On the Cubicity of Interval Graphs

A k-cube (or ``a unit cube in k dimensions'') is defined as the Cartesian product R-1 x . . . x R-k where R-i (for 1 <= i <= k) is an interval of the form [a(i), a(i) + 1] on the real line. The k-cube representation of a graph G is a mapping of the vertices of G to k-cubes such that the k-cubes corresponding to two vertices in G have a non-empty intersection if and only if the vertices are adjacent. The cubicity of a graph G, denoted as cub(G), is defined as the minimum dimension k such that G has a k-cube representation. An interval graph is a graph that can be represented as the intersection of intervals on the real line - i. e., the vertices of an interval graph can be mapped to intervals on the real line such that two vertices are adjacent if and only if their corresponding intervals overlap. We show that for any interval graph G with maximum degree Delta, cub(G) <= inverted right perpendicular log(2) Delta inverted left perpendicular + 4. This upper bound is shown to be tight up to an additive constant of 4 by demonstrating interval graphs for which cubicity is equal to inverted right perpendicular log(2) Delta inverted left perpendicular.

Strong-coupling expansion for the momentum distribution of the Bose-Hubbard model with benchmarking against exact numerical results

A strong-coupling expansion for the Green's functions, self-energies, and correlation functions of the Bose-Hubbard model is developed. We illustrate the general formalism, which includes all possible (normal-phase) inhomogeneous effects in the formalism, such as disorder or a trap potential, as well as effects of thermal excitations. The expansion is then employed to calculate the momentum distribution of the bosons in the Mott phase for an infinite homogeneous periodic system at zero temperature through third order in the hopping. By using scaling theory for the critical behavior at zero momentum and at the critical value of the hopping for the Mott insulator–to–superfluid transition along with a generalization of the random-phase-approximation-like form for the momentum distribution, we are able to extrapolate the series to infinite order and produce very accurate quantitative results for the momentum distribution in a simple functional form for one, two, and three dimensions. The accuracy is better in higher dimensions and is on the order of a few percent relative error everywhere except close to the critical value of the hopping divided by the on-site repulsion. In addition, we find simple phenomenological expressions for the Mott-phase lobes in two and three dimensions which are much more accurate than the truncated strong-coupling expansions and any other analytic approximation we are aware of. The strong-coupling expansions and scaling-theory results are benchmarked against numerically exact quantum Monte Carlo simulations in two and three dimensions and against density-matrix renormalization-group calculations in one dimension. These analytic expressions will be useful for quick comparison of experimental results to theory and in many cases can bypass the need for expensive numerical simulations.

Genotypic variation in seedling root architectural traits and implications for drought adaptation in wheat (Triticum aestivum L.)

Root system characteristics are of fundamental importance to soil exploration and below-ground resource acquisition. Root architectural traits determine the in situ space-filling properties of a root system or root architecture. The growth angle of root axes is a principal component of root system architecture that has been strongly associated with acquisition efficiency in many crop species. The aims of this study were to examine the extent of genotypic variability for the growth angle and number of seminal roots in 27 current Australian and 3 CIMMYT wheat (Triticum aestivum L.) genotypes, and to quantify using fractal analysis the root system architecture of a subset of wheat genotypes contrasting in drought tolerance and seminal root characteristics. The growth angle and number of seminal roots showed significant genotypic variation among the wheat genotypes with values ranging from 36 to 56 (degrees) and 3 to 5 (plant-1), respectively. Cluster analysis of wheat genotypes based on similarity in their seminal root characteristics resulted in four groups. The group composition reflected to some extent the genetic background and environmental adaptation of genotypes. Wheat cultivars grown widely in the Mediterranean environments of southern and western Australia generally had wider growth angle and lower number of seminal axes. In contrast, cultivars with superior performance on deep clay soils in the northern cropping region, such as SeriM82, Baxter, Babax, and Dharwar Dry exhibited a narrower angle of seminal axes. The wheat genotypes also showed significant variation in fractal dimension (D). The D values calculated for the individual segments of each root system suggested that, compared to the standard cultivar Hartog, the drought-tolerant genotypes adapted to the northern region tended to distribute relatively more roots in the soil volume directly underneath the plant. These findings suggest that wheat root system architecture is closely linked to the angle of seminal root axes at the seedling stage. The implications of genotypic variation in the seminal root characteristics and fractal dimension for specific adaptation to drought environment types are discussed with emphasis on the possible exploitation of root architectural traits in breeding for improved wheat cultivars for water-limited environments.

3-D kinematical conservation laws (KCL): Evolution of a surface in R-3 - in particular propagation of a nonlinear wavefront

3-D KCL are equations of evolution of a propagating surface (or a wavefront) Omega(t), in 3-space dimensions and were first derived by Giles, Prasad and Ravindran in 1995 assuming the motion of the surface to be isotropic. Here we discuss various properties of these 3-D KCL.These are the most general equations in conservation form, governing the evolution of Omega(t) with singularities which we call kinks and which are curves across which the normal n to Omega(t) and amplitude won Omega(t) are discontinuous. From KCL we derive a system of six differential equations and show that the KCL system is equivalent to the ray equations of 2, The six independent equations and an energy transport equation (for small amplitude waves in a polytropic gas) involving an amplitude w (which is related to the normal velocity m of Omega(t)) form a completely determined system of seven equations. We have determined eigenvalues of the system by a very novel method and find that the system has two distinct nonzero eigenvalues and five zero eigenvalues and the dimension of the eigenspace associated with the multiple eigenvalue 0 is only 4. For an appropriately defined m, the two nonzero eigenvalues are real when m > 1 and pure imaginary when m < 1. Finally we give some examples of evolution of weakly nonlinear wavefronts.

Impulsivity, health-related behaviour and disease : A prospective study

In clinical settings impulsivity refers to a symptom of psychiatric disorder, but nonclinically oriented research treats impulsivity as a personality and temperament dimension. This prospective study examined whether impulsivity predicts adverse health-related behaviour and increased risk of health problems in a large, nonclinical sample of 5433 subjects working in 12 Finnish hospitals. The data were collected using two questionnaire surveys at a 2-year interval. After controlling for alcohol use at baseline, higher impulsivity predicted increased alcohol consumption at follow-up in both genders (p < .01) and was associated with increased likelihood of becoming a heavy drinker or taking up smoking (p < .05). Impulsivity also predicted an increased number of cigarettes smoked per day in the follow-up among women (p < .001), but not among men, although adjustment for the number of cigarettes smoked at baseline attenuated these associations (p = .08 for women). In men, higher impulsivity was associated with shorter sleep duration and waking up several times per night independent of baseline characteristics (p < .01), whereas in women, higher impulsivity predicted difficulty in falling asleep and waking up feeling tired after the usual amount of sleep (p < .05). In women, these associations became nonsignificant after adjustment for pre-existing somatic and psychiatric diseases. Finally, higher impulsivity was associated with an increased 2-year incidence of physician-diagnosed peptic ulcer disease (adjusted odds ratio (OR) = 2.42, 95% confidence interval (CI) = 1.21 - 4.82) and onset of depression (OR = 1.95, 95% CI = 1.28 - 2.97) after adjustment for a variety of baseline covariates. In conclusion, this study shows that in a nonclinical population, impulsivity appears to be a risk factor for various unhealthy behaviour and health problems.

Hiljainen tieto henkilöstön valinnassa : tutkimus työhaastatteluiden arvioinnissa hyödynnettävän tiedon hiljaisesta ulottuvuudesta

This study examined the fundamental question of what really matters when selecting a new employee. The study focused on tacit knowledge used by personnel recruiters when interviewing employees. Knowledge was defined as the best view available, which helps one not to act haphazardly. Tacit knowledge was also defined as a positive concept, and it was seen as a part of personnel recruiters` improving proficiency. The research topic was chosen based on the observed increase in the amount of employment interviews and their importance in society. As recruiting is becoming a more distinct profession, it was reasonable to approach the topic from an educational point of view. The following research problems guided the examination of the phenomenon: 1) Where does the interviewer seek tacit knowledge from during the employment interview? 2) How is tacit knowledge achieved during the employment interview? 3) How does the interviewer defend the significance of the tacit knowledge gained as knowledge that has influence on the selection decision? The research data was collected by interviewing six personnel recruiters who conduct and evaluate employment interviews as part of their work responsibilities. The interview themes were linked to some recently made selection decision in each organization and the preceding employment interview with the selected candidate. In order to conceptualize tacit knowledge, reflective consideration of the interview event was used in the study. The lettered research data was analyzed inductively. As a result of the study, the objects of tacit knowledge in the context of an employment interview culminated into three areas: the applicant s verbal communication, the applicant s non-verbal communication and the interaction between interview participants. Observations directed toward those objects were shown to be intentional and three schemes were found behind them: experiences from previous interviews, applicant s application papers and the aptitude for the work responsibilities. The question of gaining knowledge was answered with the concept of procedural knowledge. Personnel recruiters were found to have four different, but interconnected ways to encounter knowledge during an employment interview: understanding, evaluative, revealing, and approving knowing. In order to explain the importance given to tacit knowledge, it was examined in connection with the most prevalent practices in the personnel selection industry. The significance of knowledge as the kind of knowledge that has an impact on the decision was supported by references to collective opinion (other people agree with it), circumstance (interview s short duration), or using some instrument (structured interview). The study revealed new aspects of employment selection process through examining tacit knowledge. The characteristics of the inductive analysis of the research data may also be utilized, when applicable, in tacit knowledge research within other contexts.

Opetussuunnitelman mallin jäsennys : sisältö ja pedagogiikka kokonaisuuden rakentajina

Structuring of the Curriculum Design: Content and Pedagogy Constructing the Whole The object of this qualitative study is to structure curriculum design by drawing from the characteristics of subject content and pedagogy. The aim is to first outline the forms of content and pedagogy within the National Core Curriculum for Basic Education. By analysing these forms I then aim to construct a general view of the curriculum’s structure and its developmental potential as it relates to both current and future pedagogical and intellectual interests. The written curriculum is examined as part of the educational guidance system, which means that it is an administrative and juridical document that governs teacher action and has a pedagogical and intellectual character. Didactical schools, curriculum ideologies and curriculum-determinants are all discussed as means of approaching the curriculum model. Curriculum content itself is defined by the different forms and conceptions of knowledge. The representation of curriculum content can be defined to be either specific or integrated. Curriculum pedagogy is in turn defined on the basis of the prevailing conception of learning and teaching. The pedagogy within the curriculum can be open or closed depending on the extent of pedagogical freedom allowed. An examination of the pedagogical dimension also covers the subject of the interfaces between formal education and informal learning, which must be taken into consideration when developing school pedagogy and therefore also in the curriculum. The data of the study consists of two curriculum documents: The Finnish National Core Curriculum for Basic Education issued in 1994 and the present National core curriculum for basic education issued in 2004. The primary method used in the study is theory-based content analysis. On the one hand the aim of the analysis is to determine if the structure, i.e., model, of the curricula is built from unconnected, self-contained elements, or whether the separate parts make a coherent whole. On the other hand, the aim is also to examine the pedagogical features the two curricula contain. The basis of the study is not the systematic comparison of the curriculum documents, yet an analysis of two very distinct documents must also be based on an examination of their inherent differences. The results of the study show that the content in the analysed documents is not integrated. The boundaries between divisions are clearly defined and the curricula are subject-oriented and based on theoretical propositional knowledge. The pedagogy is mainly closed and based on strong guidance of content, structured student evaluation and measurable learning experiences. However, curriculum documents do have representations of integrated content: the themes covered early on in the core curriculum guidelines of 1994 permeate systematically the different divisions of the curriculum. The core curriculum guidelines of 2004 in turn reveal skills which create connections between subjects. The guidelines’ utilise out-of-school environments and accommodate learner experiences, and focus on flexible studying and emphasize individual learner needs. These characteristics reveal an open form of pedagogy. In light of these results, it is possible to reach an understanding of the content and pedagogical development possibilities of the curriculum. The essential viewpoints are then the setting of thematically-oriented aims as a basis for content development, the curriculum’s pedagogical structuring on the basis of the learning process and the enhancement of connections between curricular content and pedagogy in a purposeful way. Keywords: curriculum, curriculum theory, curriculum design, core curriculum guidelines, teaching content, pedagogy

Young, gifted and spiritual -The case of Finnish sixth-grade pupils

The aim of this study was to explore the spirituality of Finnish academically gifted 12 13-year old pre-adolescents (N = 101). Their spirituality was investigated through the following three questions: (1) What is their relationship to religion? (2) How do they perceive transcendence? and (3) How does their search for meaning integrate into their lives? A total of 60 girls and 41 boys participated in the study. They attend a special school, Helsingin Suomalainen yhteiskoulu, in Helsinki, Finland. The school includes classes from grade 3 to upper secondary school and has an entrance test. This study is part of a research project called Actualizing Finnish Giftedness which is funded by the Finnish Academy between 2000 2007 and is led by Professor Tirri. The research project is based on Gardner s Multiple Intelligences theory (Gardner 1993) and on Hay s (1998) work on spirituality. The data in this study was gathered in 2003 and 2004. It includes both qualitative and quantitative material. The emphasis is on data gathered with interviews. The mixed method approach was used as the methodological framework for connecting the qualitative content analysis, phenomenological approach and the quantitative tests of this study. The results of the sub-studies are reported in full in the four original articles. First, the articles show that the pupils connect religion mainly with Christian institutions and do not consider religion and spirituality to overlap. Second, the articles show that the pupils believe in God and the interference of God in their lives and they think that reality includes a spiritual dimension. Third, the pupils had four kinds of existentially significant interests: personal, transcendental, cosmic and ethical. Cosmic interests were especially highlighted in the article concerning boys as nature and science were reported to be integral sources for their existential thinking. In addition, perceptions on God seemed to be connected to the individual s perception on the meaning of life. In RE, spiritual development has been a constant topic of interest since the late eighties. Likewise, recently in gifted education there have been discussions concerning spiritual intelligence (Gardner 1999) and spirituality of the gifted (Kerr & Cohn 2001). Based on the empirical results of the study, this study concludes that education wishing to promote spiritual development should aim at being existentially relevant to the pupils and use their existential search as an integrative framework for their individual talents and skills.

Do UNESCO Schools in Finland Prepare Their Students for the Future? : A Study of Their School-based Curriculums

The purpose of the research was to study how Finnish lower-stage schools participating in the international network of UNESCO schools, also called the Associated Schools Project (ASP), prepare their students for the future at the level of their school-based curriculums. In the research, the future trends were discussed, and the importance of their consideration in educational practice was explained from a global viewpoint: Based on the examination of today's problematic world state, and development trends characterized by globalization, the challenges and demands set for schooling and education in the future were discussed. Understanding the significance of an individual's action and responsibility was considered to be the central resource for building a more just and sustainable future. The study was grounded on a theoretical model developed by the researcher, which combined the models of Dalin & Rust (1996) and UNESCO (Delors et al. 1996) about future-oriented learning. The model consists of four basic elements of curriculum; "Nature", "Culture", "Myself", and "Others", and four dimension of learning; "Learning to know", "Learning to do", "Learning to live together" and "Learning to be". The model represents the holistic aspect of educational theory, and its aim is to maintain a balance between its different components. The research material composed of ten lower-stage UNESCO schools' school-based curriculums. They were analyzed using the theoretical model by the methology of content analysis. The research results were notably consistent between the different schools. They showed cultural learning and learning concerned with "myself" to be clearly more emphasized than learning referring to nature and other people. In addition, they reflected the central position of subjects, knowledge and skills, thus leaving the development of the pupils' personalities, and particularly learning concerned with living with other people, in a marginal role. The question about whether the schools prepare for the future interms of their curriculums, was discussed in the light of the results. The research offered a way and a model to approach the relationship between education and the future, and to evaluate schools' future-orientation. Based on the results, the schools are suggested to lay more stress on learning concerned with nature and other people, and focus more on developing the mental capasities of their pupils and competencies they need for living with other people. Above all, what the present societies require of schools is education which produces balanced and broadly aware human beings who have the mental strength to face the challenges of the future and abilities to direct it along the lines they desire. Keywords: future, curriculum, content analysis

Luonnoksia käsityön ruumiillisuudesta. : Käsityö Maurice Merleau-Pontyn ruumiinfenomenologian valossa.

Purpose This study focused on craft from a standpoint of phenomenological philosophy and craft was interpreted through Maurice Merleau-Ponty’s phenomenology of the body. The main focus was the physical phase of the craft process, wherein a product is made from material. The aim was to interpret corporality in craft. There is no former research focusing on lived body in craft science. Physical, bodily making is inalienable in craft, but it is not articulated. Recent discussion has focused on craft as ”whole”, which emphasizes designing part in the process, and craft becomes conceptualized with the theories of art and design. The axiomatic yet silenced basis of craft, corporality, deserves to become examined as well. That is why this study answers the questions: how craft manifests in the light of phenomenology of the body and what is corporality in craft? Methods In this study I cultivated a phenomenological attitude and turned my exploring eye on craft ”in itself”. In addition I restrained myself from mere making and placed myself looking at the occurrence of craft to describe it verbally. I read up Maurice Merleau-Ponty’s phenomenology of the body on his principal work (2002) and former interpretations of it. Interpreting and understanding textual data were based on Gadamer’s hermeneutics, and the four-pronged composition of the study followed Koski’s (1995) version of the Gadamerian process of textual interpretation. Conclusions In the construction of bodily phenomenology craft was to be contemplated as a mutual relationship between the maker and the world materializing in bodily making. At the moment of making a human being becomes one with his craft, and the connection between the maker, material and the equipment appears as communication. Operational dimension was distinctive in the intentionality of craft, which operates in many ways, also in craft products. The synesthesia and synergy of craft were emphasized and craft as bodily practice came to life through them. The moment of making appeared as situation generating time and space, where throwing oneself into making may give the maker an experience of upraise beyond the dualism of mind and body. The conception of the implicit nature of craft knowledge was strengthened. In the light of interpretation it was possible to conceptualize craft as a performance and making ”in itself” as a work of art. In that case craft appeared as bodily expression, which as an experience approaches art without being it after all. The concept of aesthetic was settled into making as well. Bodily and phenomenological viewpoint on craft gave material to critically contemplate the concept of “whole craft” (kokonainen käsityö) and provided different kind of understanding of craft as making.

Intergenerational Transfer of Sabbath Observance : How is Religious Tradition Transferred to Children among Finnish Seventh-day Adventists?

This study examined religious home education in educational, psychological, and sociological context. Growing up within a religious denomination is a process of learning the rules, norms, opinions, and attitudes, which serve to make the individual an active member of the group. It is a process of transferring the cultural inheritance between generations. Sabbathkeeping can be regarded as a strong indicator of the Seventh-day Adventist value system, which is also why I have concentrated on this specific issue in my study. The purpose of the study was to find out, how the Sabbath is transferred from parents to children among Finnish Adventists. It was also examined how parents could make the day of rest positively exceptional for children, and how the parental authoritativeness affects the process of transference. According to Bull & Lockhart s (1989) theory, the amount of Adventist generations in family history influences the transfer of religious tradition. This study aimed to find out whether or not this theory would apply to the present-day Finland. The nature of religious development among Adventist young people was also one of the interests of the research. The methods used in the study were in-depth interviews (n = 10) and a survey (n = 106). The majority of the interviewees was young adults (age 15-30) grown up in Adventist families. The interviews were taped and transcribed for the study, and survey answers were analysed with SPSS-data analysis program. The amount of survey questionnaires evaluated was 106, whole population of 15-30 year-old Finnish Adventists being about one thousand. Democratic relationship between parents and children, parents' example, encouragement to own thinking, and positive experiences of Sabbath and the whole religion, including the social dimension of the Adventism, seem to be some of the most significant factors in transference of religious tradition. Both too severe and too permissive education were considered to lead to similar results: unsuccessful transfer of values, or even rebellion and adopting a totally opposite way of life than that of the parents. In this study the amount of Adventist generations in family history does not correlate significantly with the end results of value transference. Keywords: Sabbath, intergenerational, value transference, religious home education Avainsanat: sapatti, arvojen siirtyminen vanhemmilta lapsille, uskonnollinen kotikasvatus

Valence bond analysis of the Kondo chain Hamiltonian

Accurate extrapolations for the ground state energy per site of the one - dimensional Kondo chain system is obtained from exact finite system calculations carried out employing a valence bond scheme. An analysis of the ground state wave function indicates that the localized spin is quenched for all nonzero values of the Kondo exchange constant in one dimension.

An elementary approach to gap theorems

Using elementary comparison geometry, we prove: Let (M, g) be a simply-connected complete Riemannian manifold of dimension >= 3. Suppose that the sectional curvature K satisfies -1-s(r) <= K <= -1, where r denotes distance to a fixed point in M. If lim(r ->infinity) e(2r) s(r) = 0, then (M, g) has to be isometric to H-n.The same proof also yields that if K satisfies -s(r) <= K <= 0 where lim(r ->infinity) r(2) s(r) = 0, then (M, g) is isometric to R-n, a result due to Greene and Wu.Our second result is a local one: Let (M, g) be any Riemannian manifold. For a E R, if K < a on a geodesic ball Bp (R) in M and K = a on partial derivative B-p (R), then K = a on B-p (R).

Effects of Isothermal and Adiabatic Thermal Loadings on Size and Strain Rate Dependence of Copper Nanowire

In the present paper, the size and strain rate effects on ultra-thin < 100 >/{100} Cu nanowires at an initial temperature of 10 K have been discussed. Extensive molecular dynamics (MD) simulations have been performed using Embedded atom method (EAM) to investigate the structural behaviours and properties under high strain rate. Velocity-Verlet algorithm has been used to solve the equation of motions. Two different thermal loading cases have been considered: (i) Isothermal loading, in which Nose-Hoover thermostat is used to maintain the constant system temperature, and (ii) Adiabatic loading, i.e., without any thermostat. Five different wire cross-sections were considered ranging from 0.723 x 0.723 nm(2) to 2.169 x 2.169 nm(2) The strain rates used in the present study were 1 x 10(9) s(-1), 1 x 10(8) s(-1), and 1 x 10(7) s(-1). The effect of strain rate on the mechanical properties of copper nanowires was analysed, which shows that elastic properties are independent of thermal loading for a given strain rate and cross-sectional dimension of nanowire. It showed a decreasing yield stress and yield strain with decreasing strain rate for a given cross- section. Also, a decreasing yield stress and increasing yield strain were observed for a given strain rate with increasing cross-sectional area. Elastic modulus was found to be similar to 100 GPa, which was independent of processing temperature, strain rate, and size for a given initial temperature. Reorientation of < 100 >/{100} square cross-sectional copper nanowire into a series of stable ultra-thin Pentagon copper nanobridge structures with dia of similar to 1 nm at 10 K was observed under high strain rate tensile loading. The effect of isothermal and adiabatic loading on the formation of such pentagonal nanobridge structure has been discussed.

Improving the estimation of probability of bidder participation in procurement auctions

Anticipating the number and identity of bidders has significant influence in many theoretical results of the auction itself and bidders’ bidding behaviour. This is because when a bidder knows in advance which specific bidders are likely competitors, this knowledge gives a company a head start when setting the bid price. However, despite these competitive implications, most previous studies have focused almost entirely on forecasting the number of bidders and only a few authors have dealt with the identity dimension qualitatively. Using a case study with immediate real-life applications, this paper develops a method for estimating every potential bidder’s probability of participating in a future auction as a function of the tender economic size removing the bias caused by the contract size opportunities distribution. This way, a bidder or auctioner will be able to estimate the likelihood of a specific group of key, previously identified bidders in a future tender.