Business analysis has been an important factor of success of software projects and business analysts are listed among top jobs of the future. However, training of effective business analysts is challenging and requires individualized professional development programs. This paper extends the previous research on the balanced approach to training business analyst with use of techniques, underlying competencies development and talent-oriented approaches. It argues for the need of unified theory which can be considered as a conceptual framework for integrating the background approaches. It applies integrative studies which allow to capture a broader scope of phenomena. The following research methods are in use: interpretation with meta-knowledge which explains the context of discovery and the values of the background approaches, cross-border analysis which allows to focus on connections and overlapping between the background approaches, and searching for common ground with use of conscious and non-conscious cognitive processes similar to forming habits or semi-automatic human behaviors. The findings deliver many interesting explanations of the phenomena as well as suggestions for practical use of this approach. For example, use of explicit descriptions of strengths (in terms of patterns of thought, feeling and behavior) for competence development; use of business analysis techniques for competence development; need for entire spectrum of competencies of business analyst comparing to specific strengths; possible problems with following the experts; and perspective of thinking in terms of forming and re-forming effective cognitive processes for more comfort in business analysts’ training.

Word sense induction (WSI) aims to automatically discover the different senses of a word from contextual usage without predefined sense inventories. However, existing distributional clustering methods often suffer from dominant-sense bias and struggle to correctly identify minority senses. In this paper, we propose a definition-anchored reclassification framework for WSI that leverages large language models (LLMs) to generate explicit sense descriptions and refine cluster assignments. Unlike purely distributional approaches, our method integrates semantic definitions into the induction process. Our method improves instance-level alignment by introducing a trade-off with global structural consistency, as it shifts the decision process from geometric clustering to definition-based semantic matching. Experiments on the SemEval-2010 and SemEval-2013 datasets demonstrate that the proposed method consistently outperforms traditional clustering baselines and existing WSI systems across both structural metrics (NMI and V-measure) and instance-level metrics (F-B3 and Fuzzy-F-B3). In particular, our approach effectively mitigates dominant-sense bias and improves the recovery of minority senses by preserving them as distinct clusters while correctly assigning their instances. These results suggest that explicit semantic representations generated by LLMs provide a promising direction for addressing long-standing challenges in unsupervised word sense induction. Furthermore, unlike purely distributional clustering approaches, our method explicitly introduces LLM-generated semantic definitions as anchors, enabling more robust mitigation of dominant-sense bias and improved recall of minority senses.

Background/Objectives: Vision-language models (VLMs) such as GPT (Generative Pre-Trained Transformer) have shown potential for medical image interpretation; however, challenges remain in generating reliable radiological findings in clinical practice, as exemplified by dental pathologies. This study proposes a Self-correction Loop with Structured Output (SLSO) framework as an integrated processing methodology to enhance the accuracy and reliability of AI-generated findings for jaw cysts in dental panoramic radiographs. Methods: Dental panoramic radiographs with jaw cysts were used to implement a 10-step integrated processing framework incorporating image analysis, structured data generation, tooth number extraction, consistency checking, and iterative regeneration. The framework functioned as an external validation mechanism for GPT outputs. Performance was compared against the conventional Chain-of-Thought (CoT) method across seven evaluation items: transparency, internal structure, borders, root resorption, tooth displacement, relationships with other structures, and tooth number. Results: The SLSO framework improved output accuracy for multiple items compared to the CoT method, with the most notable improvements observed in tooth number identification, tooth displacement detection, and root resorption assessment. In successful cases, consistently structured outputs were achieved after up to five regenerations. The framework enforced explicit negative finding descriptions and suppressed hallucinations, although accurate identification of extensive lesions spanning multiple teeth remained limited. Conclusions: This investigation established the feasibility of the proposed integrated processing methodology and provided a foundation for future validation studies with larger, more diverse datasets.

Blind image quality assessment (BIQA) without reference images remains significantly challenging due to the fact that perceptual quality is largely determined by subtle, spatially localized distortions. However, existing Contrastive Language–Image Pre-training (CLIP)-based methods exhibit limited sensitivity to fine-grained degradations such as local blur, noise, compression artifacts, and exposure inconsistencies, since they are optimized for global semantic alignment. To overcome these limitations, we propose a fine-grained vision–language framework that enhances distortion-aware representation by considering both fine-grained visual and detailed textual domains. Specially, our method employs a fine-grained CLIP architecture in conjunction with explicit textual descriptions to enable the effective identification of subtle regional degradations. Furthermore, a parameter-efficient prompt-tuning strategy is utilized to facilitate the learning of task-adaptive prompt representations tailored to image quality assessment (IQA). Extensive experiments on three widely used in-the-wild IQA benchmarks show that the proposed method achieves strong consistency with human subjective judgments: our training-free FGCLIP-IQA reaches a maximum SROCC of 0.732 on KonIQ-10k, outperforming the vanilla CLIP-IQA baseline, while the prompt-tuned FGCLIP-IQA+ further achieves a maximum SROCC of 0.909 on KonIQ-10k with only a small number of learnable parameters and exhibits robust cross-dataset generalization capabilities. These results demonstrate that the fine-grained vision–language alignment shows great potential for future development, and provides an efficient and accurate solution for the BIQA task.

This work investigates the influence of the fluctuation term in the formulation of the homogenized constitutive tensor within a multiscale approach applied to the analysis of heterogeneous media. A phase-field constitutive model is used, coupled with the multilevel finite element method, which allows for the simultaneous consideration of macro and micro scales. The phase-field model enables the diffuse representation of fractures, capturing the evolution of the displacement field and crack propagation without the need for an explicit description of the fracture geometry. This makes the model particularly useful for materials like concrete, which may exhibit complex cracking patterns. At the macroscopic scale, the material's constitutive behavior is not directly defined; it must be obtained from solving the microscopic scale, where the local material properties, such as variations in stress and strain, are better represented. The connection between the scales requires defining homogenized parameters that adequately represents the material’s behavior. Literature suggests that this transition cannot be done through a simple average of the local constitutive tensors, as this approach disregards important fluctuations in the displacement field. To ensure theoretical consistency, the inclusion of a fluctuation term is required, which depends on the inverse of the stiffness matrix of the microscale problem. However, calculating this term results in a significant computational cost. With the multiscale implementation in place, comparative tests were conducted between simulations with and without the fluctuation tensor, evaluating both the accuracy of the results and the impact on processing time. All implementations were carried out using INSANE, an open-source platform developed by the Department of Structural Engineering (DEES) at the Federal University of Minas Gerais (UFMG).

In this work, we present a theoretical and computational approach that combines real-time propagation of the electronic wave function, the GW/BSE formalism for the electronic structure of ground and excited states, the theory of open quantum systems, and the phase-cycling method to compute two-dimensional electronic spectra (2DES) of molecular systems under realistic excitation conditions. The advantage of this strategy is that it combines the accuracy of first-principle calculations such as GW/BSE with an explicit description of the employed laser pulses. This allows for better adherence to experimental setups. We apply the proposed methodology to benzene, chlorophyll b, and a benzene-phenol dimer, also including a pure electronic dephasing in the time propagation. The calculated 2DES maps reveal clear signatures of stimulated emission and excited-state absorption, as well as coherence dynamics as a function of the population time, both in the absence and presence of pure dephasing. Comparison with experimental and theoretical published data has been carried out, when available.

Autism research has predominantly focused on Western contexts, with limited studies in Vietnamese cultural settings. Through conducting a systematic scoping review, we aimed to map (a) the landscape of autism research in Vietnamese cultural contexts, (b) the quality of the research, and (c) the extent of autism community involvement in the research. A total of 137 studies met our inclusion criteria. A growing body of literature pertained to autism in Vietnamese cultural contexts, largely conducted in Viet Nam (87%). Much of the literature focused on Services and Supports (39%), as well as Interventions (20%). Key themes identified from the research were the centrality of family, the importance of school and education, and identifying a cause of autism. Quality appraisals of the studies - using the Mixed Methods Appraisal Tool, a Westernised tool - indicated that the studies were largely of low quality. There was limited autism community involvement in the research, with studies often lacking an explicit description of the nature of community involvement. Priority areas for future research include better understanding how rigour is understood in a Vietnamese research context, improving the clarity of data reporting and actively involving the Vietnamese autism community in the research process.Lay abstractAutism research has mostly focused on Western contexts, with few studies in Vietnamese cultural contexts. In this study, we reviewed all the research we could find on autism in Vietnamese cultural contexts, to map out what this research 'looks like'. We found 137 studies on autism in Vietnamese cultural contexts, and most of this research was conducted in Viet Nam. The studies were often focused in the areas of Services and Supports as well as Interventions. Looking for common themes in the research, we found that studies emphasised the importance of family, the importance of school and education, and the need to find the causes of autism. We used the Mixed Methods Appraisal Tool, a Westernised tool, to evaluate the quality of the research, and we found that a lot of the research was rated as 'low quality'. There were few examples of clear autism community involvement in the research. Key areas for the field to focus on in the future include reflecting on how the quality of the research is evaluated in Global South countries such as Viet Nam, and how best to include the autism community in the research process.

Abstract Motivated by the limitations of cluster algebra techniques in detecting imaginary modules, we build on the representation-theoretic framework developed by the first author and Chari to extend the construction of such modules beyond previously known cases, which arise from the tensor product of a higher-order Kirillov–Reshetikhin module and its dual. Our first main result gives an explicit description of the socle of tensor products of two snake modules, assuming the corresponding snakes form a covering pair of ladders. By considering a higher-order generalization of the covering relation, we describe a sequence of inclusions of highest- $$\ell $$ ℓ -weight submodules of such tensor products. We conjecture all the quotients of subsequent modules in this chain of inclusions are simple and imaginary, except for the socle itself, which might be real. We prove the first such quotient is indeed simple and, assuming an extra mild condition, we also prove it is imaginary, thus giving rise to new classes of imaginary modules within the category of finite-dimensional representations of quantum loop algebras in type A .

The long root geometry A n , { 1 , n } ( 𝕂 ) for the special linear group SL ( n + 1 , 𝕂 ) admits an embedding in the (projective space of) the vector space of the traceless square matrices of order n + 1 with entries in the field 𝕂 , usually regarded as the natural embedding of A n , { 1 , n } ( 𝕂 ) . S. Smith and H. Völklein in [10] have proved that the natural embedding of A 2 , { 1 , 2 } ( 𝕂 ) is relatively universal if and only if 𝕂 is either algebraic over its minimal subfield or perfect with positive characteristic. They also give some information on the relatively universal embedding of A 2 , { 1 , 2 } ( 𝕂 ) which covers the natural one, but that information is not sufficient to exhaustively describe it. The “if” part of Smith-Völklein’s result also holds true for any n , as proved by Völklein in [13] in his investigation of the adjoint modules of Chevalley groups. In this paper we give an explicit description of the relatively universal embedding of A n , { 1 , n } ( 𝕂 ) which covers the natural one. In particular, we prove that this relatively universal embedding has (vector) dimension equal to 𝔡 + n 2 + 2 n where 𝔡 is the transcendence degree of 𝕂 over its minimal subfield (if char ( 𝕂 ) = 0 ) or the generating rank of 𝕂 over 𝕂 p (if char ( 𝕂 ) = p > 0 ). Accordingly, both the “if” and the “only if” part of Smith-Völklein’s result hold true for every n ≥ 2 .

This paper aims to develop a simultaneous study of ordinal sums in BE-algebras and to apply this construction to several central notions in the theory. We first introduce the ordinal sum of a totally ordered family of BE-algebras and establish that it yields a well-defined BE-algebra in which each component embeds naturally. A detailed analysis of the resulting structure is provided, including explicit descriptions of its filters, subalgebras, and congruence relations. Building on these foundations, we characterize the behavior of dense BE-algebras, multipliers, stabilizers, and closure operators in ordinal sums, thereby refining and extending several earlier results in the literature. We provide a representation for dense BE-algebras as the ordinal sum of [Formula: see text], where [Formula: see text] is the unique two-element BE-algebra and [Formula: see text] is an arbitrary BE-algebra. This representation leads us to a categorically equivalent relation between dense BE-algebras and BE-algebras. The ordinal sum construction thus serves as a unifying framework for understanding the internal organization of BE-algebras. It offers new tools for creating various examples and transferring structural properties between their components.

The mathematical β-tilting theory idea (the mathematical β-t theory) originated from the conceptual paintings of Adachi and his colleagues in 2014 [1], and it rapidly emerged as a primary focus of investigation within representation theory(R-theory) of finite-dimensional algebras (F-D algebras ). Integrating the idea of tilt, this framework presents an efficient combinatorial and isomorphic tool for reading rotation training, silt complexes, and cluster- tilting (CT) objects within modular classes .This study provides a systematic and self-contained introduction to β-t theory , especially designed for readers with a standard background in representation theory. It aims to enable researchers to grasp the fundamental concepts without the need for extensive reference to external sources, while maintaining full commitment to high mathematical rigor. In addition, the study unifies silting theory and cluster-tilting theory (CT theory) within a common perspective, gathering in one place the basic definitions, important bijections, and mutation techniques that form the core of this field [1]. In addition to the classical foundations, the research criticizes major developments published between 2023 and 2026, including new properties of β-tilting ( β-t) finiteness for Borel–Schur algebras and group algebras of generalized symmetric groups, and their applications to Frobenius–Perron dimensions and generalized preprojective algebras [2–8]. Particular attention is given to recent developments in higher torsion classes, βd-tilting theory ( βd-t-theory) and duplicated algebras. The study concludes by highlighting several key open problems such as the classification of minimal β-tilting infinite algebras ( β-t-i algebras ) and the explicit description of the vital bijections for important families of algebras which continue to motivate current research [9].This work aims to be an accessible entry point for beginners and a comprehensive reference for active researchers in representation theory ( R- theory ) and related fields [1,2].

This work develops an energy-based reachability framework for linear fractional-order dynamical systems governed by Caputo derivatives of order α∈(0,1) in the presence of time-dependent delays acting on both the state and control channels. By combining a controllability Gramian formulation with a delay-independent algebraic characterization, explicit quantitative descriptions of reachability under finite energy constraints are obtained. It is shown that the set of terminal states attainable with bounded control energy admits a geometric characterization in terms of a Gramian-induced ellipsoidal region centered at the uncontrolled terminal state. In addition, the minimum eigenvalue of the controllability Gramian is identified as an energy-based controllability margin that provides certified reachability guarantees. Stability and sensitivity properties of the associated minimum-energy control law with respect to perturbations in the terminal target are also established. The theoretical developments are supported by implementable numerical procedures and illustrative examples that demonstrate the computation of the controllability Gramian, its spectral characteristics, and the resulting minimum-energy control inputs.

In recent years, many results have been established regarding classifications of varieties whose colength sequences are bounded by a fixed constant. In this work, we explore this theme in the setting of algebras endowed with a graded involution, called ( G , ∗ ) -algebras. We give an explicit description of the decomposition of the 〈 n 〉 -cocharacter for some important ( G , ∗ ) -algebras A, for every 〈 n 〉 = ( n 1 , … , n 2 t ) . For each algebra A, the nth colength is defined as the number of irreducible components that appear in these decompositions. Our aim is to classify varieties whose nth colengths are bounded by a fixed constant.

Abstract Let be a finite group and be an ‐ring ‐spectrum. For any ‐space and positive integer , we give an explicit description of the smallest Mackey ideal in for which the reduced th power operation is a map of Green functors. We obtain this result as a special case of a general theorem that we establish in the context of ‐Green functors. This theorem also specializes to characterize the appropriate ideal when is a ‐ring in global spectra. We give example computations for the sphere spectrum, complex ‐theory, and Morava ‐theory.

Abstract Twistor spaces are certain compact complex three‐folds with an additional real fibre bundle structure. We focus here on twistor spaces over . Such spaces are either small resolutions of double solids or they can be described as modifications of conic bundles. The last type is the more special one: they deform into double solids. We give an explicit description of this deformation, in a more general context.

Abstract An intriguing phenomenon regarding Levi-degenerate hypersurfaces is the existence of nontrivial infinitesimal symmetries with vanishing 2-jets at a point. In this work we consider polynomial models of Levi-degenerate real hypersurfaces in $$\mathbb {C}^3$$ C 3 of finite Catlin multitype. Exploiting the structure of the corresponding Lie algebra, we characterize completely models without 2-jet determination, including an explicit description of their symmetry algebras.

Abstract The main purpose of this paper is to provide an explicit description of the invariant control sets for a class of control systems induced on the unit quaternion sphere $$S^3$$ S 3 by the action of the Lorentz group $$\textrm{SO}(1,4)$$ SO ( 1 , 4 ) and then generalize it to the sphere $$S^{n-1}$$ S n - 1 . These control sets are the maximal subsets of approximate controllability for the control systems. Describing them in detail is generally challenging due to the complexity of the geometry and topology of the underlying differentiable manifold and the behavior of the vector fields defining the control system. In this work, the Lie theory and the quaternions play a fundamental role in achieving our main results.

ABSTRACT General education teachers play a crucial role in implementing inclusive education practices. Although there is a growing body of empirical research on their competence for inclusive education, there remains a lack of clear definition and uneven evidence across competence dimensions in working with students with special education needs (SEN) in inclusive settings. This scoping review aims to fill this gap by systematically reviewing studies on in-service general teachers’ competence for inclusive education. Through a comprehensive literature search across three databases, 117 relevant studies were identified. The review delineates the scope and types of empirical research, maps the characteristics of the evidence, and identifies explicit descriptions of general education teachers’ competence for inclusive education. Moreover, it conceptually maps the knowledge and skills under the competence definition referred to in these studies. The findings underscore the need/gap for further research on general education teachers’ competence for inclusive education, utilising multi-informant approaches, covering diverse student populations across multiple countries, and employing randomised control research designs and longitudinal methodologies. This review also highlights the necessity to clarify definitions of general teachers’ competence for inclusive education, which hold implications for both future research and practice improvement.

In this paper we study higher even Gaussian maps of the canonical bundle on hyperelliptic curves and we determine their rank, giving explicit descriptions of their kernels. Then we use this descriptions to investigate the hyperelliptic Torelli map $j_h$ and its second fundamental form. We study isotropic subspaces of the tangent space $T_{{\mathcal H}_g, [C]}$ to the moduli space ${\mathcal H}_g$ of hyperelliptic curves of genus $g$ at a point $[C]$, with respect to the second fundamental form $ρ_{HE}$ of $j_h$. In particular, for any Weierstrass point $p \in C$, we construct a subspace $V_p$ of dimension $\lfloor\frac{g}{2} \rfloor$ of $T_{{\mathcal H}_g, [C]}$ generated by higher Schiffer variations at $p$, such that the only isotropic tangent direction $ζ\in V_p$ for the image of $ρ_{HE}$ is the standard Schiffer variation $ξ_p$ at the Weierstrass point $p \in C$.

Abstract We prove that over an algebraically closed field of characteristic $$p>0$$ p > 0 there are exactly, up to isomorphism, n infinitesimal commutative unipotent k -group schemes of order $$p^n$$ p n with one-dimensional Lie algebra, and we explicitly describe them. We consequently obtain an explicit description of all infinitesimal subgroup schemes of any supersingular elliptic curve over an algebraically closed field, recovering all their $$p^n$$ p n -torsions as well. Finally, we use these results to answer a question of Brion on rational actions of infinitesimal commutative unipotent group schemes on curves.