Relative Version Research Articles

Satiation-Based Theory of Frugal Materialism

Frugal materialism is a tendency of consumer demand to become more elastic in product durability in response to a tightening budget constraint. This paper proposes a value function-based model of frugal materialism and establishes a close theoretical link between frugal materialism and the slope of value satiation as defined in the decision analytic literature; for both their absolute and relative versions, frugal materialism and increasing value satiation are nearly equivalent to each other. Only some shapes of the value function are thus compatible with frugal materialism, and the shape restrictions involve concepts familiar from models of decision making under risk, even though the proposed model of frugal materialism does not involve any risk. Under the additional assumption of relative risk neutrality, the demand for risky assets of a frugally materialistic consumer should exhibit well-known behavioral patterns associated with increasing risk aversion, and there is only a narrow possibility for frugal materialism to coexist with precautionary saving behavior.

Identifiability analysis of the fixed‐effects one‐parameter logistic positive exponent model

AbstractIn addition to the usual slope and location parameters included in a regular two‐parameter logistic model (2PL), the logistic positive exponent (LPE) model incorporates an item parameter that leads to asymmetric item characteristic curves, which have recently been shown to be useful in some contexts. Although this model has been used in some empirical studies, an identifiability analysis (i.e., checking the (un)identified status of a model and searching for identifiablity restrictions to make an unidentified model identified) has not yet been established. In this paper, we formalize the unidentified status of a large class of fixed‐effects item response theory models that includes the LPE model and related versions of it. In addition, we conduct an identifiability analysis of a particular version of the LPE model that is based on the fixed‐effects one‐parameter logistic model (1PL), which we call the 1PL‐LPE model. The main result indicates that the 1PL‐LPE model is not identifiable. Ways to make the 1PL‐LPE useful in practice and how different strategies for identifiability analyses may affect other versions of the model are also discussed.

A novel classification of dyslipidaemia through the analysis of five million lipid profiles: an unsupervised machine learning approach

Abstract Background Dyslipidemia encompasses a wide range of lipoprotein disorders categorised through two classifications (Fredrickson-Levy [FL] or Sniderman).(1,2) However, both classifications are criticised for relying on incomplete knowledge of lipoprotein metabolism, especially with the emergence of novel treatment options and variations in individual treatment responses.(3) Clustering, an unsupervised machine learning (ML) algorithm that can process a wide range of variables, has the potential to unmask patient groups with distinct molecular profiles and unique therapeutic targets that can inform more effective prevention strategies for cardiovascular disease (CVD).(4) Aim We aimed to use unsupervised ML algorithms to discover intrinsic dyslipidaemia categories from lipoprotein measurements, recognise the necessary components of lipid panels for classification, and analyse the similarities between the newly formed clusters, FL and Sniderman classifications. Methods Lipid profiles of 5,080,248 patients were obtained from the ‘Very Large Database of Lipids’ database. This yielded up to 78 blood components per patient, including at least 31 lipoprotein variables. The analysis involved unsupervised K-means clustering with optimised values for K and the subset of variables, determined in an unsupervised manner using a suitable measure of complexity. We then interpreted our clusters using probabilistic decision trees to provide compact and interpretable representations. Finally, we compared the clusters with Sniderman and FL categories. Results In a completely unsupervised fashion, we identified 14 clusters that could be matched to Sniderman categories. The confusion matrix showed total agreement of 76% (see Figure 1, left panel), relative Cohen’s kappa of 0.78 (the relative version captures accuracy on categories containing smaller numbers of patient profiles) and an accuracy of 96% on the small Type III class. Similar results were observed when matching to FL types. We accurately represented our clusters using probabilistic decision trees of small depth (see Figure 2). We discovered that the data had low intrinsic dimension and a manifold-like structure in which the different clusters could be illustrated (see Figure 1, right panel). Specifically, only 3 variables were needed to obtain our classification: apolipoprotein b, total cholesterol and triglycerides. Conclusion We showed that completely unsupervised ML techniques can uncover dyslipidaemia categories in lipoprotein profiles from a large patient population. The categories largely align with existing classifications based on prior knowledge of lipoprotein metabolism. Furthermore, few lipoprotein variables were required for categorisation (low-dimension data), which could aid in determining which lipoproteins should be measured in a clinical setting. Further analysis of the differences between ML clusters and traditional classifications is needed, which may enhance CVD risk management.

Intra-ethnic divisions and disagreement over self-determination demands in ethnic movements

Abstract Ethnic movements continue to challenge state governments globally, with many ethnic conflicts revolving around the status of groups’ territories. Yet, politically mobilized ethnic groups vary considerably in their territorial demands: some press for increased autonomy or even outright secession, while others do not make such demands at all and prefer integration in the existing state. What explains this divergence in ethnic group demands with respect to the group's territorial status? We argue that the expected benefits of ethno-regional autonomy or secession compared to integration in a centralized state differ across distinct segments within the group as a function of three structural factors: heterogeneity in the group's income sources, cultural divisions, and territorial fragmentation, leading to disagreement over self-determination demands between different political organizations representing the same ethnic group. We test our argument using an expanded version of the Ethnic Power Relations–Organizations (EPR-O) dataset. Our pre-registered study finds support for one of our hypotheses: heterogeneity in groups’ income sources increases disagreement over self-determination demands. This finding sheds new light on the structural sources of internal divisions within ethno-political movements.

Investigating the impact of dietary guidelines transition on cardiometabolic risk profile: a forensic analysis using diet quality metrics

Evaluating dietary guidelines using diet quality (DQ) offers valuable insights into the healthfulness of a population’s diet. We conducted a forensic analysis using DQ metrics to compare the Malaysian Dietary Guidelines (MDG-2020) with its former version (MDG-2010) in relation to cardiometabolic risk (CMR) for an adult Malaysian population. A DQ analysis of cross-sectional data from the Malaysia Lipid Study (MLS) cohort (n = 577, age: 20-65yrs) was performed using the healthy eating index-2015 (HEI-2015) framework in conformation with MDG-2020 (MHEI2020) and MDG-2010 (MHEI2010). Of 13 dietary components, recommended servings for whole grain, refined grain, beans and legumes, total protein, and dairy differed between MDGs. DQ score associations with CMR, dietary patterns and sociodemographic factors were examined. Out of 100, total DQ scores of MLS participants were ‘poor’ for both MHEI2020 (37.1 ± 10.3) and MHEI2010 (39.1 ± 10.4), especially among young adults, males, Malays, and those frequently ‘eating out’ as well as those with greatest adherence to Sugar-Sweetened Beverages pattern and lowest adherence to Food Plant pattern. Both metrics shared similar correlations with CMR markers, with MHEI2020 exhibiting stronger correlations with WC, BF%, TG, insulin, HOMA2-IR, and smallLDL than MHEI2010, primarily attributed to reduced refined grain serving. Notably, participants with the highest adherence to MHEI2020 scores exhibited significantly reduced odds for elevated TG (AOR 0.44, 95% CI 0.21–0.93, p = 0.030), HOMA2-IR (AOR 0.44, 95% CI 0.21–0.88, p = 0.022), and hsCRP (AOR 0.54, 95% CI 0.31–0.96, p = 0.040, compared to those with the lowest adherence. Each 5-unit increase in MHEI2020 scores reduced odds for elevated BMI (− 14%), WC (− 9%), LDL-C (− 32%), TG (− 15%), HOMA2-IR (− 9%) and hsCRP (− 12%). While MHEI2020 scores demonstrated better calibration with CMR indicators, the overall sub-optimally ‘poor’ DQ scores of this population call for health promotion activities to target the public to achieve adequate intake of healthful fruits, non-starchy vegetables and whole grain, and moderate intake of refinedgrain, added sugar and saturated fat.

Bavard duality for the relative Gromov seminorm

The relative Gromov seminorm is a finer invariant than stable commutator length where a relative homology class is fixed. We show a duality result between bounded cohomology and the relative Gromov seminorm, analogously to Bavard duality for scl. We give an application to computations of scl in graphs of groups. We also explain how our duality result can be given a purely algebraic interpretation via a relative version of the Hopf formula. Moreover, we show that this leads to a natural generalisation of a result of Calegari on a connection between scl and the rotation quasimorphism.

On certain star versions of the Hurewicz property using ideals

Abstract This article is a continuation of the study of star-𝓘-Hurewicz and strongly star-𝓘-Hurewicz properties done in [Das et al.:On certain variations of 𝓘-Hurewicz property, Topology Appl. 251 (2018), 363–376]. We primarily consider and study the relative versions of star-𝓘-Hurewicz and strongly star-𝓘-Hurewicz properties. We study their relationships with the star-Hurewicz, strongly star-Hurewicz, star-𝓘-Hurewicz, strongly star-𝓘-Hurewicz and similar other properties. Few related games are also studied.

Relative versions of star-Menger property

Abstract Motivated by Bonanzinga and Maesano (2022), we introduce and study the new relative versions of star-Menger property related to some properties studied lately by Kočinac et al. (2022) and Bonanzinga et al. (2023). In this paper, we provide some examples to understand their relationships with other relativizations of star selection principles. Further, we investigate the behaviour of these spaces under various mappings.

Unstability problem of real analytic maps

AbstractAs well known, the stability of proper maps is characterized by the infinitesimal stability. In the present paper, we study the counterpart in real analytic context. In particular, we show that the infinitesimal stability does not imply stability; for instance, a Whitney umbrella is not stable. A main tool for the proof is a relative version of Whitney's analytic approximation theorem that is shown by using H. Cartan's Theorems A and B.

On the Choice of Variable for Quantization of Conformal GR

The possibility of using spin connection components as basic quantization variables of a conformal version of general relativity is studied. The considered model contains gravitational degrees of freedom and a scalar dilaton field. The standard tetrad formalism is applied. Properties of spin connections in this model are analyzed. Secondary quantization of the chosen variables is performed. The gravitational part of the model action turns out to be quadratic with respect to the spin connections. So at the quantum level, the model looks trivial, i.e., without quantum self-interactions. Meanwhile the correspondence to general relativity is preserved at the classical level.

Isolated auto-citrullinated regions of PADI4 associate to the intact protein without altering their disordered conformation

PADI4 is one of the human isoforms of a group of enzymes intervening in the conversion of arginine to citrulline. It is involved in the development of several types of tumors, as well as other immunological illnesses, such as psoriasis, multiple sclerosis, or rheumatoid arthritis. PADI4 auto-citrullinates in several regions of its sequence, namely in correspondence of residues Arg205, Arg212, Arg218, and Arg383. We wanted to study whether the citrullinated moiety affects the conformation of nearby regions and its binding to intact PADI4. We designed two series of synthetic peptides comprising either the wild-type or the relative citrullinated versions of such regions – i.e., a first series of peptides comprising the first three arginines, and a second series comprising Arg383. We studied their conformational properties in isolation by using fluorescence, far-ultraviolet (UV) circular dichroism (CD), and 2D1H NMR. Furthermore, we characterized the binding of the wild-type and citrullinated peptides in the two series to the intact PADI4, by using isothermal titration calorimetry (ITC), fluorescence, and biolayer interferometry (BLI), as well as by molecular docking simulations. We observed that citrullination did not alter the local conformational propensities of the isolated peptides. Nevertheless, for all the peptides in the two series, citrullination slowed down the kinetic koff rates of the binding reaction to PADI4, probably due to differences in electrostatic effects compared to the presence of arginine. The affinities of PADI4 for unmodified peptides were slightly larger than those of the corresponding citrullinated ones in the two series, but they were all within the same range, indicating that there were no relevant variations in the thermodynamics of binding due to sequence effects. These results highlight details of the self-citrullination of PADI4 and, more generally, of possible auto-catalytic mechanisms taking place in vivo for other citrullinating enzymes or, alternatively, in proteins undergoing citrullination passively.

A Fourier transform for Banach–Colmez spaces

We define and study an \ell -adic Fourier transform for a relative version of Banach–Colmez spaces (over a perfectoid space which is not necessarily a geometric point), which can be thought of as some analytic analogue of the \ell -adic Fourier transform for unipotent perfect group schemes. We explicitly describe it on some examples.

Covering-Based Intuitionistic Hesitant Fuzzy Rough Set Models and Their Application to Decision-Making Problems

In this paper, we present four categories of covering-based intuitionistic hesitant fuzzy rough set (CIHFRS) models using intuitionistic hesitant fuzzy β-neighborhoods (IHF β-neighborhoods) and intuitionistic hesitant fuzzy complementary β-neighborhoods (IHFC β-neighborhoods. Through theoretical analysis of covering-based IHFRS models, we propose the intuitionistic hesitant fuzzy TOPSIS (IHF-TOPSIS) technique for order of preference by similarity to an ideal solution, addressing multicriteria decision-making (MCDM) challenges concerning the assessment of IHF data. A compelling example aptly showcases the suggested approach. Furthermore, we address MCDM problems regarding the assessment of IHF information based on CIHFRS models. Through comparison and analysis, it is evident that addressing MCDM problems by assessing IHF data using CIHFRS models proves more effective than utilizing intuitionistic fuzzy data with CIFRS models or hesitant fuzzy information with CHFRS models. IHFS emerges as a unique and superior tool for addressing real-world challenges. Additionally, covering-based rough sets (CRSs) have been successfully applied to decision problems due to their robust capability in handling unclear data. In this study, by combining CRSs with IHFS, four classes of CIFRS versions are established using IHF β-neighborhoods and IHFC β-neighborhoods. A corresponding approximation axiomatic system is developed for each. The roughness and precision degrees of CBIHFRS models are specifically talked about. The relationship among these four types of IHFRS versions and existing related versions is presented based on theoretical investigations. A method for MCDM problems through IHF information, namely, IHF-TOPSIS, is introduced to further demonstrate its effectiveness and applicability. By conducting a comparative study, the effectiveness of the suggested approach is evaluated.

Thin links and Conway spheres

When restricted to alternating links, both Heegaard Floer and Khovanov homology concentrate along a single diagonal $\delta$ -grading. This leads to the broader class of thin links that one would like to characterize without reference to the invariant in question. We provide a relative version of thinness for tangles and use this to characterize thinness via tangle decompositions along Conway spheres. These results bear a strong resemblance to the L-space gluing theorem for three-manifolds with torus boundary. Our results are based on certain immersed curve invariants for Conway tangles, namely the Heegaard Floer invariant $\operatorname {HFT}$ and the Khovanov invariant $\widetilde {\operatorname {Kh}}$ that were developed by the authors in previous works.

Deformations and cohomology theory of Ω-Rota-Baxter algebras of arbitrary weight

In this paper, we introduce the concepts of relative and absolute Ω-Rota-Baxter algebras of weight λ, which can be considered as a family algebraic generalization of relative and absolute Rota-Baxter algebras of weight λ. We study the deformations of relative and absolute Ω-Rota-Baxter algebras of arbitrary weight. Explicitly, we construct an L∞[1]-algebra via the method of higher derived brackets, whose Maurer-Cartan elements correspond to relative Ω-Rota-Baxter algebra structures of weight λ. For a relative Ω-Rota-Baxter algebra of weight λ, the corresponding twisted L∞[1]-algebra controls its deformations, which leads to the cohomology theory of it, and this cohomology theory can interpret the formal deformations of the relative Ω-Rota-Baxter algebra. Moreover, we also obtain the corresponding results for absolute Ω-Rota-Baxter algebras of weight λ from the relative version.

Comparing finite viscoelastic constitutive relations and variational principles in modeling gastrointestinal soft tissue deformation

The mechanical attributes of soft tissues within the gastrointestinal (GI) tract are crucial for the effective operation of the GI system, and alterations in these properties may play a role in motility-related disorders. Various constitutive modeling approaches have been suggested to comprehend the response of soft tissues to diverse loading conditions. Among these, hyperelastic constitutive models based on finite elasticity have gained popularity. However, these models fall short in capturing rate- and time-dependent tissue properties. In contrast, finite viscoelastic models offer a solution to overcome these limitations. Nevertheless, the development of a suitable finite viscoelastic model, coupled with a variational formulation for efficient finite element (FE) implementation, remains an ongoing challenge. This study aims to address this gap by developing diverse finite viscoelastic constitutive relations and applying them to characterize soft tissue. Furthermore, the research explores the creation of compressible, nearly incompressible, and incompressible versions of viscoelastic constitutive relations, along with their variational formulation, to facilitate efficient FE implementation. The proposed model demonstrates remarkable accuracy in replicating experimental results, achieving an R2 value exceeding 0.99.

Experimental and theoretical study on high-temperature creep of VT6 titanium alloy under multi-axial loading conditions

In the framework of damage mechanics, we discuss a new mathematical model that describes the kinetics of the stress–strain state and damage accumulation during material degradation by the mechanism of long-term strength under complex multiaxial stress state. An experimental and theoretical technique is proposed for determination of material parameters and scalar constitutive functions for damaged media based on specially set experiments on laboratory specimens. The results of experimental studies and numerical simulations of short-term high-temperature creep of VT6 titanium alloy under uniaxial and multiaxial loading are presented. Numerical results are compared with the data obtained through experiments. Particular attention is paid to simulating the process of unsteady creep for complex deformation modes, accompanied by rotation of main areas of stress, strain and creep strain tensors. It is shown that the developed version of the constitutive relations of the damaged media enables us to describe the processes of unsteady creep and long-term strength of structural alloys under multiaxial stress with the accuracy sufficient for engineering calculations.

Mirror P=W conjecture and extended Fano/Landau-Ginzburg correspondence

The mirror P=W conjecture, formulated by Harder-Katzarkov-Przyjalkowski [27], predicts a correspondence between weight and perverse filtrations in the context of mirror symmetry. In this paper, we revisit this conjecture through the lens of mirror symmetry for a Fano pair (X,D), where X is a smooth Fano variety and D is a simple normal crossing divisor. We introduce its mirror object as a multi-potential analogue of a Landau-Ginzburg (LG) model, which we call the hybrid LG model. This model is expected to capture the mirrors of all irreducible components of D. We study the topological aspects, particularly the perverse filtration, and the Hodge theory of hybrid LG models, building upon the work of Katzarkov-Kontsevich-Pantev [32]. As an application, we discover an interesting upper bound on the multiplicativity of the perverse filtration for a hybrid LG model. Additionally, we propose a relative version of the homological mirror symmetry conjecture and explain how the mirror P=W conjecture naturally emerges from it.

Gromov–Hausdorff convergence of metric pairs and metric tuples

We study the Gromov–Hausdorff convergence of metric pairs and metric tuples and prove the equivalence of different natural definitions of this concept. We also prove embedding, completeness and compactness theorems in this setting. Finally, we get a relative version of Fukaya's theorem about quotient spaces under Gromov–Hausdorff equivariant convergence and a version of Grove–Petersen–Wu's finiteness theorem for stratified spaces.

Application of the Field Hyperspectral Sensing to Estimate the Oxidation-Reduction Potential (ORP) in Tropical Urban Waters

Oxidation-reduction potential (ORP) is one of the critical water quality parameters used in determining the biochemical condition of water, especially in wastewater treatment. Conventional measurement of ORP requires physical contact with the water samples. A relative version of the ORP measurement that is faster and requires non-contact with the water can be helpful, especially for environmental monitoring. One way to perform this is by measuring the radiated electromagnetic wave from water bodies such as drainage, rivers, and streams that are exposed to sunlight. The reflected radiation from various water samples was obtained using a handheld hyperspectral sensor that is sensitive to 350 – 250 nm radiation and the ORP measurement was performed using the water quality probes sensor equipped with the ORP sensor. Forty-four water samples were taken from multiple locations, including rivers, tributaries, drainage, and streams. Our analysis revealed that the wave spectra at 654 nm can estimate ORP values ranging from 0 to 500 with moderate performance (R² = 0.581). The reflectance spectra need to undergo normalization, and the second derivative filtering of the Savitsky-Golay is required to obtain such desired results. This preliminary experiment demonstrated that the ORP estimation is plausible using the hyperspectral remote sensor with moderate accuracy for water that potentially experiences nitrification, denitrification, carbonaceous biochemical oxygen demand, and phosphorus waste.