliary transition zone assembly, and non-canonical Wnt signaling mediated by its extracellular domain. How TMEM67 performs these two separate functions is not known. We identify a cleavage motif in the extracellular domain of TMEM67 cleaved by the extracellular matrix metalloproteinase ADAMTS9. This cleavage regulates the abundance of two functional forms: a C-terminal portion which localizes to the ciliary transition zone regulating ciliogenesis, and a non-cleaved form which regulates Wnt signaling. By characterizing three TMEM67 ciliopathy patient variants within the cleavage motif utilizing mammalian cell culture and C. elegans, we show the cleavage motif is essential for cilia structure and function, highlighting its clinical significance. We generated a non-cleavable TMEM67 mouse model which develop severe ciliopathies phenocopying Tmem67-/- mice, but in contrast, transduces normal Wnt signaling, substantiating the existence of two functional forms of TMEM67.

RTide: Automating the Tidal Response Method

Abstract Nonstationary tidal processes, such as tidal rivers and storm surge, present challenges for analysis and prediction because their inherent nonstationarity encumbers the use of standard tidal analysis tools like harmonic analysis. Moreover, specialized approaches impose problem‐specific functional forms and rely on auxiliary data, limiting their applicability across different nonstationary tidal processes. Although Munk and Cartwright's tidal response method avoids these assumptions, its lack of automation has hindered broader application. Here, we develop a nonparametric, automated response‐based analysis procedure. Our approach embeds a class of neural networks capable of representing any arbitrary Volterra series—the mathematical basis of the response method—within the classic framework. Our model facilitates the inclusion of meteorological and other non‐tidal forcing. By explicitly accounting for nonstationarity, our method yields improved astronomical tidal estimates. We further devise a strategy to extract physical insights from the learned model, demonstrating its utility in studying the interaction and modulation of astronomical tides by external forcing. By taking a nonparametric approach, our framework enables the investigation of phenomena that heretofore could not be accounted for straightforwardly, as illustrated by several case studies on tide–surge interaction, riverine tides, and storm surge. These applications, and more, can be replicated with just three lines of code using the open‐source Python package, RTide.