Integral Domain Research Articles

Logical characterizations of algebraic circuit classes over integral domains

AbstractWe present an adapted construction of algebraic circuits over the reals introduced by Cucker and Meer to arbitrary infinite integral domains and generalize the $\mathrm{AC}_{\mathbb{R}}$ and $\mathrm{NC}_{\mathbb{R}}^{}$ classes for this setting. We give a theorem in the style of Immerman’s theorem which shows that for these adapted formalisms, sets decided by circuits of constant depth and polynomial size are the same as sets definable by a suitable adaptation of first-order logic. Additionally, we discuss a generalization of the guarded predicative logic by Durand, Haak and Vollmer, and we show characterizations for the $\mathrm{AC}_{R}$ and $\mathrm{NC}_R^{}$ hierarchy. Those generalizations apply to the Boolean $\mathrm{AC}$ and $\mathrm{NC}$ hierarchies as well. Furthermore, we introduce a formalism to be able to compare some of the aforementioned complexity classes with different underlying integral domains.

On the Unit Group of the Integral Group Ring Z(S_3×C_3)

Describing the group of units in the integral group ring is a famous and classical open problem. Let S_3 and C_3 be the symmetric group of order 6 and a cyclic group of order 3, respectively. In this paper, a description of the units of the integral group ring Z(S_3×C_3) of the direct product group S_3×C_3 concerning a complex representation of degree two is given. As a result, a part of the conjecture which is introduced in (Low, 2008) and related to group rings over a complex integral domain is resolved using representation theory.

Modeling of Induction Motors and Variable Speed Drives for Multi-Domain System Simulations Using Modelica and the OpenIPSL Library

This paper introduces an innovative method for characterizing, implementing, and validating both three-phase and single-phase induction motor models, accompanied by a variable speed drive model. The primary goal is to investigate interactions between the electrical power grid and other dynamic domains (e.g., thermofluidic) that impact motor/load drive behavior. Our approach involves establishing a mechanical interface based on a physically meaningful equation linking motor torque/speed to the electrical model in the phasor domain. This allows seamless integration of diverse domain subsystems into a unified multi-domain model using Modelica v4.0.0 and the OpenIPSL library v3.0.1, overcoming co-simulation limitations. The proposed model, which requires only one Modelica-compliant tool for simulation, introduces additional dynamics through the mechanical interface, enabling explicit simulation of load disturbances based on constitutive physics. This deepens our understanding of dynamic interactions between the electrical power domain and other subsystems connected through the motor. We detail the modeled components using mathematical equations and textual descriptions, emphasizing the Modelica modeling approach. Simulation examples validate the implementation, demonstrating the multi-domain modeling capabilities of the newly developed components.

Technological Pedagogical and Content Knowledge (TPACK) Integration in Teaching Music : A Perception of High School Music Teacher

This study aims to describe the perceptions of TPACK integration among high school music teachers in Bandung, West Java province, Indonesia. This study used mixed-methods with a sequential explanatory design. The research subjects consist of 19 respondents. In the first phase, quantitative data were obtained through questionnaires and analyzed using descriptive and inferential statistical techniques. In the second phase, in an effort to explore the results of the questionnaire, qualitatively conducted interviews as well as observations. The findings of this study showed that integration of each TPACK domain in music teaching was perceived as high confidence. Each domain, from one to another, positively correlated with varied interpretations. Demographic characteristics, both gender and tenure, did not show contrasting differences in confidence. This perception is the impact of the teacher education process that has been experienced, involvement in a number of trainings that have been followed, support from stakeholders in the procurement and enrichment of educational and technological resources, and the dynamics of the times that force them to be adaptive and innovative towards technological developments.

UNALTERED: A FILE INTEGRATION MANAGEMENT SYSTEM

In today's interconnected world, where digital data underpins nearly every aspect of modern life, ensuring the integrity and security of files is paramount. This abstract provides a concise yet comprehensive overview of the multifaceted domain of file integrity and security. File integrity is the assurance that data remains unchanged and reliable, essential for maintaining trust and accountability. However, achieving and maintaining file integrity poses numerous challenges, including the ever-evolving threat landscape, complex IT infrastructures, and regulatory compliance mandates. To address these challenges, organizations employ a variety of strategies and technologies. Encryption, access controls, and digital signatures are deployed to protect files from unauthorized access and tampering, while file integrity monitoring (FIM) solutions continuously scrutinize files for any alterations. Moreover, robust security policies, employee training programs, and incident response plans are integral components of a proactive approach to file integrity and security. By fostering a culture of security awareness and investing in advanced technologies, organizations can effectively mitigate risks and safeguard their digital assets. Keywords: Encryption, Fostering, Integrity, Monitoring, tampering, Unauthorized.

A Computational Linguistic Approach to Study Border Theory at Scale

Border Theory suggests individuals createborders to manage the transitions between work and family (or, more generally, life) domains. The degree of separation or integration of domains across borders has an impact on the balance between work and life. Previous studies have shown individuals who perceive balance between work and life domains tend to be more satisfied with their lives, reporting higher physical and mental health. At times of crisis, such as during a pandemic, borders can be disrupted, affecting work-life balance and leading to a short- or long-term negative impact on well-being. Border theory provides a systematic lens through which to study these changes. However, changes cannot be studied using interviews or diaries as these are not at the scale required when societal disruptions occur. In this paper, we explore the feasibility of using a computational linguistic approach to operationalize border theory at scale, using readily available social media data. In particular, we make two main contributions. First, we design metrics to measure key characteristics of borders. This involves the application of a transformer-based topic modeling technique, BERTopic, to detect topics from social media data. Second, we apply this operationalization to a case study of around a million tweets posted by nearly two hundred teachers and journalists in the UK from the beginning of 2019 to the end of 2022. In so doing, we longitudinally study and compare the changes in borders between work and life before, during, and after COVID-19 lockdown periods.

Sequestration of membrane cholesterol by cholesterol-binding proteins inhibits SARS-CoV-2 entry into Vero E6 cells

Membrane lipids and proteins form dynamic domains crucial for physiological and pathophysiological processes, including viral infection. Many plasma membrane proteins, residing within membrane domains enriched with cholesterol (CHOL) and sphingomyelin (SM), serve as receptors for attachment and entry of viruses into the host cell. Among these, human coronaviruses, including severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), use proteins associated with membrane domains for initial binding and internalization. We hypothesized that the interaction of lipid-binding proteins with CHOL in plasma membrane could sequestrate lipids and thus affect the efficiency of virus entry into host cells, preventing the initial steps of viral infection. We have prepared CHOL-binding proteins with high affinities for lipids in the plasma membrane of mammalian cells. Binding of the perfringolysin O domain four (D4) and its variant D4E458L to membrane CHOL impaired the internalization of the receptor-binding domain of the SARS-CoV-2 spike protein and the pseudovirus complemented with the SARS-CoV-2 spike protein. SARS-CoV-2 replication in Vero E6 cells was also decreased. Overall, our results demonstrate that the integrity of CHOL-rich membrane domains and the accessibility of CHOL in the membrane play an essential role in SARS-CoV-2 cell entry.

Incorporating IL7 receptor alpha signaling in the endodomain of B7H3-targeting chimeric antigen receptor T cells mediates antitumor activity in glioblastoma.

CAR-T-cell therapy has shown promise in treating hematological malignancies but faces challenges in treating solid tumors due to impaired T-cell function in the tumor microenvironment. To provide optimal T-cell activation, we developed a B7 homolog 3 protein (B7H3)-targeting CAR construct consisting of three activation signals: CD3ζ (signal 1), 41BB (signal 2), and the interleukin 7 receptor alpha (IL7Rα) cytoplasmic domain (signal 3). We generated B7H3 CAR-T cells with different lengths of the IL7Rα cytoplasmic domain, including the full length (IL7R-L), intermediate length (IL7R-M), and short length (IL7R-S) domains, and evaluated their functionality in vitro and in vivo. All the B7H3-IL7Rα CAR-T cells exhibited a less differentiated phenotype and effectively eliminated B7H3-positive glioblastoma in vitro. Superiority was found in B7H3 CAR-T cells contained the short length of the IL7Rα cytoplasmic domain. Integration of the IL7R-S cytoplasmic domain maintained pSTAT5 activation and increased T-cell proliferation while reducing activation-induced cell death. Moreover, RNA-sequencing analysis of B7H3-IL7R-S CAR-T cells after coculture with a glioblastoma cell line revealed downregulation of proapoptotic genes and upregulation of genes associated with T-cell proliferation compared with those in 2nd generation B7H3 CAR-T cells. In animal models, compared with conventional CAR-T cells, B7H3-IL7R-S CAR-T cells suppressed tumor growth and prolonged overall survival. Our study demonstrated the therapeutic potential of IL7Rα-incorporating CAR-T cells for glioblastoma treatment, suggesting a promising strategy for augmenting the effectiveness of CAR-T cell therapy.

Galerkin finite block method with Lagrange multipliers method for cracked solids in functionally graded materials

This paper presents the application of the Galerkin Finite Block Method (GFBM) to address cracked solids associated with Functionally Graded Materials (FGMs), leveraging the foundational principles of the Galerkin method. The equilibrium equations pertinent to FGMs are articulated in their weak form. Employing Chebyshev polynomials as shape functions, the GFBM integrates mapping techniques to accommodate irregular finite or semi-infinite physical domains. Boundary and continuity conditions are enforced through the Lagrange Multiplier Method. The domain integrals are calculated through either analytical or numerical integration. The proposed method can easily solve the edge crack or diagonal crack problem by using the crack opening displacement method. The accuracy and convergence of the proposed method are illustrated through a selection of numerical examples. The obtained numerical solutions are verified with analytical solutions and the results from the Finite Element Method.

Semigroup rings which are strongly nil-clean

Strongly nil-cleanness and uniquely nil-cleanness are two important clean properties of rings. The aim of this paper is to answer when a semigroup ring is strongly or uniquely nil-clean. We obtain conditions on a coefficient ring together with conditions on a semigroup that completely characterize when the corresponding semigroup ring is strongly nil-clean. Moreover, when the coefficient ring is an integral domain, we characterize when the corresponding semigroup ring is uniquely nil-clean.

On the relation of CMIP6 GCMs errors at RCM driving boundary condition zones and inner region for Central Europe region

Global climate models (GCMs) are essential for studying the climate system and climate change projections. Due to their coarse spatial resolution, downscaling is necessary on the regional scale. Regional climate models (RCMs) represent a standard solution for this issue. Nevertheless, the boundary conditions provided by GCMs unavoidably influence the outputs of RCMs. This study evaluates CMIP6 GCMs regarding the variables relevant to RCM boundary conditions. Particular focus is on the simulation of CNRM-ESM2-1, which is being used as a driving model for convection-permitting ALARO-Climate RCM, used as one source feeding new Czech climate change scenarios. The analysis is conducted over the boundaries and inside the RCM integration domain. Firstly, an evaluation of CFSR and ERA5 reanalyses against radiosondes is performed to choose an appropriate reference dataset for upper air variables. A high correlation between the two studied reanalysis and radiosondes was revealed, and it slightly decreases at the upper tropospheric levels. ERA5 is then chosen as the reference for the boundary analysis. Over the inner region, the simulated mean annual cycle of impact-relevant variables is validated against E-OBS. The CNRM-ESM2-1 performs well regarding near-surface variables over the Czech Republic, but it exhibits larger errors along the boundaries, especially for air temperature and specific humidity. The GCM performance in simulating the upper air atmospheric variables used as RCM boundary conditions relates rather weakly to the GCM performance in simulating the near-surface parameters in the inner region in terms of parameters relevant for impact studies.

Addressing arbitrary body forces in 2D elasticity coupling the Radial Basis Integration Method with boundary elements

A boundary-domain integral formulation inevitably arises when the boundary element method (BEM) is applied for solving the differential equation that governs linear elastostatic problems with body forces. Although the domain integrals introduced by the body forces can be evaluated using internal cells this destroys the boundary-only meshing feature of BEM and makes the integration processes inefficient. This paper shows that these problems can be solved more efficiently without using internal cells by the Radial Basis Integration Method (RBIM) which employs a meshless quadrature obtained by performing boundary-only offline computations. Using RBIM, weakly singular domain integrals can be computed via a simple selective quadrature procedure, whereas, strong singular domain integrals may be computed using two schemes: The first, is based on the same selective quadrature procedure, and the second is based on the singularity separation scheme. The present method, unlike classical radial integration method (RIM), does not have problems in calculating integrals in concave or multiple-connected domains. The results obtained in some 2D linear elastostatic problems with arbitrary body forces show that this method can be as accurate as RIM but less time-consuming than the latter. This method could be applied to other engineering problems involving source terms.

A physics-informed neural network framework to investigate nonlinear and heterogenous shrinkage of drying plant cells

This paper introduces a novel Physics-Informed Neural Network-based (PINN-based) multi-domain computational framework to analyse nonlinear and heterogeneous morphological variations of plant cells during drying. Here, two distinct models are involved: PINN-MT to simulate mass transfer; and PINNNS to simulate nonlinear shrinkage. The models are coupled to examine cellular morphological changes resulting from moisture loss during drying. Firstly, the coupled framework, in tandem with homogeneous conditions, operates in parallel, allowing the mutual parameters to update between models. This approach demonstrates ability to approximate homogeneous cellular shrinkage within a tissue, factoring in the influence of surrounding plant cells. Secondly, non-uniform cell wall properties and heterogeneous boundary conditions are incorporated into this computational framework through domain decomposition. Inherent capabilities of neural networks allow for seamless integration of multiple domains, with additional loss terms introduced at interfaces. The framework shows capacity to account for drastic and non-uniform morphological variations of plant cells even under extreme drying conditions, which is the key novelty and has been a challenging task for existing traditional computational methods. Hence, the proposed computational approach offers an innovative avenue for understanding nonlinear and heterogeneous morphological variations not only for plant cells, but also for soft matter in general.

A multimesh finite element method for integral nonlocal elasticity using mesh-decoupling technique

This study presents a generalized multimesh nonlocal finite element method (M2-FEM) that addresses several long-standing challenges in the numerical simulation of Eringen’s integral elasticity theories, often used to model nonlocal effects. The major challenges in the numerical simulation of integral boundary value problems are primarily rooted in the coupling of the spatial discretization of the global (parent) and integral (child) domains, which severely restricts both the applicability and the computational efficiency of existing algorithms by imposing an implicit trade-off between the accuracy of the child domain and the resources required by the overall parent domain. One of the defining contributions of this study consists in the development of a mesh-decoupling technique that generates isolated sets of meshes such that the parent and child domains can be discretized and approximated independently. This mesh-decoupling has multi-fold advantages on the simulation of integral theories such that, when compared to existing state-of-the-art techniques, the proposed algorithm achieves a greater ability to adopt generalized integral kernel functions, the ability to handle non-regular (non-rectangular) domains via unstructured meshing, and simultaneously better numerical accuracy and efficiency (hence allowing greater flexibility in both mesh size and computational cost trade-off decisions). Both benchmark studies and several case studies are conducted to assess the effectiveness of M2-FEM. Simulation results confirm that M2-FEM can accurately simulate integral nonlocal problems and demonstrate its multi-fold computational advantages over existing mesh-coupling-based nonlocal finite element methods. Overall, the proposed M2-FEM algorithm is very general and it can be applied to a variety of integral theories, even beyond nonlocal elasticity.

Religious and Counseling Discourses in Clinical Practice

The study expands the authors' previous findings to examine counseling and religious discourses more closely. Three themes were identified: value of Catholic Christian faith for life and counseling; autonomy and obedience; and healing, renewal, and the call to serve. Interview transcripts were reviewed through the lens of constructs from discourse analysis, including hegemony, analogization, and dialogism. Dialectics between the domains of counseling and religion were identified in the samples of discourses and their analyses. The results indicate the potential for integration of domains and strengthening of religious and counselor identities.

Post-publication research integrity concerns in randomized clinical trials: A scoping review of the literature.

Post-publication handling of integrity concerns in randomized clinical trials (RCTs) is a contentious matter. We undertook a scoping systematic review to map the literature regarding post-publication integrity issues in RCTs. Following prospective registration (https://osf.io/pgxd8) we initially searched PubMed and Scopus but subsequently extended it to include the Cochrane Library, and Google Scholar databases without language, article type or publication time restriction until November 2022. Reviewers independently selected published articles covering any aspect of post-publication research integrity concerns in RCTs. The study findings grouped within domains relating to issues concerning post-publication integrity were extracted in duplicate, verified by a third reviewer, and then tabulated. The initial search captured 3159 citations, of which 89 studies were included in the review. Cross-sectional studies constituted the majority of included studies (n = 34, 38.2%), followed by systematic reviews (n = 10, 11.2%), methodology reviews/studies (n = 9, 10.1%) and other types of descriptive studies (n = 8, 9.0%). A total of 21 articles (23.6%) covered the domain on general issues, 25 (28.1%) in the journal's instructions and policies domain, eight (9.0%) in the editorial and peer review domain, one (1.1%) in the correspondence and complaints (post-publication peer review) domain, 12 (13.5%) in the investigation for concerns domain, six (6.7%) in the post-investigation decisions and sanctions domain, none in the critical appraisal guidance domain, five (5.6%) in the integrity assessment in systematic reviews domain, and 26 (29.2%) in the recommendations for future research domain. A total of 12 of the selected articles (13.5%) covered two (n = 9) or three (n = 3) different domains. Various research integrity domains and issues covering post-publication aspects of RCT integrity were captured and gaps were identified, mostly related with the necessary implications for all stakeholders to improve research transparency. There is an urgent need for a multistakeholder consensus towards creating specific statements for addressing post-publication integrity concerns in RCTs.

Zero-bin subtraction and the qT spectrum beyond leading power

In this paper, we present an algorithm to construct the qT distribution at NLO accuracy to arbitrary power precision, including the assembly of suitable zero-bin subtrahends, in a mathematically well-defined way for a generic choice of rapidity-divergence regularisation prescription. In its derivation, we divide the phase space into two sectors, the interior of the integration domain as well as the integration boundary, which we include here for the first time. To demonstrate the applicability and usefulness of our algorithm, we calculate the N2LP corrections for Higgs hadroproduction for the first time. We observe that our approximate N2LP-accurate qT spectra replicate the asymptotic behaviour of the full QCD calculation to a much better degree than the previously available results, both within the qT → 0 limit and in the large-qT domain for all the involved partonic processes. While playing a minor role at larger transverse momenta, we show that the newly incorporated boundary contribution plays a vital role in the qT → 0 limit, where any subleading power accuracy would be lost without them. In particular, our N2LP-accurate qT expansion can approximate the exact qT distribution up to qT ≈ 30 GeV at the percent level for rapidities |YH| ≲ 3.

Variations of Sleep Patterns and Their Relations with Positive and Negative Domains of Schizophrenia in Eastern Indian Population

Abstract Objectives: Schizophrenia is a persistent and incapacitating psychiatric condition characterized by symptoms with positive, negative, affective, and cognitive domains. Sleep disturbances represent an important facet of this disorder, impacting both the quality of life and influencing its overall outcome. In the cross-sectional study, we intended to investigate the polysomnographic findings of patients with schizophrenia showing predominantly positive symptoms as opposed to those presenting with predominantly negative symptoms and also as compared to normal population. Methods: This study had a cross-sectional design, involving the recruitment of 60 medication-naive patients diagnosed with schizophrenia according to the ICD-10 criteria and 30 study participants representing normal population. The cases were subdivided into two groups: one characterized by predominantly positive symptoms and the other characterized by predominantly negative symptoms. Both the groups received overnight polysomnography, and study variables were recorded. Results: All the sleep parameters were deranged in patients with schizophrenia as compared to normal controls in the general population, with significantly more pronounced differences found in those with predominant positive symptoms for most variables (p < 0.001). The only exception was the duration of N3 (slow-wave sleep) which was significantly decreased in patients with negative symptoms compared to those with positive symptoms (p < 0.001). But no significant differences were found between the negative and positive symptom domain groups in mean rapid eye movement (REM) latency, duration of N1 and N2 sleep, and total percentage of REM sleep. Conclusion: This study highlights substantial variations in sleep patterns between the negative and positive symptom domains of schizophrenia and also as compared to the general population. Further study is imperative to explore the link between circadian integrity and symptoms of the various domains of schizophrenia.

On the determination of the quasi-static evolution of brittle plane cracks via stationarity principle

The crack front evolution in brittle solids is commonly modelled by defining some crack increment criterion, which can be derived from considerations on the stress singularity, from the definition of a dissipative potential, from the introduction of phenomenological concepts such as the crack mobility, and so on. In this work, we faced the problem with no allowance for any crack increment criterion, but using only the elastic properties, the fracture energy, and a stationarity principle. We will show that these ingredients are enough for determining the equilibrium and the quasi-static evolution of generally shaped three-dimensional brittle plane cracks. In doing this, we pointed out some new insight on the crack front motion, a set of new, generalised, domain integrals for measuring the pointwise crack ‘tension’, and a rigorous calculation of the intersection angle between the crack front and the free surface.

SCTBEM: A scaled coordinate transformation boundary element method with 99-line MATLAB code for solving Poisson's equation

This study introduces the scaled coordinate transformation boundary element method (SCTBEM), a novel boundary-type method for solving three-dimensional potential problems. To apply the BEM to complex problems, it is common practice to use the fundamental solution corresponding to the partial governing equation operator to establish the integral equation. However, this approach introduces the domain integral, which may jeopardize the dimensionality reduction advantages of BEM. To preserve the benefits of dimensionality reduction, this study proposes a novel domain integral transformation method named SCT. The SCT is purely a mathematical operation that does not rely on a particular solution of the operators, which requires only discretization on the surface of the structure while remaining analytical in the radial direction. An even more significant advantage is that the lower-order singularity can be eliminated by the coordinate translation technique. To facilitate the wider adoption of BEM, the authors present an open-source 99-line MATLAB code. Numerical results demonstrate that the SCTBEM exhibits high numerical accuracy even when dealing with complex models.