Complex and Hypercomplex Discrete Fourier Transforms Based on Matrix Exponential Form of Euler's Formula

We show that the discrete complex, and numerous hypercomplex, Fourier transforms defined and used so far by a number of researchers can be unified into a single framework based on a matrix exponential version of Euler's formula $e^{j\theta}=\cos\theta+j\sin\theta$, and a matrix root of -1 isomorphic to the imaginary root $j$. The transforms thus defined can be computed using standard matrix multiplications and additions with no hypercomplex code, the complex or hypercomplex algebra being represented by the form of the matrix root of -1, so that the matrix multiplications are equivalent to multiplications in the appropriate algebra. We present examples from the complex, quaternion and biquaternion algebras, and from Clifford algebras Cl1,1 and Cl2,0. The significance of this result is both in the theoretical unification, and also in the scope it affords for insight into the structure of the various transforms, since the formulation is such a simple generalization of the classic complex case. It also shows that hypercomplex discrete Fourier transforms may be computed using standard matrix arithmetic packages without the need for a hypercomplex library, which is of importance in providing a reference implementation for verifying implementations based on hypercomplex code.Comment: The paper has been revised since the second version to make some of the reasons for the paper clearer, to include reviews of prior hypercomplex transforms, and to clarify some points in the conclusion

Põllumajandus rahvatarkuse ja teaduse vahel: folkloristi vaade

On Agricultural Sciences through the Eyes of aFolkloristAgriculture is based on understanding and respecting the patterns of nature, and the direct utilisation of nature. The ecological behavioural culture of a dweller of the land, which involves both communion with nature and taking responsibility for one’s part in the relationship, is rooted deep in our subconscious. Both a farmer and cattle breeder have harnessed the fruitfulness of the soil or the reproductionof cattle for their purposes. The scientific and technological development of agriculture is supported by basic and applied sciences. The sciences that served as the basis of agricultural technology began to evolve in the 18th and 19th century. Practical agricultural guidebooks in the first half of the 18th century still imparted old experiences. The guidelines provided often originated from Ancient Roman authorsand the Bible. As traditional and science-based agriculture began to develop separately, the 19th century brought along a breakthrough. The development of technology changes society as well as nature. Technology adapts to the needs and expectations of people and society, while it becomes easier to attain and operate. Education, upbringing,and culture as a whole will change in addition to the alteration of technology pursuant to the demands of people and culture.Science is becoming more important in order to provide enough food for all the inhabitants of the Earth in modernity as the population of the Earth is consistently growing, there is only a limited amount of agricultural land and climate change is causing regional production problems as well as uncertainty. Synthetic analogues are increasingly used in addition to the raw produce received from agriculture. As canbe said on the basis of analysing Internet forums—it is only habit that is stopping us from switching to artificial food, technologically it is already possible

User Interfaces to the Web of Data based on Natural Language Generation

We explore how Virtual Research Environments based on Semantic Web technologies support research interactions with RDF data in various stages of corpus-based analysis, analyze the Web of Data in terms of human readability, derive labels from variables in SPARQL queries, apply Natural Language Generation to improve user interfaces to the Web of Data by verbalizing SPARQL queries and RDF graphs, and present a method to automatically induce RDF graph verbalization templates via distant supervision

Lifting the quality and effectiveness of mathematics education provision in English-medium schools in Aotearoa New Zealand: What will it take?

Mathematics education in English-medium schools in Aotearoa New Zealand currently reproduces inequity. There is widespread concern about overall levels of student achievement and who participates and who succeeds. Rapid, and accelerating, social and technological change impacts what students need to know in mathematics and statistics and increases its significance. There are fundamental debates about how mathematics education should respond to inequity and rapid change. Content and pedagogy are both contested spaces. Research in mathematics education tends to exacerbate rather than resolve this contestation. In this cacophony it is hard to hear marginalised voices and yet these groups are the most impacted by current practices. Mathematics education is entwined with other curriculum areas and has far-reaching consequences; therefore, policy has to treat improving system performance as a complex problem requiring intervention at multiple levels to achieve equitable outcomes for students

Mother adolescent storytelling: associations between maternal emotion socialization and adolescent well-being and emotional development

[EMBARGOED UNTIL 6/1/2023] Within the context of family storytelling, parent-adolescent conversations are a rich, yet underexplored, means of capturing parental emotion socialization and its impacts on adolescents' emotional development (Fivush, et al., 2006b). Furthermore, adolescent autobiographical storytelling allows mothers to promote healthy development; the ways mothers socialize during discussions of past events has meaningful impacts on adolescent adjustment and self-esteem (Bohanek et al., 2008; Habermas and Reese, 2015). Therefore, the present study aims to examine maternal socialization behaviors during adolescent autobiographical storytelling and the ways these behaviors influence adolescent well-being and adjustment. Forty-five mother-adolescent (ages 12-16) dyads discussed three life stories together; these stories were coded for global and specific socialization behaviors. Results reveal that mothers utilize different socialization behaviors by adolescent gender and age, and unsupportive socialization strategies are negatively associated with adolescent well-being and academic motivation. Furthermore, adolescent emotion regulation does moderate the effects of mothers' socialization behaviors for adolescent outcomes. Implications of these findings and ways to further explore the variety of socialization strategies analyzed are discussed.Includes bibliographical references

Instantaneous frequency and amplitude of complex signals based on quaternion Fourier transform

The ideas of instantaneous amplitude and phase are well understood for signals with real-valued samples, based on the analytic signal which is a complex signal with one-sided Fourier transform. We extend these ideas to signals with complex-valued samples, using a quaternion-valued equivalent of the analytic signal obtained from a one-sided quaternion Fourier transform which we refer to as the hypercomplex representation of the complex signal. We present the necessary properties of the quaternion Fourier transform, particularly its symmetries in the frequency domain and formulae for convolution and the quaternion Fourier transform of the Hilbert transform. The hypercomplex representation may be interpreted as an ordered pair of complex signals or as a quaternion signal. We discuss its derivation and properties and show that its quaternion Fourier transform is one-sided. It is shown how to derive from the hypercomplex representation a complex envelope and a phase. A classical result in the case of real signals is that an amplitude modulated signal may be analysed into its envelope and carrier using the analytic signal provided that the modulating signal has frequency content not overlapping with that of the carrier. We show that this idea extends to the complex case, provided that the complex signal modulates an orthonormal complex exponential. Orthonormal complex modulation can be represented mathematically by a polar representation of quaternions previously derived by the authors. As in the classical case, there is a restriction of non-overlapping frequency content between the modulating complex signal and the orthonormal complex exponential. We show that, under these conditions, modulation in the time domain is equivalent to a frequency shift in the quaternion Fourier domain. Examples are presented to demonstrate these concepts

Ultrasonic Continuous Wave Spirometer

There exists a problem of accurately performing spirographic measurements under physical stress situations. Existing systems, which use mechanical structures in the measurement process, have response times that are too slow, or are too bulky to be considered portable. The proposed system solves these problems and has a number of attractive characteristics. The system uses relatively inexpensive solid state electronic components which implies a minimal of mechanical parts; portability; and a linear, fast response time. The system presented in this thesis determines the velocity and temperature fluctuations of the human breath by measuring the difference and sum of the transit times for two continuous sound waves travelling in opposite directions along the air path. The information about the transit times is contained in the phase differencces of the two sound waves across the path. A phase-locked loop is used to keep the differences across the parth constant, irrespective of air - and sound - velocity variations. Therefore, the phase information is converted to frequency variations in the phase-locked loop

Targeted Training of the Decision Rule Benefits Rule-Guided Behavior in Parkinson’s Disease

The impact of Parkinson’s disease (PD) on rule-guided behavior has received considerable attention in cognitive neuroscience. The majority of research has used PD as a model of dysfunction in fronto-striatal networks, but very few attempts have been made to investigate the possibility of adapting common experimental techniques in an effort to identify the conditions that are most likely to facilitate successful performance. The present study investigated a targeted training paradigm designed to facilitate rule learning and application using rule-based categorization as a model task. Participants received targeted training in which there was no selective-attention demand (i.e., stimuli varied along a single, relevant dimension) or non-targeted training in which there was selective-attention demand (i.e., stimuli varied along a relevant dimension as well as an irrelevant dimension). Following training, all participants were tested on a rule-based task with selective-attention demand. During the test phase, PD patients who received targeted training performed similarly to control participants and outperformed patients who did not receive targeted training. As a preliminary test of the generalizability of the benefit of targeted training, a subset of the PD patients were tested on the Wisconsin card sorting task (WCST). PD patients who received targeted training outperformed PD patients who did not receive targeted training on several WCST performance measures. These data further characterize the contribution of fronto-striatal circuitry to rule-guided behavior. Importantly, these data also suggest that PD patient impairment, on selective-attention-demanding tasks of rule-guided behavior, is not inevitable and highlight the potential benefit of targeted training

Boys and literacy: Disengaging from reading

This quantitative study investigates the disparity that exists between girls and boys and how changes can be implemented to keep boys from disengaging from reading. It examines the reading materials that are available to increase boys\u27 interest in reading and discusses ways in which teachers can develop programs and parents can take action to change boys reading habits. The study employed teacher surveys and student surveys from sixth grade boys in three San Bernardino middle schools