Representation of functional dependencies in relational databases using linear graphs

Functional dependencies in relational databases are investigated. Eight binary relations, viz., (1) dependency relation, (2) equipotence relation, (3) dissidence relation, (4) completion relation, and dual relations of each of them are described. Any one of these eight relations can be used to represent the functional dependencies in a database. Results from linear graph theory are found helpful in obtaining these representations. The dependency relation directly gives the functional dependencies. The equipotence relation specifies the dependencies in terms of attribute sets which functionally determine each other. The dissidence relation specifies the dependencies in terms of saturated sets in a very indirect way. Completion relation represents the functional dependencies as a function, the range of which turns out to be a lattice. Depletion relation which is the dual of the completion relation can also represent functional dependencies and similarly can the duals of dependency, equipotence, and dissidence relations. The class of depleted sets, which is the dual of saturated sets, is defined and used in the study of depletion relations.

Optimization models for expanding a railway’s theoretical capacity

Changing the topology of a railway network can greatly affect its capacity. Railway networks however can be altered in a multitude of different ways. As each way has significant immediate and long term financial ramifications, it is a difficult task to decide how and where to expand the network. In response some railway capacity expansion models (RCEM) have been developed to help capacity planning activities, and to remove physical bottlenecks in the current railway system. The exact purpose of these models is to decide given a fixed budget, where track duplications and track sub divisions should be made, in order to increase theoretical capacity most. These models are high level and strategic, and this is why increases to the theoretical capacity is concentrated upon. The optimization models have been applied to a case study to demonstrate their application and their worth. The case study evidently shows how automated approaches of this nature could be a formidable alternative to current manual planning techniques and simulation. If the exact effect of track duplications and sub-divisions can be sufficiently approximated, this approach will be very applicable.

Type II beta-turn conformation of pivaloyl-L-prolyl-alpha-aminoisobutyryl-N-methylamide: Theoretical, spectroscopic, and X-ray studies

Pivaloyl-L-Pro-Aib-N-methylamide has been shown to possess one intramolecular hydrogen bond in (CD3)2SO solution, by 1H-nmr methods, suggesting the existence of beta -turns, with Pro-Aib as the corner residues. Theoretical conformational analysis suggests that Type II beta-turn conformations are about 2 kcal mol-1 more stable than Type III structures. A crystallographic study has established the Type II beta-turn in the solid state. The molecule crystallizes in the space group P21 with a = 5.865 Å, b = 11.421 Å, c = 12.966 Å, beta = 97.55°, and Z = 2. The structure has been refined to a final R value of 0.061. The Type II -turn conformation is stabilized by an intramolecular 4 1 hydrogen bond between the methylamide NH and the pivaloyl CO group. The conformational angles are Pro = -57.8°, Pro = 139.3°, Aib = 61.4°, and Aib = 25.1°. The Type II beta-turn conformation for Pro-Aib in this peptide is compared with the Type III structures observed for the same segment in larger peptides.

Theoretical study of the optimum performance of a two-phase flow CO2 gasdynamic laser

Theoretical optimization studies of the performance of a combustion driven premixed two-phase flow gasdynamic laser are presented. The steady inviscid nonreacting quasi-one-dimensional two-phase flow model including appropriate finite rate vibrational kinetic rates has been used in the analysis. The analysis shows that the effect of the particles on the optimum performance of the two-phase laser is very small. The results are presented in graphical form. Applied Physics Letters is copyrighted by The American Institute of Physics.

Opettajan uskomukset opetustyön lähtökohtana : näkökulmia pedagogiseen ajatteluun

The purpose of this research was to examine teacher’s pedagogical thinking based on beliefs. It aimed to investigate and identify beliefs from teachers’ speech when they were reflecting their own teaching. Placement of beliefs in levels of pedagogical thinking was also examined. The second starting point for a study was the Instrumental Enrichment -intervention, which aims to enhance learning potential and cognitive functioning of students. The goal of this research was to investigate how five main principles of the intervention come forward in teachers’ thinking. Specifying research question was: how similar teachers’ beliefs are to the main principles of intervention. The teacher-thinking paradigm provided the framework for this study. The essential concepts of this study are determined exactly in the theoretical framework. Model of pedagogical thinking was important in the examination of teachers’ thinking. Beliefs were approached through the referencing of varied different theories. Feuerstein theory of Structural cognitive modifiability and Mediated learning experience completed the theory of teacher thinking. The research material was gathered in two parts. In the first part two mathematics lessons of three class teachers were videotaped. In second part the teachers were interviewed by using a stimulated recall method. Interviews were recorded and analysed by qualitative content analysis. Teachers’ beliefs were divided in themes and contents of these themes were described. This part of analysis was inductive. Second part was deductive and it was based on theories of pedagogical thinking levels and Instrumental Enrichment -intervention. According to the research results, three subcategories of teachers’ beliefs were found: beliefs about learning, beliefs about teaching and beliefs about students. When the teachers discussed learning, they emphasized the importance of understanding. In teaching related beliefs student-centrality was highlighted. The teachers also brought out some demands for good education. They were: clarity, diversity and planning. Beliefs about students were divided into two groups. The teachers believed that there are learning differences between students and that students have improved over the years. Because most of the beliefs were close to practice and related to concrete classroom situation, they were situated in Action level of pedagogical thinking. Some teaching and learning related beliefs of individual teachers were situated in Object theory level. Metatheory level beliefs were not found. Occurrence of main principles of intervention differed between teachers. They were much more consistent and transparent in the beliefs of one teacher than of the other two teachers. Differences also occurred between principles. For example reciprocity came up in every teacher’s beliefs, but modifiability was only found in the beliefs of one teacher. Results of this research were consistent with other research made in the field. Teachers’ beliefs about teaching were individual. Even though shared themes were found, the teachers emphasized different aspects of their work. Occurrence of beliefs that were in accordance with the intervention were teacher-specific. Inconsistencies were also found within teachers and their individual beliefs.

Survival probability for a diffusive process on a growing domain

We consider the motion of a diffusive population on a growing domain, 0 < x < L(t ), which is motivated by various applications in developmental biology. Individuals in the diffusing population, which could represent molecules or cells in a developmental scenario, undergo two different kinds of motion: (i) undirected movement, characterized by a diffusion coefficient, D, and (ii) directed movement, associated with the underlying domain growth. For a general class of problems with a reflecting boundary at x = 0, and an absorbing boundary at x = L(t ), we provide an exact solution to the partial differential equation describing the evolution of the population density function, C(x,t ). Using this solution, we derive an exact expression for the survival probability, S(t ), and an accurate approximation for the long-time limit, S = limt→∞ S(t ). Unlike traditional analyses on a nongrowing domain, where S ≡ 0, we show that domain growth leads to a very different situation where S can be positive. The theoretical tools developed and validated in this study allow us to distinguish between situations where the diffusive population reaches the moving boundary at x = L(t ) from other situations where the diffusive population never reaches the moving boundary at x = L(t ). Making this distinction is relevant to certain applications in developmental biology, such as the development of the enteric nervous system (ENS). All theoretical predictions are verified by implementing a discrete stochastic model.

Applying pure mathematics: mathematics in the natural sciences

The book of nature is written in the language of mathematics. This quotation, attributed to Galileo, seemed to hold to an unreasonable1 extent in the era of quantum mechanics.

Theoretical studies on the conformation of beta-D-N-acetyl neuraminic acid (sialic acid)

The possible conformations of sialic acid were analysed using semi-empirical potential functions. The solid state conformation has approx. 0.2 kcal/mol higher energy than the minimum energy conformation. These studies suggest that in solution sialic acid may exist preponderantly in two different conformations which differ in the orientation of the terminal hydroxymethyl group of glycerol side-chain. The present model is consistent with 1H- and 13C-NMR data, but differs from the earlier models.

Visuaalis-spatiaalisten työmuistivalmiuksien yhteys (esi)matemaattisiin taitoihin ja merkitys osana matemaattisilta taidoiltaan heikkojen lasten ja nuorten kognitiivista profiilia

Tämän itsenäisistä osatutkimuksista koostuvan tutkimussarjan tavoitteena oli pyrkiä täydentämään kuvaa matemaattisilta taidoiltaan heikkojen lasten ja nuorten tiedonkäsittelyvalmiuksista selvittämällä, ovatko visuaalis-spatiaaliset työmuistivalmiudet yhteydessä matemaattiseen suoriutumiseen. Teoreettinen viitekehys rakentui Baddeleyn (1986, 1997) kolmikomponenttimallin ympärille. Työmuistikäsitys oli kuitenkin esikuvaansa laajempi sisällyttäen visuaalis-spatiaaliseen työmuistiin Cornoldin ja Vecchin (2003) termein sekä passiiviset varastotoiminnot että aktiiviset prosessointitoiminnot. Yhteyksiä työmuistin ja matemaattisten taitojen välillä tarkasteltiin viiden eri osatutkimuksen avulla. Kaksi ensimmäistä keskittyivät alle kouluikäisten lukukäsitteen hallinnan ja visuaalis-spatiaalisten työmuistivalmiuksen tutkimiseen ja kolme jälkimmäistä peruskoulun yhdeksäsluokkalaisten matemaattisten taitojen ja visuaalis-spatiaalisten työmuistitaitojen välisten yhteyksien selvittämiseen. Tutkimussarjan avulla pyrittiin selvittämään, ovatko visuaalis-spatiaaliset työmuistivalmiudet yhteydessä matemaattiseen suoriutumiseen sekä esi- että yläkouluiässä (osatutkimukset I, II, III, IV, V), onko yhteys spesifi rajoittuen tiettyjen visuaalis-spatiaalisten valmiuksien ja matemaattisen suoriutumisen välille vai onko se yleinen koskien matemaattisia taitoja ja koko visuaalis-spatiaalista työmuistia (osatutkimukset I, II, III, IV, V) tai työmuistia laajemmin (osatutkimukset II, III) sekä onko yhteys työmuistispesifi vai selitettävissä älykkyyden kaltaisella yleisellä päättelykapasiteetilla (osatutkimukset I, II, IV). Tutkimussarjan tulokset osoittavat, että kyky säilyttää ja käsitellä hetkellisesti visuaalis-spatiaalista informaatiota on yhteydessä matemaattiseen suoriutumiseen eikä yhteyttä voida selittää yksinomaan joustavalla älykkyydellä. Suoriutuminen visuaalis-spatiaalista työmuistia mittaavissa tehtävissä on yhteydessä sekä alle kouluikäisten esimatemaattisten taitojen hallintaan että peruskoulun yhdeksäsluokkalaisten matematiikan taitoihin. Matemaattisilta taidoiltaan heikkojen lasten ja nuorten visuaalis-spatiaalisten työmuistiresurssien heikkoudet vaikuttavat kuitenkin olevan sangen spesifejä rajoittuen tietyntyyppisissä muistitehtävissä vaadittaviin valmiuksiin; kaikissa visuaalis-spatiaalisen työmuistin valmiuksia mittaavissa tehtävissä suoriutuminen ei ole yhteydessä matemaattisiin taitoihin. Työmuistivalmiuksissa ilmenevät erot sekä alle kouluikäisten että kouluikäisten matemaattisilta taidoiltaan heikkojen ja normaalisuoriutujien välillä näyttävät olevan kuitenkin jossain määrin yhteydessä kielellisiin taitoihin viitaten vaikeuksien tietynlaiseen kasautumiseen; niillä matemaattisesti heikoilla, joilla on myös kielellisiä vaikeuksia, on keskimäärin laajemmat työmuistiheikkoudet. Osalla matematiikassa heikosti suoriutuvista on näin ollen selvästi keskimääräistä heikommat visuaalis-spatiaaliset työmuistivalmiudet, ja tämä heikkous saattaa olla yksi mahdollinen syy tai vaikeuksia lisäävä tekijä heikon matemaattisen suoriutumisen taustalla. Visuaalis-spatiaalisen työmuistin heikkous merkitsee konkreettisesti vähemmän mentaalista prosessointitilaa, joka rajoittaa oppimista ja suoritustilanteita. Tiedonkäsittelyvalmiuksien heikkous liittyy nimenomaan oppimisnopeuteen, ei asioiden opittavuuteen sinänsä. Mikäli oppimisympäristö ottaa huomioon valmiuksien rajallisuuden, työmuistiheikkoudet eivät todennäköisesti estä asioiden oppimista sinänsä. Avainsanat: Työmuisti, visuaalis-spatiaalinen työmuisti, matemaattiset taidot, lukukäsite, matematiikan oppimisvaikeudet

Modelling the movement of interacting cell populations: A moment dynamics approach

Mathematical models describing the movement of multiple interacting subpopulations are relevant to many biological and ecological processes. Standard mean-field partial differential equation descriptions of these processes suffer from the limitation that they implicitly neglect to incorporate the impact of spatial correlations and clustering. To overcome this, we derive a moment dynamics description of a discrete stochastic process which describes the spreading of distinct interacting subpopulations. In particular, we motivate our model by mimicking the geometry of two typical cell biology experiments. Comparing the performance of the moment dynamics model with a traditional mean-field model confirms that the moment dynamics approach always outperforms the traditional mean-field approach. To provide more general insight we summarise the performance of the moment dynamics model and the traditional mean-field model over a wide range of parameter regimes. These results help distinguish between those situations where spatial correlation effects are sufficiently strong, such that a moment dynamics model is required, from other situations where spatial correlation effects are sufficiently weak, such that a traditional mean-field model is adequate.

Modeling dynamic demand response using Monte Carlo simulation and interval mathematics for boundary estimation

With the rapid development of various technologies and applications in smart grid implementation, demand response has attracted growing research interests because of its potentials in enhancing power grid reliability with reduced system operation costs. This paper presents a new demand response model with elastic economic dispatch in a locational marginal pricing market. It models system economic dispatch as a feedback control process, and introduces a flexible and adjustable load cost as a controlled signal to adjust demand response. Compared with the conventional “one time use” static load dispatch model, this dynamic feedback demand response model may adjust the load to a desired level in a finite number of time steps and a proof of convergence is provided. In addition, Monte Carlo simulation and boundary calculation using interval mathematics are applied for describing uncertainty of end-user's response to an independent system operator's expected dispatch. A numerical analysis based on the modified Pennsylvania-Jersey-Maryland power pool five-bus system is introduced for simulation and the results verify the effectiveness of the proposed model. System operators may use the proposed model to obtain insights in demand response processes for their decision-making regarding system load levels and operation conditions.