Construction Of Representations Research Articles

Bases of tensor products and geometric Satake correspondence

The geometric Satake correspondence can be regarded as a geometric construction of rational representations of a complex connected reductive group G . In their study of this correspondence, Mirković and Vilonen introduced algebraic cycles that provide a linear basis in each irreducible representation. Generalizing this construction, Goncharov and Shen define a linear basis in each tensor product of irreducible representations. We investigate these bases and show that they share many properties with the dual canonical bases of Lusztig.

DETERMINANTS, MEASUREMENT AND MANAGEMENT OF PERFORMANCE IN SMALL AND MEDIUM-SIZED ENTERPRISES

Small and medium-sized enterprises (SMEs) are considered the backbone of economic growth, as they play a vital role in the economic development of any country, they contribute to the provision of job opportunities and act as suppliers of goods and services to large companies. Despite the role of SMEs in national economies, as well as their importance in promoting competitiveness and employment, the author believes that the SMEs performance determinants and their impact on performance measurement and management have not been sufficiently studied in Latvia. The aim of the research is to explore the SMEs performance determinants and their impact on performance measurement and management. The research is based on the analysis of scientific publications. General research methods are used in the research: information analysis and synthesis, logically – constructive, monographic, data grouping and graphical representation methods. As a result, the impact of the SMEs performance determinants on the measurement and management of SME performance are explored, and the conceptual framework for measuring and managing SME performance is developed.

Confronting gendered constructions of refugee deservingness and representations: Syrian refugee women strategising for humanitarian aid in Turkey

ABSTRACT This study shows how Syrian refugee women living in Ankara cope with their systematically enforced dependency on humanitarian aid through individual and collective agency as they negotiate their inclusion into categories of deservingness and attempt to maintain this inclusion. We argue that the gendered discourses used to delineate deservingness categories in the humanitarian field clash heavily with the portrayal of Syrian refugees in Turkish public discourse. Our qualitative data demonstrate how notions in the humanitarian field about women’s role in the family as nurturing homemakers, assumptions about their innate docility as vulnerable refugees and the contrasting portrayals in Turkish society of Syrian refugee women as sexualised threats to the Turkish family shape their agentive negotiations and subsequently lead to multiple tensions. We also highlight how the centrality of gender in the discursive framing of refugees in Turkey produces the idealised refugee in the figure of the widowed refugee mother. By problematising how refugee women’s agency play out, we intervene in the discussion about the gendered terrains of refugeehood and provide empirical weight for the exploration of the paradoxes in the humanitarian field that refugee women struggle to resolve.

A New Orientation Detection Method for Tilting Insulators Incorporating Angle Regression and Priori Constraints

The accurate detection of insulators is an important prerequisite for insulator fault diagnosis. To solve the problem of background interference and overlap caused by the axis-aligned bounding boxes in the tilting insulator detection tasks, we construct an improved detection architecture according to the scale and tilt features of the insulators from several perspectives, such as bounding box representation, loss function, and anchor box construction. A new orientation detection method for tilting insulators based on angle regression and priori constraints is put forward in this paper. Ablation tests and comparative validation tests were conducted on a self-built aerial insulator image dataset. The results show that the detection accuracy of our model was increased by 7.98% compared with that of the baseline, and the overall detection accuracy reached 82.33%. Moreover, the detection effect of our method was better than that of the YOLOv5 detection model and other orientation detection models. Our model provides a new idea for the accurate orientation detection of insulators.

Computational Thinking Situations in Mathematics classes: an analysis of Elementary School textbook collections

This study aims to analyze how textbook collections, approved by the Programa Nacional do Livro Didático, address the algorithms construction for solving geometric problems. This is a qualitative research, based on assumptions of Content Analysis. The analysis was based on situations related to Computational Thinking and geometric concepts, contained in eight collections of Elementary School textbooks, showing skills of the Base Nacional Comum Curricular. We found that of the skills associated with Computational Thinking, EF06MA23 contained the largest number of situations involving algorithms construction. As for the representations proposed for the organization of the algorithm, approximately 46% of the mobilizations carried out were approached by exploring natural language and 41% in the flowchart/schema representation. Furthermore, only 9 situations explore different types of representation in the algorithm construction. The algorithm represented in programming language was identified in only two collections, which suggest the use of visual programming environments/software.

Bundle theoretic descriptions of massive single-particle state spaces; with a view toward relativistic quantum information theory

Relativistic Quantum Information Theory (RQI) is a flourishing research area of physics, yet, there has been no systematic mathematical treatment of the field. In this paper, we suggest bundle theoretic descriptions of massive single-particle state spaces, which are basic building blocks of RQI. In the language of bundle theory, one can construct a vector bundle over the set of all possible motion states of a massive particle, in whose fibers the moving particle’s internal quantum state as perceived by a fixed inertial observer is encoded. A link between the usual Hilbert space description is provided by a generalized induced representation construction on the L 2-section space of the bundle. The aim of this paper is two-fold. One is to communicate the basic ideas of RQI to mathematicians and the other is to suggest an improved formalism for single-particle state spaces that encompasses all known massive particles including those which have never been dealt with in the RQI literature. Some of the theoretical implications of the formalism will be explored at the end of the paper.

Computational complexity when constructing rational plans for program execution in a given field of parallel computers

Objectives. The construction of rational plans (schedules) for parallel program execution (PPE) represents a challenging problem due to its ambiguity. The aim of this work is to create methods for developing such plans and specialized software for implementing these methods, which are based on the internal properties of algorithms, primarily on the property of internal (hidden) parallelism.Methods. The main method for developing PPE plans was the construction, analysis, and purposeful transformation of the stacked-parallel form (SPF) of information graphs of algorithms (IGA). The SPF was transformed by transferring operators from tier to tier of the SPF (this event was taken as an elementary step in determining the computational complexity of scenario execution). As a transformation tool, a method for developing transformation scenarios in the scripting programming language Lua was used. Scenarios were created by a heuristic approach using a set of Application Programming Interface (API) functions of the developed software system. These functions formed the basis for a comprehensive study of the parameters of the IGA and its SPF representation for the subsequent construction of a PPE plan applying to a given field of parallel computers.Results. Features of the internal properties of the algorithms that affect the efficiency of SPF transformations were identified during the course of computational experiments. Comparative indices of the computational complexity of obtaining PPE plans and other parameters (including code density, etc.) were obtained for various SPF transformation scenarios. An iterative approach to improving heuristic methods favors developing optimal schemes for solving the objective problem.Conclusions. The developed software system confirmed its efficiency for studying the parameters of hidden parallelism in arbitrary algorithms and rational use in data processing. The approach of using a scripting language to develop heuristic methods (scenarios) for the purposeful transformation of IGA forms showed great flexibility and transparency for the researcher. The target consumers of the developed methods for generating schedules for parallel execution of programs are, first of all, developers of translators and virtual machines, and researchers of the properties of algorithms (for identifying and exploiting the potential of their hidden parallelism). The developed software and methods have been successfully used for a number of years for increasing student competence in data processing parallelization at Russian universities.

Does Working Memory Capacity Predict Literal and Inferential Comprehension of Bilinguals’ Digital Reading in a Multitasking Setting?

The ubiquity of multitasking has led researchers to investigate its potential costs for reading and learning (Clinton‐Lisell, 2021). While some studies have not shown detrimental effects of multitasking for reading comprehension (Bowman et al., 2010; Cho et al., 2015; Pashler et al., 2013), one particular study has found a benefit of multitasking (Tran et al., 2013). These results, nevertheless, do not converge with the findings of recent meta-analyses, which have suggested both a negative effect of multitasking for reading comprehension (Clinton‐Lisell, 2021), as well as the disruptive effects of listening to lyrical music while reading for comprehension (Vasilev et al., 2018). Previous research seems to converge with the theories of how working memory copes with the complexity of reading as a process, since several subprocesses must be orchestrated so that the ultimate goal of reading – the construction of a mental representation – is fully achieved (Tomitch, 2020). In addition to that, no previous study has investigated reading as a multilevel construct in which both literal and inferential comprehension (Alptekin & Erçetin, 2010; Kintsch, 1998) is assessed in a multitasking setting. With that in mind, we investigated whether working memory capacity, measured by the Self-Administrable Reading Span Test (Oliveira et al., 2021), predicts proficient bilinguals’ performance in literal and inferential comprehension, by means of comprehension questions (Pearson & Johnson, 1978) and reading times, under a multitasking setting in two conditions – listening to lyrical music (experimental) as opposed to listening to non-lyrical music (control). Multiple linear regression analyses revealed that working memory capacity significantly predicted inferential, but not literal comprehension nor reading times, and only when participants were listening to lyrical music. Results are discussed both in terms of the effects of multitasking on reading comprehension as well as the role of working memory in language comprehension.

Efficient Multi Port-Based Teleportation Schemes

In this manuscript we analyse generalised port-based teleportation (PBT) schemes, allowing for transmitting more than one unknown quantum state (or a composite quantum state) in one go, where the state ends up in several ports at Bob’s side. We investigate the efficiency of our scheme discussing both deterministic and probabilistic case, where parties share maximally entangled states. It turns out that the new scheme gives better performance than various variants of the optimal PBT protocol used for the same task. All the results are presented in group-theoretic manner depending on such quantities like dimensions and multiplicities of irreducible representations in the Schur-Weyl duality. The presented analysis was possible by considering the algebra of permutation operators acting on <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> systems distorted by the action of partial transposition acting on more than one subsystem. Considering its action on the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n-$ </tex-math></inline-formula> fold tensor product of the Hilbert space with finite dimension, we present construction of the respective irreducible matrix representations, which are in fact matrix irreducible representations of the Walled Brauer Algebra. I turns out that the introduced formalism, and symmetries beneath it, appears in many aspects of theoretical physics and mathematics - theory of anti ferromagnetism, aspects of gravity theory or in the problem of designing quantum circuits for special task like for example inverting an unknown unitary.

Heterogeneous graph construction and node representation learning method of Treatise on Febrile Diseases based on graph convolutional network

ObjectiveTo construct symptom-formula-herb heterogeneous graphs structured Treatise on Febrile Diseases (Shang Han Lun,《伤寒论》) dataset and explore an optimal learning method represented with node attributes based on graph convolutional network (GCN). MethodsClauses that contain symptoms, formulas, and herbs were abstracted from Treatise on Febrile Diseases to construct symptom-formula-herb heterogeneous graphs, which were used to propose a node representation learning method based on GCN − the Traditional Chinese Medicine Graph Convolution Network (TCM-GCN). The symptom-formula, symptom-herb, and formula-herb heterogeneous graphs were processed with the TCM-GCN to realize high-order propagating message passing and neighbor aggregation to obtain new node representation attributes, and thus acquiring the nodes’ sum-aggregations of symptoms, formulas, and herbs to lay a foundation for the downstream tasks of the prediction models. ResultsComparisons among the node representations with multi-hot encoding, non-fusion encoding, and fusion encoding showed that the Precision@10, Recall@10, and F1-score@10 of the fusion encoding were 9.77%, 6.65%, and 8.30%, respectively, higher than those of the non-fusion encoding in the prediction studies of the model. ConclusionNode representations by fusion encoding achieved comparatively ideal results, indicating the TCM-GCN is effective in realizing node-level representations of heterogeneous graph structured Treatise on Febrile Diseases dataset and is able to elevate the performance of the downstream tasks of the diagnosis model.

Is the Reindeer Run Endless?

Abstract This article presents an anthropological analysis of the relationship between landscape, culture, and identity of Indigenous Peoples of the North of Yakutia. The topic of the study is focused on an important marker and resource of identity that encompasses the landscapes of the North, its physical, geographical, natural, and climatic features, the integrated system of northern occupations and traditional practices—the domestic reindeer. This research also considers various cultural texts and personal and collective narratives of the “imagination” and “experience” of the cold space associated with reindeer in the construction and modern representations of the ethnicity of Indigenous Peoples of the North.

Принципи та моделі експертно-аналітичної методології підтримки формування адаптивних організаційних рішень за умов глибокої невизначеності

The paper depicts and analyzes Expert-Analytical Methodology named EAM DMDU to support Proactive Anti-crisis Decisions within Organizational Systems under deep uncertainty. Complex tools are proposed for Decisions Domain Knowledge analytical operation. The Benefit is no essential resource demands while keeping the basic principles to deal with deep uncertainty (uncertainties and inconsisten- cies eliciting; Decision vulnerabilities searching instead prediction; threats resilience priority over effectiveness). EAM DMDU enables Deliberative multi-staged Process for Adaptive Decision forming aimed at expected future conflict situation solving. The Process stages are: Problem situation Analysis, Impact on Problem Situation Goal Proposition, Goal proposals Assessment; Efforts for Goal achieving Proposals; Effort Proposals Assessment; reference Proposal option Selection and Decision adaptations accordingly to Decision Frame changes Recommendation. Knowledge operation is enabled with the procedures such as: formal analysis, individual expert assessment, Decision elements deliberative forming. EAM DMDU common information space of is based on Domain Ontology and ensures equal participants’ awareness, expert judgments with their arguments constructive representation and knowledge reuse. Expert-analytical Selection of Proposals uses their Perspectivity Model. It is a sub-goals hierarchy to achieve the goal being formed over previous Process stages. Hierarchy knot is represented with ontologically formalized definition for State of the Art corresponding sub-goal achievement. Leaf node depicts State of the Art with explicit expert Estimates of Certainty factor (from the Stanford model) being provided concerning its implementation through Decision element Proposal being assessed. The Estimate’s arguments are elements of information space used by expert. Under incomplete certainty of element expert provides its boundary values and State of the Art estimates both pessimistic and optimistic. Perspectivity Model contains also conditions for goal achievement violation being caused with environmental threats. Procedures for Estimates formal integration up to Model provide extreme estimates of Proposals Perspectivity and Robustness regarding current uncertainty. Under unsatisfactory properties of integrated Estimates their deliberative adjustment is carried out using Uncertainty Map and arguments provided. The final reference Decision contains selected Goal-Means option and guides to adapt it when decision frame changes. Further research is carried out for EAM DMDU instrumental tools development and its usage for defense resource management.

On the evaluation of disease progression modelling in Alzheimer's Disease

AbstractBackgroundAlzheimer's Disease (AD) is a heterogeneous condition that can be viewed as a continuum involving multiple stages from cognitively normal to mild cognitive impairment and finally dementia. Recent works in Disease Progression Modelling (DPM) have attempted to use biomarkers to construct representations of progression that are more informative of patients' status than clinical diagnosis alone. However, there is no clear consensus (Figure 1) regarding the choice of evaluation methods or metrics to facilitate model comparison. We propose the use a simple, universally applicable biomarker‐based baseline to estimate patient‐realigning time‐shifts and subsequently evaluate it against multiple released DPM methods.MethodWe computed an abnormality score for 2439 patients from the Alzheimer's Disease Neuroimaging Initiative (ADNI) by averaging the normalised values collected for 12 biomarkers representative of amyloid, tau, neurodegeneration, and cognition. Abnormality ranges were determined from 251 amyloid‐positive patients. These scores were compared to values from published DPM models (Figure 3). Additionally, all methods were benchmarked in different ways, including diagnosis classification and cluster analysis.ResultWe found that, despite its simplicity, our abnormality score reasonably separated patients according to their diagnosis (Figure 2). Computed scores also correlated significantly with those of other methods (Figure 3, Pearson correlations up to 0.891). While our approach only required cross‐sectional information, other methods rely on longitudinal data. Our method performed similarly to others in the cutoff‐based disease classification task, with test F1‐scores of 0.734 and 0.890 in the harder tasks of CN/MCI and AD/MCI, respectively (Table 1). In a three‐class setting, all methods including our baseline showed a good level of agreement, with Rand indices all above 0.6 (Figure 4).ConclusionA significant challenge in DPM for AD lies in estimating a proxy for patient realignment, which is crucial to describe individuals on a common disease continuum. We have proposed a method to calculate an abnormality score at the baseline visit, which can be trivially extended to longitudinal data and help interpret progression in follow‐ups. We hope that future work considers more principled evaluation procedures, facilitating meaningful comparisons between DPMs.

Bodily Practices and Healthy Bodies: Representations of Gymnastics in a Brazilian Women’s Magazine (1940–1950)

This research aims to understand the influence of bodily practices, especially gymnastics, in the construction of representations of a healthy body conveyed in a Brazilian women's magazine in the 1940s and 1950s. We use records from the Jornal das Moças magazine for the analysis based on the theoretical and methodological assumptions of cultural history. The results show that gymnastics for women was linked to body maintenance and used as a tool for establishing a body standard, thus disciplining and shapingthe construction of women's health concepts, determined by the aesthetic bias of that period: a slim body as an ideal standard of beauty and health.

Do visual constructs in social science textbooks evince gender stereotypes and bias? A case study from India

ABSTRACT India presents a heterogeneous socio-economic ethos, rooted within structures of patriarchy and caste, rendering any transformation of traditional gender roles, increasingly challenging. Gender socialisation begins in childhood and is assimilated through schools. Students imbibe gender concepts through textbooks and classroom experiences, which either reinforce their social perceptions or influence them to critique inequalities and bias. Adopting a multi-pronged approach through feminist critical discourse analysis (FCDA) and content analysis, this research evaluates the images used in Indian school social science textbooks, for constructs of gender representation, structures, and stereotyping. The research reveals that gender structures depicted in textbooks foster patriarchy and gender bias. There is minimal effort to depict feminist activism and little scope to foster gender reflexivity and social debate, which only sustains stereotypical perceptions of gender roles within Indian society.

Multi-switches and representations of braid groups

We introduce the notion of a (virtual) multi-switch which generalizes the notion of a (virtual) switch. Using (virtual) multi-switches we introduce a general approach of how to construct representations of (virtual) braid groups by automorphisms of algebraic systems. As a corollary we introduce new representations of virtual braid groups which generalize several previously known representations.

Psychology of home and Ukrainian migrants’ socio-psychological adaptation abroad

Study goal and methods. Study of the course of socio-psychological adaptation of Ukrainian refugees abroad, their perceptions of home and host country, as well as intergroup interaction between Ukrainian refugees and the autochthonous population. The research was conducted within the framework of the scientific approach to intergroup interaction as the dynamics of conscious and unconscious. Case study of narratives of Ukrainian migrants as a form of representation of individual meanings and thematic construction of experience was conducted. Conclusions. A structured life world that integrates the experience associated with the evacuation of refugees from Ukraine and the new stage of life abroad, based on the construction of personal experience into meaningful event blocks, is a prerequisite for successful socio-psychological adaptation and acculturation in the host country. During integration into the host society migrants learn new relevant communicative and social roles. Group support provided to refugees by other Ukrainians in a similar situation as well as by representatives of the host country and volunteers is of great importance. The limitations of the study are related to the situational nature of narrative interviews, the variability of events and meanings that are significant for the individual at the moment. Prospects for further research include the study of age-specific features of socio-psychological adaptation abroad and the temporal dynamics of this process. Practical Importance. Data from the original descriptive study of the socio-psychological processes of acculturation indicate the importance of group support and experience construction in overcoming stress and can be used in the provision of psychosocial support to Ukrainian military migrants

Masonry in the Context of Sustainable Buildings: A Review of the Brick Role in Architecture

The process of combining various parts to create a structure is called building. The most effective and significant component of any construction is masonry. The Colosseum, buildings from ancient Greece and Rome, Central American buildings, and Mycenaean structures all used this material as one of their primary building elements. The oldest form is dry masonry of irregularly shaped stones. The ecological qualities of masonry, as a restorative material with a low impact on the environment, as well as the environmental control capacity of the massive wall, bring masonry back to attention as a suitable material for sustainable building in the context of current concerns for sustainable architecture. This article takes the form of a review of the journey of masonry as the primary construction material—from prehistoric structures to modern-day edifices. This article will go through the fundamentals of masonry construction to support its usage in structures throughout history and in many architectural styles, as a crucial representation of human construction in architectural history. This article aims to create a historical review, presenting masonry as an essential building material and assessing its role in the history of building materials.

Airy sheaves for reductive groups

We construct a class of ℓ $\ell$ -adic local systems on A 1 $\mathbb {A}^1$ that generalizes the Airy sheaves defined by N. Katz to reductive groups. These sheaves are finite field analogues of generalizations of the classical Airy equation y ′ ′ ( z ) = z y ( z ) $y^{\prime \prime }(z)=zy(z)$ . We employ the geometric Langlands correspondence to construct the sought-after local systems as eigenvalues of certain rigid Hecke eigensheaves, following the methods developed by Heinloth, Ngô, and Yun. The construction is motivated by a special case of Adler and Yu's construction of tame supercuspidal representations. The representations that we consider can be viewed as deeper analogues of simple supercuspidals. For GL n $\mathrm{GL}_n$ , we compute the Frobenius trace of the local systems in question and show that they agree with Katz's Airy sheaves. We make precise conjectures about the ramification behavior of the local systems at ∞ $\infty$ . These conjectures, in particular, imply cohomological rigidity of Airy sheaves.

Mapping Modern JVM Language Code to Analysis-Friendly Graphs: A Study with Kotlin

Kotlin is a modern JVM language, gaining adoption rapidly and becoming Android official programming language. With its wide usage, the need for code analysis of Kotlin is increasing. Exposing code semantics explicitly with a properly structured format is the first step in code analysis and the construction of such representation is the foundation for downstream tasks. Recently, graph-based approaches became a promising way of encoding source code semantics. However, this work mainly focuses on representation learning with limited interpretability and shallow domain knowledge. The known evolvements of code semantics in new-generation programming languages have been overlooked. How to establish an effective mapping between naturally concise Kotlin source code with graph-based representation needs to be studied by analyzing known language features. Moreover, the feasibility of enhancing the mapping with code semantics automatically learned from the program needs to be explored. In this paper, we first propose a first-sight, rule-based mapping method, using composite representation with AST, CFG, DFG and language features. To examine the possibility of exposing code semantics in the mapped graph, we use Latent Semantic Indexing-based source code summarization to learn more features of each method, and then enrich the attributes of the corresponding node in the graph. We evaluate these mapping strategies with comparative experiments by simulating a code search solution as a downstream task. The experiment result shows that the graph-based method with built-in language features outperforms the text-based way without introducing greater complexity. Comparative experiments also prove that adding code semantics to the graph benefits the capacity of downstream tasks. When exploring the whole mapping process, our study explicitly revealed the practical barriers to extracting and exposing the hidden semantics from Kotlin source code, which may help enlighten source code representations for other modern languages.