Consistent Set Research Articles

A boolean-algebraic approach to completeness for normal modal predicate logics

This paper introduces an innovative methodology for demonstrating completeness for normal modal predicate logics. Traditional proofs typically involve constructing canonical models, wherein possible worlds are defined as maximal consistent sets possessing specific properties, with a heavy reliance on the Barcan Formula to affirm the existence of these worlds. Our approach deviates from the classical method by utilizing Boolean algebras and ultrafilters to construct models. Unlike conventional methods, our construction of possible worlds does not depend on the Barcan Formula; rather, these properties are ensured by Tarski’s Lemma. Furthermore, our proof distinguishes itself from other Boolean-algebraic completeness proofs in two key respects: it employs Kripke semantics instead of algebraic semantics and exclusively relies on ultrafilters, thereby offering a more concise approach. This methodology facilitates a natural extension from modal propositional logic to modal predicate logics and circumvents the added complexity of Q-filters. In our model, the equivalence class of each theorem of a normal modal predicate logic is a member of all worlds, while the equivalence class of each non-theorem is a member of some worlds. Consequently, the structure of these worlds ensures that non-theorems are false in the model.

Solar convective velocities: Updated helioseismic constraints

Modeling heat transport by convection is one of the most challenging aspects of solar and stellar physics. The literature currently provides apparently inconsistent observational estimates of the strength of large-scale convective flows in the upper layers of the solar convection zone. In addition, the large-scale convective flows predicted from numerical simulations are substantially stronger than some of the observational inferences in the literature. The current work aims to provide a consistent presentation of some of the main results in the literature both from observations and simulations. To achieve this aim, we carry out an analysis of published estimates of the strength of solar convection at different spatial scales. In particular, we employ a consistent set of conventions to compute the kinetic energy density in the east-west flows. This establishes a clear baseline for future work. The main conclusion is that there are inconsistencies between different observational results and also differences between observations and simulations. This conclusion is important as it demonstrates a need to determine the sources of the inconsistencies between different observational inferences and also to determine the missing ingredients in simulations of solar subsurface convection.

Inequivalent [formula omitted]-graded brackets, n-bit parastatistics and statistical transmutations of supersymmetric quantum mechanics

Given an associative ring of Z2n-graded operators, the number of inequivalent brackets of Lie-type which are compatible with the grading and satisfy graded Jacobi identities is bn=n+⌊n/2⌋+1. This follows from the Rittenberg-Wyler and Scheunert analysis of “color” Lie (super)algebras which is revisited here in terms of Boolean logic gates.The inequivalent brackets, recovered from Z2n×Z2n→Z2 mappings, are defined by consistent sets of commutators/anticommutators describing particles accommodated into an n-bit parastatistics (ordinary bosons/fermions correspond to 1 bit). Depending on the given graded Lie (super)algebra, its graded sectors can fall into different classes of equivalence expressing different types of particles (bosons, parabosons, fermions, parafermions). As a consequence, the assignment of certain “marked” operators to a given graded sector is a further mechanism to induce inequivalent graded Lie (super)algebras (the basic examples of quaternions, split-quaternions and biquaternions illustrate these features).As a first application we construct Z22 and Z23-graded quantum Hamiltonians which respectively admit b2=4 and b3=5 inequivalent multiparticle quantizations (the inequivalent parastatistics are discriminated by measuring the eigenvalues of certain observables in some given states). The extension to Z2n-graded quantum Hamiltonians for n>3 is immediate.As a main physical application we prove that the N-extended, one-dimensional supersymmetric and superconformal quantum mechanics, for N=1,2,4,8, are respectively described by sN=2,6,10,14 alternative formulations based on the inequivalent graded Lie (super)algebras. The sN numbers correspond to all possible “statistical transmutations” of a given set of supercharges which, for N=1,2,4,8, are accommodated into a Z2n-grading with n=1,2,3,4 (the identification is N=2n−1).In the simplest N=2 setting (the 2-particle sector of the de Alfaro-Fubini-Furlan deformed oscillator with sl(2|1) spectrum-generating superalgebra), the Z22-graded parastatistics imply a degeneration of the energy levels which cannot be reproduced by ordinary bosons/fermions statistics.

Ground and Excited Electronic Structure Analysis of FeH with Correlated Wave Function Theory and Density Functional Approximations.

FeH is one of the most challenging diatomic molecules to study under electronic structure theory. Here, we have successfully studied 22 electronic states of FeH using ab initio multireference configuration interaction (MRCI), Davidson-corrected MRCI (MRCI+Q), and coupled cluster singles, doubles, and perturbative triples [CCSD(T)] levels of theory. We report their potential energy curves (PECs), excitation energies, dissociation energies, equilibrium electronic configurations, and a series of spectroscopic constants with the use of augmented triple-ζ, quadruple-ζ, and quintuple-ζ quality correlation consistent basis sets. The scalar relativistic effects and active space and core electron correlation contribution on the properties of FeH are also explored. The use of a large CASSCF active space that includes 4s, 4p, 3d, and 4d orbitals of Fe and the 1s of H is critical for producing accurate full PECs with proper dissociations and predicting the exact order of the electronic states. Our findings are in harmony with the experimental results available in the literature and will serve as reference values for future studies of FeH. Furthermore, with the use of PECs, the total internal partition function sum (TIPS) of FeH was calculated across a range of temperatures. Finally, we exploited the single-reference nature of the a6Δ of FeH and its ionized product FeH+ (X5Δ) to evaluate the associated density functional theory (DFT) errors on their dissociation energies and spectroscopic parameters.

Giant quadrupole resonances within neutron-induced α-particle emission?

The particular conditions for the recent measurement of 91Zr(n,α)88Sr reaction cross sections at incident energies below 5.3 MeV [Phys. Rev. C 106, 064602 (2022)] as well as a previous detailed analysis of other reaction channels involving neutrons incident on 91Zr, using a consistent set of model parameters, have two main advantages. First, the close agreement between the calculated and experimentally obtained data for the incident energy associated mainly with the ground-state activation provides strong support for the α-particle optical potential involved in this analysis. Second, a further underestimation of the cross section is observed around the energy corresponding to the isoscalar giant quadrupole resonance (ISGQR), beyond any model parameter uncertainty. This underestimation is consistent with previous observations of ISGQR-like α-particle decay of excited nuclei for neutron-induced reactions in the mass range 54≤A≤98. To phenomenologically identify the ISGQR-like behavior, a comparison is made between their strengths and the ISGQR strengths measured through the (γ,α) reaction and inelastic scattering of 3He and α-particles. Additionally, an isotope effect, possibly related to the decrease in Q-value with the target-nuclei asymmetry parameter, supports the observation of a low energy-weighted sum rule (EWSR) fraction for the ISGQR-like strength function in the excited nucleus 92Zr.

Methodology of comparative studies on the relative effectiveness of COVID-19 vaccines: a systematic review

Objectives: This study aimed to comprehensively outline the methodological approaches used in published research comparing the vaccine effectiveness (VE) of coronavirus disease 2019 (COVID-19) vaccines.Methods: A systematic search was conducted on June 13, 2024, to identify comparative studies evaluating the effectiveness of mRNA versus non-mRNA and monovalent versus bivalent COVID-19 vaccines. We screened titles, abstracts, and full texts, collecting data on publication year, country, sample size, study population composition, study design, VE estimates, outcomes, and covariates. Studies that reported relative VE (rVE) were analyzed separately from those that did not.Results: We identified 25 articles comparing rVE between mRNA and non-mRNA COVID-19 vaccines, as well as between monovalent and bivalent formulations. Among the studies assessing VE by vaccine type, 126 did not provide rVE estimates. Comparative VE studies frequently employed retrospective cohort designs. Among the definitions of rVE used, the most common were hazard ratio and absolute VE, calculated as (1−odds ratio)×100. Studies were most frequently conducted in the United Kingdom and the United States, and the most common outcome was infection. Most targeted the general population and assessed the VE of mRNA vaccines using the AstraZeneca vaccine as a reference. A small proportion, 7.3% (n=11), did not adjust for any variables. Only 3 studies (2.0%) adjusted for all core confounding variables recommended by the World Health Organization.Conclusion: Few comparative studies of COVID-19 vaccines have incorporated rVE methodologies. Reporting rVE and employing a consistent set of covariates can broaden our understanding of COVID-19 vaccines.

The Flu-ID: A New Evidence-Based Method of Assessing Fluency in Aphasia.

Assessing fluency in aphasia is diagnostically important for determining aphasia type and severity and therapeutically important for determining appropriate treatment targets. However, wide variability in the measures and criteria used to assess fluency, as revealed by a recent survey of clinicians (Gordon & Clough, 2022), results in poor reliability. Furthermore, poor specificity in many fluency measures makes it difficult to identify the underlying impairments. Here, we introduce the Flu-ID Aphasia, an evidence-based tool that provides a more informative method of assessing fluency by capturing the range of behaviors that can affect the flow of speech in aphasia. The development of the Flu-ID was based on prior evidence about factors underlying fluency (Clough & Gordon, 2020; Gordon & Clough, 2020) and clinical perceptions about the measurement of fluency (Gordon & Clough, 2022). Clinical utility is maximized by automated counting of fluency behaviors in an Excel template. Reliability is maximized by outlining thorough guidelines for transcription and coding. Eighteen narrative samples representing a range of fluency were coded independently by the authors to examine the Flu-ID's utility, reliability, and validity. Overall reliability was very good, with point-to-point agreement of 86% between coders. Ten of the 12 dimensions showed good to excellent reliability. Validity analyses indicated that Flu-ID scores were similar to clinician ratings on some dimensions, but differed on others. Possible reasons and implications of the discrepancies are discussed, along with opportunities for improvement. The Flu-ID assesses fluency in aphasia using a consistent and comprehensive set of measures and semi-automated procedures to generate individual fluency profiles. The profiles generated in the current study illustrate how similar ratings of fluency can arise from different underlying impairments. Supplemental materials include an analysis template, extensive guidelines for transcription and coding, a completed sample, and a quick reference guide. https://doi.org/10.23641/asha.27078199.

Comparative analysis of quantum two-way time transfer and quantum round-trip time transfer in consistent spatiotemporal settings

In this study, we conducted experiments using a single energy-time entangled biphoton source to compare the performance of quantum two-way time transfer (Q-TWTT) and quantum round-trip time transfer (Q-RTTT) under consistent spatiotemporal conditions. By conducting experiments with different fiber links of 11.3 km, 22.4 km, and 55.6 km, while ensuring uniform photon counts received by the single-photon detectors, we measured standard deviations (SDs) and stabilities of the time offsets. The measured SDs for Q-TWTT and Q-RTTT were 0.46 ps and 0.65 ps over the 11.3 km fiber, 1.14 ps and 1.3 ps over the 22.4 km fiber, 3.98 ps and 4.39 ps over the 55.6 km fiber, respectively. These results show good agreement with theoretical predictions, and the smaller SDs for Q-TWTT can be directly attributed to protocol-specific factors related to system symmetry. The long-term time stabilities of Q-TWTT and Q-RTTT were evaluated in terms of time deviation (TDEV). At an average time of 12680 s, the measured TDEVs were 0.49 ps and 0.63 ps for the 11.3 km fiber, 0.59 ps and 0.7 ps for the 22.4 km fiber, 1.01 ps and 1.36 ps for the 55.6 km fiber, respectively. The results validate that Q-TWTT exhibits superior time transfer performance compared to Q-RTTT, highlighting the advantages of Q-TWTT in practical applications.

The Role of Nudges and Behavioral Interventions in Financial Decision Making

Financial decision-making, both at individual and institutional levels, plays a critical role in determining economic outcomes. Traditional economic theory posits that individuals are rational agents who make decisions based on complete information and a consistent set of preferences. However, behavioral economics has challenged this notion, highlighting cognitive biases, heuristics, and social influences that can drive suboptimal decisions. Nudges and behavioral interventions have emerged as tools to guide individuals toward better financial choices without restricting their freedom of choice. The purpose of this research is to present a descriptive investigation of behavioral interventions and nudges in financial decision-making. The main cognitive biases influencing financial behavior are first described, and then several nudge kinds and their applicability in diverse financial contexts— retirement savings, debt management, spending control, and investment decisions—are explored. Along with reviewing empirical data on nudges' efficacy, the paper addresses the ethical issues surrounding their application and pinpoints the variables that affect their effectiveness. This study aims to educate consumers, financial institutions, and policymakers about the potential advantages and constraints of behavioral interventions by providing a thorough overview of how nudges might impact financial decision-making. Keywords: Nudges, Behavioral Intervention, Financial Decision-Making, Cognitive Biases, Financial Literacy.

Single unit electrophysiology recordings and computational modeling can predict octopus arm movement.

The octopus simplified nervous system holds the potential to reveal principles of motor circuits and improve brain-machine interface devices through computational modeling with machine learning and statistical analysis. Here, an array of carbon electrodes providing single-unit electrophysiology recordings were implanted into the octopus anterior nerve cord. The number of spikes and arm movements in response to stimulation at different locations along the arm were recorded. We observed that the number of spikes occurring within the first 100ms after stimulation were predictive of the resultant movement response. Computational models showed that temporal electrophysiological features could be used to predict whether an arm movement occurred with 88.64% confidence, and if it was a lateral arm movement or a grasping motion with 75.45% confidence. Both supervised and unsupervised methods were applied to gain streaming measurements of octopus arm movements and how their motor circuitry produces rich movement types in real time. Deep learning models and unsupervised dimension reduction identified a consistent set of features that could be used to distinguish different types of arm movements. These models generated predictions for how to evoke a particular, complex movement in an orchestrated sequence for an individual motor circuit.

Storm surge modelling along European coastlines: The effect of the spatio-temporal resolution of the atmospheric forcing

The spatio-temporal resolution of atmospheric forcing plays a key role in the accuracy of simulated storm surges with hydrodynamic numerical models. Here, we generate five hydrodynamic hindcasts of coastal storm surges along the European Atlantic and the Mediterranean Sea coasts, forced with atmospheric fields of varying temporal (hourly and daily) and spatial (0.25° to 2°) resolution since 1940. Our results, that are validated with insitu tide gauge observations, show that storm surges obtained with daily forcing underestimate the magnitude of coastal extreme sea level events by up to 50% compared to hourly simulations and observations. Nevertheless, low-resolution simulations capture the temporal variability of storm surges, including strong episodes. Furthermore, taking advantage of the consistent set of coastal storm surge hindcasts, we demonstrate that storm surges forced with daily mean atmospheric fields, when bias corrected via quantile mapping, provide accurate values of daily maxima as calculated by a high-resolution hindcast. This transformation paves the way to obtain daily maxima storm surge estimates from low-resolution atmospheric fields, as those typically provided by large-scale and global climate models, at a lower computational cost.

Evaluation of an Optimal Method for Ordering Hierarchical Matchkeys in Data Linkage at the Office for National Statistics

The quality of linkage techniques has a direct impact on the quality of statistics produced on the linked data, and as such, ensuring linkage algorithms are of the highest quality is a vital mission of the Office for National Statistics (ONS). Deterministic hierarchical matchkeys are a linkage technique that applies a list of conditions to classify links, where records can only be linked once. The aim of the hierarchy is to classify correct links by running higher precision matchkeys first, removing linked records from the matching pool, and then running lower quality keys so that they are less likely to make incorrect links. Currently, no optimal method for ordering match-keys exists. Here we present novel research on a generalisable algorithmic approach to finding optimal matchkey orderings. A deterministic loop over a consistent set of matchkeys was used to link ONS’s 2021 Census to the 2021 Census Coverage Survey (CCS). A range of experimental ordering methods were implemented. Gold standard linked data was used for quality determination to produce metrics such as precision and recall for grading and comparing the experimental ordering methods. The required expertise of the user and computational efficiency were considered when comparing and recommending ordering methods. Removing historically subjective matchkey ordering methods and replacing with a deterministic ordering algorithm, can lead to better data linkage outcomes with reductions in linkage error. This can provide greater confidence to users of official statistics that linked data underpinning them are more reliable, trustworthy, and meaningful.

Water Dynamics in Fish Collagen Gels-Insight from NMR Relaxometry.

1H spin-lattice relaxation experiments have been performed for gels based on fish collagen in order to analyze water dynamics. The covered frequency range ranges from 10 kHz to 10 MHz; in some cases, the temperature has varied as well. The relaxation data have been reproduced in terms of two models of water motion-a model including two relaxation contributions associated with the diffusion of water molecules on the macromolecular surfaces and a second model being just a phenomenological power law. The concept of surface diffusion has led to a very good agreement with the experimental data and a consistent set of parameters, with the diffusion coefficients being about five orders of magnitude slower compared to bulk water for one of the pools and considerably faster for the second one (smaller by factors between 2 and 20 compared to bulk water). In some cases, the attempt to reproduce the data in terms of a power law has led to a good agreement with the experimental data (the power law factor varying between 0.41 and 0.57); however, in other cases, the discrepancies are significant. This outcome favors the concept of surface diffusion.

Synthesis, Antimicrobial, DNA Interactions, In Vitro Cytotoxicity, and Cell Cycle Analysis Efficiency of Newly Nano‐Sized Cu (II), Ni (II), Co (II), and Zn (II) Thio‐Schiff Base Complexes of 2‐((E)‐((4,5‐Dimethyl‐2‐(((E)‐4‐Methylbenzylidene)Amino)Phenyl)imino)Methyl)‐Benzenethiol

ABSTRACTNano‐sized bivalent metal complexes, specifically [M(L)2] with L = 2‐((E)‐((4,5‐dimethyl‐2‐(((E)‐4‐methylbenzylidene)amino)phenyl)‐imino)methyl)benzenethiol] (C23H22N2S) and M = Cu (II) (C1), Co (II) (C2), Ni (II) (C3), and Zn (II) (C4), underwent synthesis and subsequent characterization. Elemental analyses, infrared, NMR, mass, electronic, magnetic susceptibility, conductivity assessments, and X‐ray diffraction studies were used to assess our bivalent metal complexes. DFT studies were used to study the tautomeric equilibrium of the tridentate thio‐Schiff base ligand (HL), via the DFT\B3LYP method in connection with a 6–311G* correlation consistent basis set. Two tautomers, which are thione and thiol forms, were studied to estimate the predominant one. The metal formed four coordinated with the tridentate N2S donor thio‐Schiff base to form octahedral geometry complexes. The SEM, TEM, XRD, AFM, and EDX of the studied complexes unveiled distinct and strong diffraction peaks, signifying their crystalline nature and providing evidence of their particle sizes being within the nano‐size. The crystal sizes calculated for all complexes were determined to be ranging from 27.73 to 76.39 nm. The interactions between metal complexes and calf thymus DNA, and their potential for mimicking insulin activity, were investigated in a controlled lab setting by measuring their ability to inhibit alpha‐amylase. The antimicrobial potential of thio‐Schiff base ligand (HL) plus complexes (C1–C4) were tested. The viscosity and UV–Vis absorption determinations were utilized to assess the calf thymus DNA (CT‐DNA) interaction with the nano‐sized metal (II) chelates. Our flow cytometry data indicate significant levels of apoptosis and cell cycle arresting in both liver and breast cancer cell lines.

Anomaly Detection for Power Quality Analysis Using Smart Metering Systems.

The problem of Power Quality analysis is becoming crucial to ensuring the proper functioning of complex systems and big plants. In this regard, it is essential to rapidly detect anomalies in voltage and current signals to ensure a prompt response and maximize the system's availability with the minimum maintenance cost. In this paper, anomaly detection algorithms based on machine learning, such as One Class Support Vector Machine (OCSVM), Isolation Forest (IF), and Angle-Based Outlier Detection (ABOD), are used as a first tool for rapid and effective clustering of the measured voltage and current signals directly on-line on the sensing unit. If the proposed anomaly detection algorithm detects an anomaly, further investigations using suitable classification algorithms are required. The main advantage of the proposed solution is the ability to rapidly and efficiently detect different types of anomalies with low computational complexity, allowing the implementation of the algorithm directly on the sensor node used for signal acquisition. A suitable experimental platform has been established to evaluate the advantages of the proposed method. All the different models were tested using a consistent set of hyperparameters and an output dataset generated from the principal component analysis technique. The best results achieved included models reaching 100% recall and a 92% F1 score.

Green Web Meter: Structuring and Implementing a Real-Time Digital Sustainability Monitoring System

The central aim of this paper is to present the Green Web Meter software, which is designed to support the measurement of the digital ESG performance of websites and web apps, as well as providing sound-based analytic tools for improving their overall quality. In this work, we will discuss the process our research team adhered to in order to provide a basic structure to the general framework of our tool, select a consistent set of KPIs that are suitable for automated real-time tracking, and determine the proper calculation methods to compute the final scores on which the ESG assessment is based. Specifically, we began from the analysis of the UNI PdR 147 guidelines on digital sustainability, highlighting the relevance of the quality construct, and subsequently selected three quality assessment models (E-S Qual, Sitequal, and Webqual 4.0) to define the core references to structure the basic framework. Starting from this general perspective, we proceeded to define the eight related KPIs and the individual scores based on the automatic calculations.

Development of a signs and symptoms outcome measure for caregivers of patients with methylmalonic acidemia and propionic acidemia (MMAPAQ)

Background and objectiveMethylmalonic acidemia (MMA) and propionic acidemia (PA) are rare inborn errors of metabolism with shared signs and symptoms that are associated with significant morbidity and mortality. No disease-specific clinical outcomes assessment instruments for MMA and/or PA currently exist to capture the patient perspective in clinical trials. Because patients with these conditions are generally young and have cognitive impairments, an observer-reported outcome (ObsRO) instrument is crucial. We report results from qualitative research supporting development of the Methylmalonic Acidemia and Propionic Acidemia Questionnaire (MMAPAQ), a signs and symptoms ObsRO measure for caregivers of patients with MMA and/or PA. MethodsConcept elicitation (CE) interviews were conducted with 35 participants across 2 studies who were aged ≥18 years and caregivers of patients with a confirmed diagnosis of MMA or PA, and an additional 5 patients aged ≥6 years with MMA or PA in Study 1, to identify core signs/symptoms for inclusion in the MMAPAQ. All interviews were conducted in English. Study 2 included cognitive interviews (CI) with caregivers and clinical experts to further assess content validity. CE and a conceptual framework review were also conducted with clinical experts to further support findings. ResultsA consistent set of signs/symptoms of MMA and PA were reported by eligible caregivers interviewed in study 1 (n = 21) and study 2 (n = 14), representing 11 patients with MMA and 20 with PA. Based on concepts reported in study 1, a draft instrument was constructed and compared with the Pediatric Quality of Life Inventory™ (PedsQL™) and Family Impact module, demonstrating face validity for measuring key signs/symptoms important to patients and caregivers. The PedsQL™ and Family Impact modules were preferred to assess patient and caregiver impacts. Two waves of CE and CIs were conducted in study 2, with wave 1 resulting in removal of 7 items and other revisions to improve clarity, and wave 2 resulting in modification of examples used for 2 items. The final instrument consisted of the following 7 items assessed over the past 7 days using a Likert-type response scale ranging from “never” to “very often”: uncontrollable or involuntary movements, dehydration, rapid breathing at rest, appearing lethargic, appearing disinterested in eating, refusing to eat, and vomiting. ConclusionsThis study establishes the content validity of the MMAPAQ as the first ObsRO questionnaire for measuring core signs and symptoms of MMA and PA in clinical trials and community research. Scoring and psychometric measurement properties of the MMAPAQ will be established in future studies. The PedsQL™ was found to have face validity in measuring concepts that affect the MMA and PA patient populations and should also be considered for use in clinical trials in MMA and PA.

In need of improvement: archaeological evidence of river management in South-Eastern Australia

AbstractPatterns of river modification since settler invasion of southern Australia are the product of a specific set of deep-seated and implicit cultural values concerning the purpose and function of waterways. Rivers have been dammed, diverted, dredged and straightened to meet a range of human needs and objectives. Such changes are routinely described as ‘improvements’ but there is a lack of critical engagement with what ‘improvement’ might mean. Interventions carried out initially on an ad hoc basis, and later more systematically with state support, collectively shed light on the persistent underlying drive to ‘Improve’ nature and society that has permeated Western thought since the Enlightenment. Here we use the example of one river system, the Loddon, to analyse ways in which Improvement intersected with settler engagement with Australian rivers. We argue that settler interventions have been informed by a consistent set of understandings about the purpose of rivers. The characteristics of water management infrastructure along the Loddon reveal how the river fell short of the settler-colonial ideal and why they thought it needed to be Improved at all.

Delocalization-ratio analysis of 3-center bonding in position-space for closo-boranes and related systems: Approaching the styx picture and beyond.

Closo-boron hydrides BnHn 2- (n = 5-12) are a conceptually well understood class of compounds. For these and a few related prototype compounds, both the local and the global picture of 3-center bonding are extracted from position-space quantities based on the electron density and the pair density. For this purpose, three-center delocalization indices between quantum theory of atoms in molecules (QTAIM) atoms in position space are used to develop a consistent set of local bond and triangle, and global cluster delocalization ratios (DRs), which are quantitatively compared with conceptual Γ values derived from the styx code for each cluster. Combination of the cluster DRs with associated effective numbers of skeletal electron sharing (SES) for selected cluster surface edges, triangles, or the whole cluster yields effective styx type values describing the trend and even the size of the conceptual styx codes for closo-boranes BnHn 2- and related systems with increasing cluster size n reasonably well. For nonuniform cluster topologies, the different vertex degrees are shown to cause systematic 3-center wise bond delocalization effects for the associated edges and triangles of different average vertex degrees. Extension of DR analysis beyond the styx type triangular cluster-surface bonding corresponds to a triangulation of multicentric bonding. The cluster-wise results keep indicating consistency with the mixed 2- and 3-center bonding approach. The successfully established chemical meaning of the local edge, triangle, and global cluster DRs and their associated SES values constitutes the basis for systematic investigations of mixed 2- and 3-center bonding scenarios in particular in intermetallic and related (endohedral) cluster compounds in the future.

Spatial Predictive Modeling of Liver Fluke Opisthorchis viverrine (OV) Infection under the Mathematical Models in Hexagonal Symmetrical Shapes Using Machine Learning-Based Forest Classification Regression

Infection with liver flukes (Opisthorchis viverrini) is partly due to their ability to thrive in habitats in sub-basin areas, causing the intermediate host to remain in the watershed system throughout the year. Spatial modeling is used to predict water source infections, which involves designing appropriate area units with hexagonal grids. This allows for the creation of a set of independent variables, which are then covered using machine learning techniques such as forest-based classification regression methods. The independent variable set was obtained from the local public health agency and used to establish a relationship with a mathematical model. The ordinary least (OLS) model approach was used to screen the variables, and the most consistent set was selected to create a new set of variables using the principal of component analysis (PCA) method. The results showed that the forest classification and regression (FCR) model was able to accurately predict the infection rates, with the PCA factor yielding a reliability value of 0.915. This was followed by values of 0.794, 0.741, and 0.632, respectively. This article provides detailed information on the factors related to water body infection, including the length and density of water flow lines in hexagonal form, and traces the depth of each process.