Search results for: Equivalent transformation

Authors: G. Candel, D. Naccache

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t-SNE is an embedding method that the data science community has widely used. It helps two main tasks: to display results by coloring items according to the item class or feature value; and for forensic, giving a first overview of the dataset distribution. Two interesting characteristics of t-SNE are the structure preservation property and the answer to the crowding problem, where all neighbors in high dimensional space cannot be represented correctly in low dimensional space. t-SNE preserves the local neighborhood, and similar items are nicely spaced by adjusting to the local density. These two characteristics produce a meaningful representation, where the cluster area is proportional to its size in number, and relationships between clusters are materialized by closeness on the embedding. This algorithm is non-parametric. The transformation from a high to low dimensional space is described but not learned. Two initializations of the algorithm would lead to two different embedding. In a forensic approach, analysts would like to compare two or more datasets using their embedding. A naive approach would be to embed all datasets together. However, this process is costly as the complexity of t-SNE is quadratic, and would be infeasible for too many datasets. Another approach would be to learn a parametric model over an embedding built with a subset of data. While this approach is highly scalable, points could be mapped at the same exact position, making them indistinguishable. This type of model would be unable to adapt to new outliers nor concept drift. This paper presents a methodology to reuse an embedding to create a new one, where cluster positions are preserved. The optimization process minimizes two costs, one relative to the embedding shape and the second relative to the support embedding’ match. The embedding with the support process can be repeated more than once, with the newly obtained embedding. The successive embedding can be used to study the impact of one variable over the dataset distribution or monitor changes over time. This method has the same complexity as t-SNE per embedding, and memory requirements are only doubled. For a dataset of n elements sorted and split into k subsets, the total embedding complexity would be reduced from O(n2) to O(n2/k), and the memory requirement from n2 to 2(n/k)2 which enables computation on recent laptops. The method showed promising results on a real-world dataset, allowing to observe the birth, evolution and death of clusters. The proposed approach facilitates identifying significant trends and changes, which empowers the monitoring high dimensional datasets’ dynamics.

Keywords: Concept drift, data visualization, dimension reduction, embedding, monitoring, reusability, t-SNE, unsupervised learning.

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Authors: R. Clancy, M. Ahern, D. O’Sullivan, K. Bruton

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The manufacturing industry is currently undergoing a digital transformation as part of the mega-trend Industry 4.0. As part of this phase of the industrial revolution, traditional manufacturing processes are being combined with digital technologies to achieve smarter and more efficient production. To successfully digitally transform a manufacturing facility, the processes must first be digitized. This is the conversion of information from an analogue format to a digital format. The objective of this study was to explore the research area of digitizing manufacturing data as part of the worldwide paradigm, Industry 4.0. The formal methodology of a systematic mapping study was utilized to capture a representative sample of the research area and assess its current state. Specific research questions were defined to assess the key benefits and limitations associated with the digitization of manufacturing data. Research papers were classified according to the type of research and type of contribution to the research area. Upon analyzing 54 papers identified in this area, it was noted that 23 of the papers originated in Germany. This is an unsurprising finding as Industry 4.0 is originally a German strategy with supporting strong policy instruments being utilized in Germany to support its implementation. It was also found that the Fraunhofer Institute for Mechatronic Systems Design, in collaboration with the University of Paderborn in Germany, was the most frequent contributing Institution of the research papers with three papers published. The literature suggested future research directions and highlighted one specific gap in the area. There exists an unresolved gap between the data science experts and the manufacturing process experts in the industry. The data analytics expertise is not useful unless the manufacturing process information is utilized. A legitimate understanding of the data is crucial to perform accurate analytics and gain true, valuable insights into the manufacturing process. There lies a gap between the manufacturing operations and the information technology/data analytics departments within enterprises, which was borne out by the results of many of the case studies reviewed as part of this work. To test the concept of this gap existing, the researcher initiated an industrial case study in which they embedded themselves between the subject matter expert of the manufacturing process and the data scientist. Of the papers resulting from the systematic mapping study, 12 of the papers contributed a framework, another 12 of the papers were based on a case study, and 11 of the papers focused on theory. However, there were only three papers that contributed a methodology. This provides further evidence for the need for an industry-focused methodology for digitizing and analyzing manufacturing data, which will be developed in future research.

Keywords: Analytics, digitization, industry 4.0, manufacturing.

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Authors: Victoria L. Nkosi, Parvaneh Farhangpour

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Often a Grade 12 certificate is perceived as a passport to tertiary education and the minimum requirement to enter the world of work. In spite of its importance, many students do not make this milestone in South Africa. It is important to find out why so many students still fail in spite of transformation in the education system in the post-apartheid era. Given the complexity of education and its context, this study adopted a case study design to examine one historically underperforming high school in Bushbuckridge, Mpumalanga Province, South Africa in 2013. The aim was to gain a understanding of the inner and outer school contextual factors associated with the high failure rate among Grade 12 students.  Government documents and reports were consulted to identify factors in the district and the village surrounding the school and a student survey was conducted to identify school, home and student factors. The randomly-sampled half of the population of Grade 12 students (53) participated in the survey and quantitative data are analyzed using descriptive statistical methods. The findings showed that a host of factors is at play. The school is located in a village within a municipality which has been one of the poorest three municipalities in South Africa and the lowest Grade 12 pass rate in the Mpumalanga province.   Moreover, over half of the families of the students are single parents, 43% are unemployed and the majority has a low level of education. In addition, most families (83%) do not have basic study materials such as a dictionary, books, tables, and chairs. A significant number of students (70%) are over-aged (+19 years old); close to half of them (49%) are grade repeaters. The school itself lacks essential resources, namely computers, science laboratories, library, and enough furniture and textbooks. Moreover, teaching and learning are negatively affected by the teachers’ occasional absenteeism, inadequate lesson preparation, and poor communication skills. Overall, the continuous low performance of students in this school mirrors the vicious circle of multiple negative conditions present within and outside of the school. The complexity of factors associated with the underperformance of Grade 12 students in this school calls for a multi-dimensional intervention from government and stakeholders. One important intervention should be the placement of over-aged students and grade-repeaters in suitable educational institutions for the benefit of other students.

Keywords: Inner context, outer context, over-aged students, vicious circle.

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Authors: E. J. Cilliers

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It is the living conditions in the cities that determine the future of our livelihood. “To change life, we must first change space"- Henri Lefebvre. Sustainable development is a utopian aspiration for South African cities (especially the case study of the Gauteng City Region), which are currently characterized by unplanned growth and increasing urban sprawl. While the reasons for poor environmental quality and living conditions are undoubtedly diverse and complex, having political, economical and social dimensions, it is argued that the prevailing approach to layout planning in South Africa is part of the problem. This article seeks a solution to the problem of sustainability, from a spatial planning perspective. The spatial planning tool, the urban development boundary, is introduced as the concept that will ensure empty talk being translated into a sustainable vision. The urban development boundary is a spatial planning tool that can be used and implemented to direct urban growth towards a more sustainable form. The urban development boundary aims to ensure planned urban areas, in contrast to the current unplanned areas characterized by urban sprawl and insufficient infrastructure. However, the success of the urban development boundary concept is subject to effective implementation measures, as well as adequate and efficient management. The concept of sustainable development can function as a driving force underlying societal change and transformation, but the interface between spatial planning and environmental management needs to be established (as this is the core aspects underlying sustainable development), and authorities needs to understand and implement this interface consecutively. This interface can, however, realize in terms of the objectives of the planning tool – the urban development boundary. The case study, the Gauteng City Region, is depicted as a site of economic growth and innovation, but there is a lack of good urban and regional governance, impacting on the design (layout) and function of urban areas and land use, as current authorities make uninformed decisions in terms of development applications, leading to unsustainable urban forms and unsustainable nodes. Place and space concepts are thus critical matters applicable to planning of the Gauteng City Region. The urban development boundary are thus explored as a planning tool to guide decision-making, and create a sustainable urban form, leading to better environmental and living conditions, and continuous sustainability.

Keywords: Urban planning, sustainable urban form, urbandevelopment boundary, planning tool.

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Authors: Malte Brettel, Niklas Friederichsen, Michael Keller, Marius Rosenberg

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The German manufacturing industry has to withstand an increasing global competition on product quality and production costs. As labor costs are high, several industries have suffered severely under the relocation of production facilities towards aspiring countries, which have managed to close the productivity and quality gap substantially. Established manufacturing companies have recognized that customers are not willing to pay large price premiums for incremental quality improvements. As a consequence, many companies from the German manufacturing industry adjust their production focusing on customized products and fast time to market. Leveraging the advantages of novel production strategies such as Agile Manufacturing and Mass Customization, manufacturing companies transform into integrated networks, in which companies unite their core competencies. Hereby, virtualization of the process- and supply-chain ensures smooth inter-company operations providing real-time access to relevant product and production information for all participating entities. Boundaries of companies deteriorate, as autonomous systems exchange data, gained by embedded systems throughout the entire value chain. By including Cyber-Physical-Systems, advanced communication between machines is tantamount to their dialogue with humans. The increasing utilization of information and communication technology allows digital engineering of products and production processes alike. Modular simulation and modeling techniques allow decentralized units to flexibly alter products and thereby enable rapid product innovation. The present article describes the developments of Industry 4.0 within the literature and reviews the associated research streams. Hereby, we analyze eight scientific journals with regards to the following research fields: Individualized production, end-to-end engineering in a virtual process chain and production networks. We employ cluster analysis to assign sub-topics into the respective research field. To assess the practical implications, we conducted face-to-face interviews with managers from the industry as well as from the consulting business using a structured interview guideline. The results reveal reasons for the adaption and refusal of Industry 4.0 practices from a managerial point of view. Our findings contribute to the upcoming research stream of Industry 4.0 and support decision-makers to assess their need for transformation towards Industry 4.0 practices. 

Keywords: Industry 4.0., Mass Customization, Production networks, Virtual Process-Chain.

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Authors: Francis Deinmodei W. Poazi, Jasmine O. Tamunosiki-Amadi, Maurice Fems

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In recent times the resource-based view (RBV) of strategic management has recorded a sizeable attention yet there has not been a considerable scholarly and managerial discourse, debate and attention. As a result, this paper gives special bit of critical reasoning as well as top-notch analyses and relationship between RBV and organizational innovation. The study examines those salient aspects of RBV that basically have the will power in ensuring the organization's capacity to go for innovative capability. In achieving such fit and standpoint, the paper joins other relevant academic discourse and empirical evidence. To this end, a reasonable amount of contributions in setting the ground running for future empirical researches would have been provided. More so, the study is guided and built on the following strength and significance: Firstly, RBV sees resources as heterogeneity which forms a strong point of strength and allows organisations to gain competitive advantage. In order words, competitive advantage can be achieved or delivered to the organization when resources are distinctively utilized in a valuable manner more than the envisaged competitors of the organization. Secondly, RBV is significantly influential in determining the real resources that are available in the organization with a view to locate capabilities within in order to attract more profitability into the organization when applied. Thus, there will be more sustainable growth and success in the ever competitive and emerging market. Thus, to have succinct description of the basic methodologies, the study adopts both qualitative as well as quantitative approach with a view to have a broad samples of opinion in establishing and identifying key and strategic organizational resources to enable managers of resources to gain a competitive advantage as well as generating a sustainable increase and growth in profit. Furthermore, a comparative approach and analysis was used to examine the performance of RBV within the organization. Thus, the following are some of the findings of the study: it is clear that there is a nexus between RBV and growth of competitively viable organizations. More so, in most parts, organizations have heterogeneous resources domiciled in their organizations but not all organizations as it was specifically and intelligently adopting the tenets of RBV to strengthen heterogeneity of resources which allows organisations to gain competitive advantage. Other findings of this study reveal that of managerial perception of RBV with respect to application and transformation of resources to achieve a profitable end. It is against this backdrop, the importance of RBV cannot be overemphasized; the study is strongly convinced and think that RBV view is one focal and distinct approach that is focused on internal to outside strategy which engenders sourcing or generating resources internally as well as having the quest to apply such internally sourced resources diligently to increase or gain competitive advantage.

Keywords: Competitive advantage, innovation, organisation, recognition, resource-based view.

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Authors: Lorenzo Casagrande, Antonio Bonati, Ferdinando Auricchio, Antonio Occhiuzzi

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This paper summarizes the results of a survey on smart non-structural element dynamic dissipation when installed in modern high-rise mega-frame prototypes. An innovative glazed curtain wall was designed using Shape Memory Alloy (SMA) joints in order to increase the energy dissipation and enhance the seismic/wind response of the structures. The studied buildings consisted of thirty- and sixty-storey planar frames, extracted from reference three-dimensional steel Moment Resisting Frame (MRF) with outriggers and belt trusses. The internal core was composed of a CBF system, whilst outriggers were placed every fifteen stories to limit second order effects and inter-storey drifts. These structural systems were designed in accordance with European rules and numerical FE models were developed with an open-source code, able to account for geometric and material nonlinearities. With regard to the characterization of non-structural building components, full-scale crescendo tests were performed on aluminium/glass curtain wall units at the laboratory of the Construction Technologies Institute (ITC) of the Italian National Research Council (CNR), deriving force-displacement curves. Three-dimensional brick-based inelastic FE models were calibrated according to experimental results, simulating the fac¸ade response. Since recent seismic events and extreme dynamic wind loads have generated the large occurrence of non-structural components failure, which causes sensitive economic losses and represents a hazard for pedestrians safety, a more dissipative glazed curtain wall was studied. Taking advantage of the mechanical properties of SMA, advanced smart joints were designed with the aim to enhance both the dynamic performance of the single non-structural unit and the global behavior. Thus, three-dimensional brick-based plastic FE models were produced, based on the innovated non-structural system, simulating the evolution of mechanical degradation in aluminium-to-glass and SMA-to-glass connections when high deformations occurred. Consequently, equivalent nonlinear links were calibrated to reproduce the behavior of both tested and smart designed units, and implemented on the thirty- and sixty-storey structural planar frame FE models. Nonlinear time history analyses (NLTHAs) were performed to quantify the potential of the new system, when considered in the lateral resisting frame system (LRFS) of modern high-rise MRFs. Sensitivity to the structure height was explored comparing the responses of the two prototypes. Trends in global and local performance were discussed to show that, if accurately designed, advanced materials in non-structural elements provide new sources of energy dissipation.

Keywords: Advanced technologies, glazed curtain walls, non-structural elements, seismic-action reduction, shape memory alloy.

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Authors: Michal Lysek, Mike Danilovic, Jasmine Lihua Liu

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HMS Industrial Networks AB has been recognized as one of the most innovative companies in the industrial communication industry worldwide. The creation of their Anybus innovation during the 1990s contributed considerably to the company’s success. From inception, HMS’ employees were innovating for the purpose of creating new business (the creation phase). After the Anybus innovation, they began the process of internationalization (the commercialization phase), which in turn led them to concentrate on cost reduction, product quality, delivery precision, operational efficiency, and increasing growth (the growth phase). As a result of this transformation, performing new radical innovations have become more complicated. The purpose of our research was to explore the dynamics of innovation at HMS from the aspect of key actors, activities, and events, over the three phases, in order to understand what led to the creation of their Anybus innovation, and why it has become increasingly challenging for HMS to create new radical innovations for the future. Our research methodology was based on a longitudinal, retrospective study from the inception of HMS in 1988 to 2014, a single case study inspired by the grounded theory approach. We conducted 47 interviews and collected 1 024 historical documents for our research. Our analysis has revealed that HMS’ success in creating the Anybus, and developing a successful business around the innovation, was based on three main capabilities – cultivating customer relations on different managerial and organizational levels, inspiring business relations, and balancing complementary human assets for the purpose of business creation. The success of HMS has turned the management’s attention away from past activities of key actors, of their behavior, and how they influenced and stimulated the creation of radical innovations. Nowadays, they are rhetorically focusing on creativity and innovation. All the while, their real actions put emphasis on growth, cost reduction, product quality, delivery precision, operational efficiency, and moneymaking. In the process of becoming an international company, HMS gradually refocused. In so doing they became profitable and successful, but they also forgot what made them innovative in the first place. Fortunately, HMS’ management has come to realize that this is the case and they are now in search of recapturing innovation once again. Our analysis indicates that HMS’ management is facing several barriers to innovation related path dependency and other lock-in phenomena. HMS’ management has been captured, trapped in their mindset and actions, by the success of the past. But now their future has to be secured, and they have come to realize that moneymaking is not everything. In recent years, HMS’ management have begun to search for innovation once more, in order to recapture their past capabilities for creating radical innovations. In order to unlock their managerial perceptions of customer needs and their counter-innovation driven activities and events, to utilize the full potential of their employees and capture the innovation opportunity for the future.

Keywords: Barriers to innovation, dynamics of innovation, in search of excellence and innovation, radical innovation.

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Authors: Joan Antony

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Outcome in any learning process should target three goals – propelling the underachiever’s engagement in the learning process, enhancing the drive to achieve, and modifying attitudes and beliefs in his/her capabilities. An intervention study with a three-pronged approach incorporating self-regulatory training targeting three categories of strategies – cognitive, metacognitive and motivational – was designed adopting the before and after control-experimental group design. The evaluation of the training process was based on pre- and post-intervention measures obtained through three indices of measurement – academic scores based on grades on school examinations and comprehension tests, affective variables scores and level of strategy use obtained through responses on scales and questionnaires, and content analysis of subjective responses to open-ended probes. The evaluation relied on three sources – student, teacher and parent. The t-test results for the experimental and control groups on the pre- and post-intervention measurements indicate a significant increase on comprehension tasks for the experimental group. Though statistically significant difference was not found on the school examination scores for the experimental group, there was considerable decline in performance for the control group. Analysis of covariance (ANCOVA) was applied on the scores obtained on affective variables, namely, self-esteem, personal achievement goals, personal ego goals, personal task goals, and locus of control. The experimental group showed increase in personal achievement goals and personal ego goals as compared to the control group. Responses given by the experimental group to the open-ended probes on causal attributions indicated a considerable shift from external to internal causes when moving from the pre- to post-intervention stage. ANCOVA results revealed significantly higher use of learning strategies inclusive of mental learning strategies, behavioral learning strategies, self-regulatory strategies, and an improvement in study orientation encompassing study habits and study attitudes among the experimental group students. Parents and teachers reported significant progressive transformation towards constructive engagement with study material and self-imposed regulation. The implications of this study are three-fold: firstly, strategies training (cognitive, metacognitive and motivational) should be embedded into daily classroom routine; secondly, scaffolding by teachers through activities based on curriculum will eventually enable students to rely more on their own judgements of effective strategy use; thirdly, enhanced confidence will radiate to the affective aspects with enduring effects on other domains of life as well. The cyclic nature of the interaction between utilizing one’s resources, managing effort and regulating emotions forms the foundation for academic achievement.

Keywords: Academic achievement, cognitive strategies, metacognitive strategies, motivational strategies.

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Authors: Igor Guatelli

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The universe of aesthetic perception entails impasses about sensitive divergences that each text or visual object may be subjected to. If approached through intertextuality that is not based on the misleading notion of kinships or similarities a priori admissible, the possibility of anachronistic, heterogeneous - and non-diachronic - assemblies can enhance the emergence of interval movements, intermediate, and conflicting, conducive to a method of reading, interpreting, and assigning meaning that escapes the rigid antinomies of the mere being and non-being of things. In negative, they operate in a relationship built by the lack of an adjusted meaning set by their positive existences, with no remainders; the generated interval becomes the remnant of each of them; it is the opening that obscures the stable positions of each one. Without the negative of absence, of that which is always missing or must be missing in a text, concept, or image made positive by history, nothing is perceived beyond what has been already given. Pairings or binary oppositions cannot lead only to functional syntheses; on the contrary, methodological disturbances accumulated by the approximation of signs and entities can initiate a process of becoming as an opening to an unforeseen other, transformation until a moment when the difficulties of [re]conciliation become the mainstay of a future of that sign/entity, not envisioned a priori. A counter-history can emerge from these unprecedented, misadjusted approaches, beginnings of unassigned injunctions and disjunctions, in short, difficult alliances that open cracks in a supposedly cohesive history, chained in its apparent linearity with no remains, understood as a categorical historical imperative. Interstices are minority fields that, because of their opening, are capable of causing opacity in that which, apparently, presents itself with irreducible clarity. Resulting from an incomplete and maladjusted [at the least dual] marriage between the signs/entities that originate them, this interval may destabilize and cause disorder in these entities and their own meanings. The interstitials offer a hyphenated relationship: a simultaneous union and separation, a spacing between the entity’s identity and its otherness or, alterity. One and the other may no longer be seen without the crack or fissure that now separates them, uniting, by a space-time lapse. Ontological, semantic shifts are caused by this fissure, an absence between one and the other, one with and against the other. Based on an improbable approximation between some conceptual and semantic shifts within the design production of architect Rem Koolhaas and the textual production of the philosopher Jacques Derrida, this article questions the notion of unity, coherence, affinity, and complementarity in the process of construction of thought from these ontological, epistemological, and semiological fissures that rattle the signs/entities and their stable meanings. Fissures in a thought that is considered coherent, cohesive, formatted are the negativity that constitutes the interstices that allow us to move towards what still remains as non-identity, which allows us to begin another story.

Keywords: Clearing, interstice, negative, remnant, spectrum.

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Authors: Moustafa Osman Mohammed

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This paper introduces topological order in descried social systems starting with the original concept of autopoiesis by biologists and scientists, including the modification of general systems based on socialized medicine. Topological order is important in describing the physical systems for exploiting optical systems and improving photonic devices. The stats of topologically order have some interesting properties of topological degeneracy and fractional statistics that reveal the entanglement origin of topological order, etc. Topological ideas in photonics form exciting developments in solid-state materials, that being; insulating in the bulk, conducting electricity on their surface without dissipation or back-scattering, even in the presence of large impurities. A specific type of autopoiesis system is interrelated to the main categories amongst existing groups of the ecological phenomena interaction social and medical sciences. The hypothesis, nevertheless, has a nonlinear interaction with its natural environment ‘interactional cycle’ for exchange photon energy with molecules without changes in topology (i.e., chemical transformation into products do not propagate any changes or variation in the network topology of physical configuration). The engineering topology of a biosensor is based on the excitation boundary of surface electromagnetic waves in photonic band gap multilayer films. The device operation is similar to surface Plasmonic biosensors in which a photonic band gap film replaces metal film as the medium when surface electromagnetic waves are excited. The use of photonic band gap film offers sharper surface wave resonance leading to the potential of greatly enhanced sensitivity. So, the properties of the photonic band gap material are engineered to operate a sensor at any wavelength and conduct a surface wave resonance that ranges up to 470 nm. The wavelength is not generally accessible with surface Plasmon sensing. Lastly, the photonic band gap films have robust mechanical functions that offer new substrates for surface chemistry to understand the molecular design structure, and create sensing chips surface with different concentrations of DNA sequences in the solution to observe and track the surface mode resonance under the influences of processes that take place in the spectroscopic environment. These processes led to the development of several advanced analytical technologies, which are automated, real-time, reliable, reproducible and cost-effective. This results in faster and more accurate monitoring and detection of biomolecules on refractive index sensing, antibody–antigen reactions with a DNA or protein binding. Ultimately, the controversial aspect of molecular frictional properties is adjusted to each other in order to form unique spatial structure and dynamics of biological molecules for providing the environment mutual contribution in investigation of changes due the pathogenic archival architecture of cell clusters.

Keywords: autopoiesis, engineering topology, photonic system molecular structure, biosensor

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Authors: Natalia Podkhodova, Olga Sheremeteva, Mariia Soldaeva

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Creating favourable conditions for students’ comprehension of mathematical content is one of the primary problems in teaching mathematics in secondary school. The fact of comprehension includes the ability to build a working situational model and thus becomes an important means of solving mathematical problems. This paper describes a holistic approach to teaching mathematics designed to address the primary challenges of such teaching; specifically, the challenge of students’ comprehension. Essentially, this approach consists of (1) establishing links between the attributes of the notion: the sense, the meaning, and the term; (2) taking into account the components of student’s subjective experience—value-based emotions, contextual, procedural and communicative—during the educational process; (3) linking together different ways to present mathematical information; (4) identifying and leveraging the relationships between real, perceptual and conceptual (scientific) mathematical spaces by applying real-life situational modelling. The article describes approaches to the practical use of these foundational concepts. Identifying how proposed methods and techniques influence understanding of material used in teaching mathematics was the primary goal. The study included an experiment in which 256 secondary school students took part: 142 in the study group and 114 in the control group. All students in these groups had similar levels of achievement in math and studied math under the same curriculum. In the course of the experiment, comprehension of two topics — “Derivative” and “Trigonometric functions”—was evaluated. Control group participants were taught using traditional methods. Students in the study group were taught using the holistic method: under teacher’s guidance, they carried out assignments designed to establish linkages between notion’s characteristics, to convert information from one mode of presentation to another, as well as assignments that required the ability to operate with all modes of presentation. Identification, accounting for and transformation of subjective experience were associated with methods of stimulating the emotional value component of the studied mathematical content (discussions of lesson titles, assignments aimed to create study dominants, performing theme-related physical exercise ...) The use of techniques that forms inter-subject notions based on linkages between, perceptual real and mathematical conceptual spaces proved to be of special interest to the students. Results of the experiment were analysed by presenting students in each of the groups with a final test in each of the studied topics. The test included assignments that required building real situational models. Statistical analysis was used to aggregate test results. Pierson criterion x2 was used to reveal statistics significance of results (pass-fail the modelling test). Significant difference of results was revealed (p < 0.001), which allowed to conclude that students in the study group showed better comprehension of mathematical information than those in the control group. The total number of completed assignments of each student was analysed as well, with average results calculated for each group. Statistical significance of result differences against the quantitative criterion (number of completed assignments) was determined using Student’s t-test, which showed that students in the study group completed significantly more assignments than those in the control group (p = 0.0001). Authors thus come to the conclusion that suggested increase in the level of comprehension of study material took place as a result of applying implemented methods and techniques.

Keywords: Comprehension of mathematical content, holistic approach to teaching mathematics in secondary school, subjective experience, technology of the formation of inter-subject notions.

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