Superpositions for nonlinear operators. I. Strong superpositions and linearizability

AbstractA notion of superposition for nonlinear operators is defined and strong and weak superpositions are distinguished. The classification and representation of operators having a strong superposition is treated. The algebra induced by the superposition on the domain of operators with strong superpositions, as well as their relation to linearizable operators is delimited. The foundations presented here are intended as a model in the development of more general classes of nonlinear operators, to be treated in two subsequent papers

Toimetamine avalik-õiguslikus televisioonis ETV näitel

The aim of the bachelor thesis “Story Editing at Public Broadcasting Television – the Example of ETV“ was to give an overview of the work assignments of story editors at the public broadcasting channel ETV and find out which are the main principles on choosing the topics they cover in the programmes. As this theme is very poorly covered in scientific field I chose to examine this topic by conducting expert interviews with 10 long-term story editors working at ETV. The study found that the post of story editors is not very well circumscribed and story editors working with different programmes have very different roles and work assignments which are mainly derived from special agreements inside the team. Television production is very much based on teamwork and there is almost no hierarchy of decision-making in the teams. The traditional role of a story editor would be helping and consulting the author of the programme but it was pointed out that there are almost no traditional story editors left in the organisation. People are increasingly universal and able to carry out the work assignments of other team members as the producer or even the director. Overall, the most typical tasks for story editors are generating ideas, conducting behind the scene interviews, sourcing and researching information and constituting the programme as a whole. It was said that story editors are nowadays frequently actually conducting the assignments of programme authors. Concerning finding and choosing the topics the most important aspect is how well the story editors are personally informed about what is happening both in Estonia and abroad. It is also essential for a story editor to have a big circle of acquaintances and specific knowledge of the area s/he is covering. While choosing the suitable topics into the programmes the most important criteria is the interest of the team members and then suitability for television (if it is possible to visualise the topic). In the case of television practical aspects are also extremely important – whether there is a free camera or enough money to go filming farther away from the capital city. Working at a public broadcasting television was associated with contrariety towards commercial television channels and the principles which associate with them like sensational journalism, dependence on ratings and advertisement money. Long-term story editors identify more with the values of the channel ETV than the theoretical and legal concept of public broadcasting media. While examining this thesis a series of additional themes and topics surfaced which shows that this branch of study should be further investigated.http://tartu.ester.ee/record=b2510421~S1*es

Ajakirjanduskriitika ajakirjanduse rollist Eesti ühiskonnas 2011-2012

Analüüsisin uurimistöös aastatel 2011-2012 ilmunud ajakirjanduskriitilisi arvamusartikleid, mille autorid ei ole ajakirjandust õppinud ega ise ajakirjanduses töötanud. Töö eesmärk oli saada teada, millisena kujutavad ajakirjandust valdkonnavälised arvamusliidrid − millisel tasandil ajakirjandust kirjeldatakse, millised ajakirjandusest rääkimise diskursused esile kerkivad ning milliseid rolle ajakirjanduselt ühiskonnas oodatakse. Uurides 16 arvamusartiklit kriitilise diskursusanalüüsi meetodil selgus, et kuigi iga kirjutaja isiklikud hoiakud ja motivatsioon artikli kirjutamiseks olid erinevad, leidus siiski arvamustes palju sarnaseid ootusi, etteheiteid ja hoiakuid. Ajakirjandust käsitleti peamiselt institutsiooni tasemel ning igasugust konkreetsete väljaannete ja ajakirjanike nimede välja toomist välditi. Kirjutajad ei eristanud isegi erameediat ja avalik-õiguslikku ringhäälingut. Mitu autorit liigitasid ajakirjandust uudisvooks ja uurivaks ajakirjanduseks, millest vaid viimast pidasid kvaliteetseks ja tõsiseks ajakirjanduseks. Diskursustest joonistusid kõige selgemalt ajakirjandusest rääkides välja äridiskursus ehk meedia muutumine tavaliseks teenuseks, mille tegijate eesmärk on võita võimalikult palju kliente ja teenida raha, ning neljanda võimu diskursus, mille puhul tõdeti, et ajakirjandusel on tänapäeval ühiskonnas arvestades oma ärihuvisid liiga suur võim. Seega heideti ajakirjandusele ette avalikkuse huvide teenimise välja vahetamist kommertshuvide vastu. Ootused ajakirjanduse rollile demokraatlikus ühiskonnas on autoritel traditsioonilised ning ühtivad McQuaili (2003) välja toodud peamiste ajakirjanduse rollidega − otsida ja vahendada tõde, valvata ühiskonna institutsioonide tegevuse üle, filtreerida infovoost välja ja tuua auditooriumini oluline ning aidata kaasa rahva ühtse identiteedi ja solidaarsuse kujunemisele. Kõige murettekitavam on tulemus, et Eesti ajakirjandust ei käsitletud enamasti kui head tegelast, vaid pigem kui kedagi, kes on oma huvide peal väljas, moonutab infot ja käitub inimestega, sh riigivalitsejatega ebaõiglaselt. Võib öelda, et analüüsitud arvamusartiklid olid valdavalt siiski pigem konkreetsete isikute emotsionaalsed sõnavõtud kui ajakirjanduse rolli demokraatlikus ühiskonnas reflekteerivad analüüsid. Lisaks saab analüüsi tulemustest järeldada, et kokku on põrganud inimeste traditsioonilised ootused ajakirjandusele ning ajakirjanduse enda identiteedikriis, mille tulemusena valitseb avalikkuses segadus ja pahameel, mille lahendust polegi veel võimalik ette näha. Arvamusliidrite ajakirjanduskriitiliste arvamusartiklite analüüsimine oli huvitav ja selle teemaga võiks kindlasti ka edasi minna, võrreldes näiteks ajakirjanike ja meediateadlaste ning meediaväliste arvamusliidrite samal perioodil kirjutatud ajakirjanduskriitikat või lugejakirju. Samuti võiks uurida põhjalikumalt ajakirjanduse ja ajakirjanike mainet inimeste silmis.http://tartu.ester.ee/record=b2657441~S1*es

Superposition rules, Lie theorem and partial differential equations

A rigorous geometric proof of the Lie's Theorem on nonlinear superposition rules for solutions of non-autonomous ordinary differential equations is given filling in all the gaps present in the existing literature. The proof is based on an alternative but equivalent definition of a superposition rule: it is considered as a foliation with some suitable properties. The problem of uniqueness of the superposition function is solved, the key point being the codimension of the foliation constructed from the given Lie algebra of vector fields. Finally, as a more convincing argument supporting the use of this alternative definition of superposition rule, it is shown that this definition allows an immediate generalization of Lie's Theorem for the case of systems of partial differential equations.Comment: 22 page

Visualizing dimensionality reduction of systems biology data

One of the challenges in analyzing high-dimensional expression data is the detection of important biological signals. A common approach is to apply a dimension reduction method, such as principal component analysis. Typically, after application of such a method the data is projected and visualized in the new coordinate system, using scatter plots or profile plots. These methods provide good results if the data have certain properties which become visible in the new coordinate system and which were hard to detect in the original coordinate system. Often however, the application of only one method does not suffice to capture all important signals. Therefore several methods addressing different aspects of the data need to be applied. We have developed a framework for linear and non-linear dimension reduction methods within our visual analytics pipeline SpRay. This includes measures that assist the interpretation of the factorization result. Different visualizations of these measures can be combined with functional annotations that support the interpretation of the results. We show an application to high-resolution time series microarray data in the antibiotic-producing organism Streptomyces coelicolor as well as to microarray data measuring expression of cells with normal karyotype and cells with trisomies of human chromosomes 13 and 21

Interactive redescription mining

Exploratory data analysis consists of multiple iterated steps: a data mining method is run on the data, the results are interpreted, new insights are formed, and the resulting knowl- edge is utilized when executing the method in a next round, and so on until satisfactory results are obtained. We focus on redescription mining, a powerful data analysis method that aims at finding alternative descriptions of the same entities, for example, ways to characterize geographical regions in terms of both the fauna that inhabits them and their bioclimatic conditions, so-called bioclimatic niches. We present Siren, a tool for interactive redescription min- ing. It is designed to facilitate the exploratory analysis of data by providing a seamless environment for mining, visu- alizing and editing redescriptions in an interactive fashion, supporting the analysis process in all its stages. We demon- strate its use for exploratory data mining. Simultaneously, Siren exemplifies the power of the various visualizations and means of interaction integrated into it; Techniques that reach beyond the task of redescription mining considered here, to other analysis methods

Structuring visual exploratory analysis of skill demand

The analysis of increasingly large and diverse data for meaningful interpretation and question answering is handicapped by human cognitive limitations. Consequently, semi-automatic abstraction of complex data within structured information spaces becomes increasingly important, if its knowledge content is to support intuitive, exploratory discovery. Exploration of skill demand is an area where regularly updated, multi-dimensional data may be exploited to assess capability within the workforce to manage the demands of the modern, technology- and data-driven economy. The knowledge derived may be employed by skilled practitioners in defining career pathways, to identify where, when and how to update their skillsets in line with advancing technology and changing work demands. This same knowledge may also be used to identify the combination of skills essential in recruiting for new roles. To address the challenges inherent in exploring the complex, heterogeneous, dynamic data that feeds into such applications, we investigate the use of an ontology to guide structuring of the information space, to allow individuals and institutions to interactively explore and interpret the dynamic skill demand landscape for their specific needs. As a test case we consider the relatively new and highly dynamic field of Data Science, where insightful, exploratory data analysis and knowledge discovery are critical. We employ context-driven and task-centred scenarios to explore our research questions and guide iterative design, development and formative evaluation of our ontology-driven, visual exploratory discovery and analysis approach, to measure where it adds value to users’ analytical activity. Our findings reinforce the potential in our approach, and point us to future paths to build on

Visualising interactions in bi- and triadditive models for three-way tables

This paper concerns the visualisation of interaction in three-way arrays. It extends some standard ways of visualising biadditive modelling for two-way data to the case of three-way data. Three-way interaction is modelled by the Parafac method as applied to interaction arrays that have main effects and biadditive terms removed. These interactions are visualised in three and two dimensions. We introduce some ideas to reduce visual overload that can occur when the data array has many entries. Details are given on the interpretation of a novel way of representing rank-three interactions accurately in two dimensions. The discussion has implications regarding interpreting the concept of interaction in three-way arrays

A grid-enabled problem solving environment for parallel computational engineering design

This paper describes the development and application of a piece of engineering software that provides a problem solving environment (PSE) capable of launching, and interfacing with, computational jobs executing on remote resources on a computational grid. In particular it is demonstrated how a complex, serial, engineering optimisation code may be efficiently parallelised, grid-enabled and embedded within a PSE. The environment is highly flexible, allowing remote users from different sites to collaborate, and permitting computational tasks to be executed in parallel across multiple grid resources, each of which may be a parallel architecture. A full working prototype has been built and successfully applied to a computationally demanding engineering optimisation problem. This particular problem stems from elastohydrodynamic lubrication and involves optimising the computational model for a lubricant based on the match between simulation results and experimentally observed data

A Comprehensive Three-Dimensional Model of the Cochlea

The human cochlea is a remarkable device, able to discern extremely small amplitude sound pressure waves, and discriminate between very close frequencies. Simulation of the cochlea is computationally challenging due to its complex geometry, intricate construction and small physical size. We have developed, and are continuing to refine, a detailed three-dimensional computational model based on an accurate cochlear geometry obtained from physical measurements. In the model, the immersed boundary method is used to calculate the fluid-structure interactions produced in response to incoming sound waves. The model includes a detailed and realistic description of the various elastic structures present. In this paper, we describe the computational model and its performance on the latest generation of shared memory servers from Hewlett Packard. Using compiler generated threads and OpenMP directives, we have achieved a high degree of parallelism in the executable, which has made possible several large scale numerical simulation experiments that study the interesting features of the cochlear system. We show several results from these simulations, reproducing some of the basic known characteristics of cochlear mechanics.Comment: 22 pages, 5 figure