On Undecidable Dynamical Properties of Reversible One-Dimensional Cellular Automata

Cellular automata are models for massively parallel computation. A cellular automaton consists of cells which are arranged in some kind of regular lattice and a local update rule which updates the state of each cell according to the states of the cell's neighbors on each step of the computation. This work focuses on reversible one-dimensional cellular automata in which the cells are arranged in a two-way in_nite line and the computation is reversible, that is, the previous states of the cells can be derived from the current ones. In this work it is shown that several properties of reversible one-dimensional cellular automata are algorithmically undecidable, that is, there exists no algorithm that would tell whether a given cellular automaton has the property or not. It is shown that the tiling problem of Wang tiles remains undecidable even in some very restricted special cases. It follows that it is undecidable whether some given states will always appear in computations by the given cellular automaton. It also follows that a weaker form of expansivity, which is a concept of dynamical systems, is an undecidable property for reversible one-dimensional cellular automata. It is shown that several properties of dynamical systems are undecidable for reversible one-dimensional cellular automata. It shown that sensitivity to initial conditions and topological mixing are undecidable properties. Furthermore, non-sensitive and mixing cellular automata are recursively inseparable. It follows that also chaotic behavior is an undecidable property for reversible one-dimensional cellular automata.

Estrutura e relações ambientais de grupos florísticos em fragmento de floresta estacional subtropical

Este estudo teve por objetivos analisar a estrutura de grupos florísticos na vegetação arbórea-arbustiva de um trecho de encosta de Floresta Estacional Subtropical, no Parque Estadual Quarta Colônia, RS, e determinar fatores ambientais importantes na ocorrência das espécies, a fim de subsidiar programas de restauração de áreas degradadas como ecossistema de referência. Para isso, foi realizado estudo fitossociológico em 12 parcelas de 200 m² (10 x 20 m), distantes 20 m entre si, distribuídas sistematicamente em quatro faixas de 100 m entre si, seguindo gradiente de topografia. Em cada parcela foram realizadas a identificação e a medição da circunferência à altura do peito (CAP) e da altura total dos indivíduos arbóreos e arbustivos, ou seja, com CAP > 15 cm, denominado componente arbóreo. Os dados do sub-bosque foram obtidos em parcelas circulares com raio de 1,78 m, instaladas no centro das parcelas de 10 x 20 m, medindo-se indivíduos com altura > 30 cm e CAP <15 cm. As variáveis ambientais foram compostas pela declividade, pela intensidade luminosa, pelas características químicas e textura do solo. Os dados foram analisados segundo a estrutura e diversidade da vegetação por meio da análise de agrupamento pelo método TWINSPAN (Two-way Indicator Species Analysis) e da ordenação pelo método CCA (Análise de Correspondência Canônica). Foi identificada a formação de dois grupos florísticos. A composição de espécies de cada grupo pertence a diferentes estágios de sucessão natural, conforme histórico de uso agrícola, e, segundo suas características funcionais, podem ser indicadas para programas de restauração florestal.

Health-related quality of life in school children: validation of instrument, child self assessment, parent-proxy assessment and school nursing documentation of health check-ups

The aims of this study were to validate an international Health-Related Quality of Life (HRQL) instrument, to describe child self and parent-proxy assessed HRQL at child age 10 to 12 and to compare child self assessments with parent-proxy assessments and school nursing documentation. The study is part of the Schools on the Move –research project. In phase one, a cross-cultural translation and validation process was performed to develop a Finnish version of Pediatric Quality of Life Inventory™ 4.0 (PedsQL™ 4.0). The process included a two-way translation, cognitive interviews (children n=7, parents n=5) and a survey (children n=1097, parents n=999). In phase two, baseline and follow-up surveys (children n=986, parents n=710) were conducted to describe and compare the child self and parent-proxy assessed HRQL in school children between the ages 10 and 12. Phase three included two separate data, school nurse documented patient records (children n=270) and a survey (children n=986). The relation between child self assessed HRQL and school nursing documentation was evaluated. Validity and reliability of the Finnish version of PedsQL™ 4.0 was good (Child Self Report α=0.91, Parent-Proxy Report α=0.88). Children reported lower HRQL scores at the emotional (mean 76/80) than the physical (mean 85/89) health domains and significantly lower scores at the age of 10 than 12 (dMean=4, p=<0.001). Agreement between child self and parent-proxy assessment was fragile (r=0,4, p=<0.001) but increased as the child grew from age 10 to 12 years. At health check-ups, school nurses documented frequently children’s physical health, such as growth (97%) and posture (98/99%) but seldom emotional issues, such as mood (2/7%). The PedsQLTM 4.0 is a valid instrument to assess HRQL in Finnish school children although future research is recommended. Children’s emotional wellbeing needs future attention. HRQL scores increase during ages between childhood and adolescence. Concordance between child self and parent-proxy assessed HRQL is low. School nursing documentation, related to child health check-ups, is not in line with child self assessed HRQL and emotional issues need more attention.

Cardiorespiratory responses during and after water exercise in pregnant and non-pregnant women

PURPOSE: to compare the blood pressure and oxygen consumption (VO2) responses between pregnant and non-pregnant women, during cycle ergometer exercise on land and in water. METHODS: ten pregnant (27 to 29 weeks of gestation) and ten non-pregnant women were enrolled. Two cardiopulmonary tests were performed on a cycle ergometer (water and land) at the heart rate corresponding to VO2, over a period of 30 minutes each. Exercise measurements consisted of recording blood pressure every five minutes, and heart rate and VO2 every 20 seconds. Two-way ANOVA was used and α=0.05 (SPSS 17.0). RESULTS: there was no difference in cardiovascular responses between pregnant and non-pregnant women during the exercise. The Pregnant Group demonstrated significant differences in systolic (131.6±8.2; 142.6±11.3 mmHg), diastolic (64.8±5.9; 74.5±5.3 mmHg), and mean blood pressure (87.0±4.1; 97.2±5.7 mmHg), during water and land exercise, respectively. The Non-pregnant women Group also had a significantly lower systolic (130.5±8.4; 135.9±8.7 mmHg), diastolic (67.4±5.7; 69.0±10.1 mmHg), and mean blood pressure (88.4±4.8; 91.3±7.8 mmHg) during water exercise compared to the land one. There were no significant differences in VO2 values between water and land exercises or between pregnant and non-pregnant women. After the first five-minute recovery period, both blood pressure and VO2 were similar to pre-exercise values. CONCLUSIONS: for pregnant women with 27 to 29 weeks of gestation, water exercise at the heart rate corresponding to VO2 is physiologically appropriate. These women also present a lower blood pressure response to exercise in water than on land.

Skill Development in Music Reading. The Eye-Movement Approach

This dissertation examined skill development in music reading by focusing on the visual processing of music notation in different music-reading tasks. Each of the three experiments of this dissertation addressed one of the three types of music reading: (i) sight-reading, i.e. reading and performing completely unknown music, (ii) rehearsed reading, during which the performer is already familiar with the music being played, and (iii) silent reading with no performance requirements. The use of the eye-tracking methodology allowed the recording of the readers’ eye movements from the time of music reading with extreme precision. Due to the lack of coherence in the smallish amount of prior studies on eye movements in music reading, the dissertation also had a heavy methodological emphasis. The present dissertation thus aimed to promote two major issues: (1) it investigated the eye-movement indicators of skill and skill development in sight-reading, rehearsed reading and silent reading, and (2) developed and tested suitable methods that can be used by future studies on the topic. Experiment I focused on the eye-movement behaviour of adults during their first steps of learning to read music notation. The longitudinal experiment spanned a nine-month long music-training period, during which 49 participants (university students taking part in a compulsory music course) sight-read and performed a series of simple melodies in three measurement sessions. Participants with no musical background were entitled as “novices”, whereas “amateurs” had had musical training prior to the experiment. The main issue of interest was the changes in the novices’ eye movements and performances across the measurements while the amateurs offered a point of reference for the assessment of the novices’ development. The experiment showed that the novices tended to sight-read in a more stepwise fashion than the amateurs, the latter group manifesting more back-and-forth eye movements. The novices’ skill development was reflected by the faster identification of note symbols involved in larger melodic intervals. Across the measurements, the novices also began to show sensitivity to the melodies’ metrical structure, which the amateurs demonstrated from the very beginning. The stimulus melodies consisted of quarter notes, making the effects of meter and larger melodic intervals distinguishable from effects caused by, say, different rhythmic patterns. Experiment II explored the eye movements of 40 experienced musicians (music education students and music performance students) during temporally controlled rehearsed reading. This cross-sectional experiment focused on the eye-movement effects of one-bar-long melodic alterations placed within a familiar melody. The synchronizing of the performance and eye-movement recordings enabled the investigation of the eye-hand span, i.e., the temporal gap between a performed note and the point of gaze. The eye-hand span was typically found to remain around one second. Music performance students demonstrated increased professing efficiency by their shorter average fixation durations as well as in the two examined eye-hand span measures: these participants used larger eye-hand spans more frequently and inspected more of the musical score during the performance of one metrical beat than students of music education. Although all participants produced performances almost indistinguishable in terms of their auditory characteristics, the altered bars indeed affected the reading of the score: the general effects of expertise in terms of the two eye- hand span measures, demonstrated by the music performance students, disappeared in the face of the melodic alterations. Experiment III was a longitudinal experiment designed to examine the differences between adult novice and amateur musicians’ silent reading of music notation, as well as the changes the 49 participants manifested during a nine-month long music course. From a methodological perspective, an opening to research on eye movements in music reading was the inclusion of a verbal protocol in the research design: after viewing the musical image, the readers were asked to describe what they had seen. A two-way categorization for verbal descriptions was developed in order to assess the quality of extracted musical information. More extensive musical background was related to shorter average fixation duration, more linear scanning of the musical image, and more sophisticated verbal descriptions of the music in question. No apparent effects of skill development were observed for the novice music readers alone, but all participants improved their verbal descriptions towards the last measurement. Apart from the background-related differences between groups of participants, combining verbal and eye-movement data in a cluster analysis identified three styles of silent reading. The finding demonstrated individual differences in how the freely defined silent-reading task was approached. This dissertation is among the first presentations of a series of experiments systematically addressing the visual processing of music notation in various types of music-reading tasks and focusing especially on the eye-movement indicators of developing music-reading skill. Overall, the experiments demonstrate that the music-reading processes are affected not only by “top-down” factors, such as musical background, but also by the “bottom-up” effects of specific features of music notation, such as pitch heights, metrical division, rhythmic patterns and unexpected melodic events. From a methodological perspective, the experiments emphasize the importance of systematic stimulus design, temporal control during performance tasks, and the development of complementary methods, for easing the interpretation of the eye-movement data. To conclude, this dissertation suggests that advances in comprehending the cognitive aspects of music reading, the nature of expertise in this musical task, and the development of educational tools can be attained through the systematic application of the eye-tracking methodology also in this specific domain.

Best practices of international double degree programmes. Case of Russian and European universities

The purpose of the Master’s thesis research is to study and disseminate the best practices of international double Master’s degree programmes organization, implementation and development. The given research is focused on two main areas: motivation of higher education institutions to start double degree programmes and best practices of double degree programme design and implementation from the perspective of building joint curriculum and organizing balanced mobility and development of existing programmes in terms of increasing their quality and attractiveness. This is a case study of the double degree programmes between Russian and European universities. The study findings reveal good developments in the field of double degree cooperation between Russian and European universities and a high motivation from both parties. The research depicts different models of building a joint curriculum and organizing academic mobility. The following areas could be outlined as development points for double degree programmes: - Personal interest and commitment of organizers of double degree programmes; - Comprehensive agreement between partners on different aspects and practicalities of the double degree programme implementation; - Promotion towards more balanced student participation and two-way mobility; - Foreign language skills improvement for students and university staff; - Joint strategy and actions in marketing and quality assurance; - Involvement of international companies; - Wider usage of e-learning technology.

Supplier codes of conduct: Acting responsibly in global supply chains

Nowadays the Western companies are considered responsible for the social and environmental issues in their whole supply chains. To influence the practices of their suppliers the Western companies have created suppliers codes of conduct (SCCs) which express their requirements. Suppliers’ compliance with the SCCs is checked through audits. The purpose of this thesis is to analyze SCCs as a means for Western companies to ensure socially and environmentally responsible actions in their global supply chains, and the sub-objectives are to find out 1) how well do the SCCs and their auditing work at suppliers’ production sites and 2) how can possible problems related to SCCs and their auditing be solved. This is a qualitative research carried out in the form of a case study with two case companies. In this study both primary and secondary data is used. The primary data is collected in the form of interviews of the case company representatives and three external experts. Based on a theoretical framework of previous research in the fields of corporate social responsibility and supply chain management, a model with eleven factors, which influence the success of SCC implementation and the auditing of SCC –implementation, is drafted. Also several different best-practices to help to solve and avoid possible problems related to SCC -implementation and auditing have been identified from previous research. Based on the findings of this study the theoretical model has been updated adding two new influential factors. It seems that how well the SCC and its auditing work at suppliers’ production sites depends on the joint effect of thirteen influential factors: buyer’s purchasing policy, supplier’s motivation, buyer’s commitment, the solving of agency problems, the contents of the SCC, supplier’s role and the buyer-supplier –relationship, complexity of supply chain, the limitations of the smaller buyers, cooperation through a business association or multi-stakeholder system, the role of supplier’s employees, SCC –related communication and supplier’s understanding, cheating in audits and the auditors. The possible problems related to SCCs and their auditing can be solved by adopting best-practices. Nine of the theoretical best-practices stand out from the findings of this study: 1) two-way communication and collecting feedback from suppliers, 2) the philosophy of continuous improvement, 3) long-term business relationships with the supplier, 4) informing the supplier about the advantages of SCC –compliance, 5) rewarding code-compliant suppliers, 6) building collaborative, good buyer-supplier relationships, 7) supporting and advising the supplier, 8) joining a business association or multi-stakeholder system and 9) interviewing supplier’s employees as a part of the audits.

Subshifts with Simple Cellular Automata

A subshift is a set of in nite one- or two-way sequences over a xed nite set, de ned by a set of forbidden patterns. In this thesis, we study subshifts in the topological setting, where the natural morphisms between them are ones de ned by a (spatially uniform) local rule. Endomorphisms of subshifts are called cellular automata, and we call the set of cellular automata on a subshift its endomorphism monoid. It is known that the set of all sequences (the full shift) allows cellular automata with complex dynamical and computational properties. We are interested in subshifts that do not support such cellular automata. In particular, we study countable subshifts, minimal subshifts and subshifts with additional universal algebraic structure that cellular automata need to respect, and investigate certain criteria of `simplicity' of the endomorphism monoid, for each of them. In the case of countable subshifts, we concentrate on countable so c shifts, that is, countable subshifts de ned by a nite state automaton. We develop some general tools for studying cellular automata on such subshifts, and show that nilpotency and periodicity of cellular automata are decidable properties, and positive expansivity is impossible. Nevertheless, we also prove various undecidability results, by simulating counter machines with cellular automata. We prove that minimal subshifts generated by primitive Pisot substitutions only support virtually cyclic automorphism groups, and give an example of a Toeplitz subshift whose automorphism group is not nitely generated. In the algebraic setting, we study the centralizers of CA, and group and lattice homomorphic CA. In particular, we obtain results about centralizers of symbol permutations and bipermutive CA, and their connections with group structures.

ANNUAL GRASSES CONTROL WITH TOPRAMEZONE IN MIXTURE WITH ALS-INHIBITING HERBICIDES

ABSTRACTPanicoid grasses are major weeds of maize and sugarcane as well as of several other important grains, including sorghum, pearl millet, and foxtail millet. Pot trials were conducted to study the activity and potential interactions of topramezone in mixture with recommended rates of rimsulfuron or nicosulfuron on three annual panicoid grasses (i.e. Echinochloa oryzoides,E.phyllopogon, and Panicum miliaceum). Target weeds were treated at the four- to five-leaf growth stage. On the basis of fresh weight reduction, topramezone alone provided 78% control of E.oryzoides, 68% control of E.phyllopogon, and 99% control of P.miliaceum. Topramezone plus rimsulfuron or nicosulfuron provided decreased control of both Echinochloa spp. compared with topramezone alone. The decreased control of E.oryzoidesand E.phyllopogon was more pronounced with rimsulfuron as a companion herbicide in the mixtures. Slightly decreased control of P.milaceum was observed with topramezone plus rimsulfuron compared with topramezone alone, but this was not the case for topramezone plus nicosulfuron. Increased topramezone rates mixed with rimsulfuron or nicosulfuron did not improve control of E.oryzoides and E.phyllopogon compared with the lowest topramezone rate. Also, increased topramezone rates mixed with rimsulfuron or nicosulfuron showed decreased control of both Echinochloa spp. when compared with either rimsulfuron or nicosulfuron alone, suggesting a two-way interaction between topramezone and the ALS-inhibiting herbicides. The above-mentioned interaction was not observed in P.miliaceum, probably related with species sensitivity to the herbicides tested. Newly introduced or naturalized panicoid grasses in maize fields may complicate selection of companion herbicides and rates for effective weed control.

Yrittäjyyskasvatus yhteistyöverkostoissa

Tutkimus käsittelee Yrittäjyyskasvatuksen Mittariston -projektia, jossa tutkimuskohteena on peruskoulun ensimmäisen asteen luokan- ja aineenopettajien näkemys ja kokemus yrittäjyyskasvatuksen verkostoyhteistyöstä. Tutkimuksen tarkoituksena oli selvittää miten hyvin opettajat tuntevat verkostoyhteistyötä, mikä on heidän tietämyksensä yrittäjyyskasvatuksesta ja kuinka tämä näkyy heidän työssään ja opetuksessaan. Tutkimuksen otos on 450 opettajaa. Tulokset analysoitiin SPSS-tilastomenetelmäohjelmalla. Tilastollisina tutkimusmenetelminä käytettiin jakaumien frekvenssianalyysiä, Faktori­analyysin Pääkomponenttianalyysiä ja Kaksisuuntaista varianssianalyysia (Anova). Tutkimuksen johtopäätöksenä voidaan todeta, että opettajien tiedot yhteistyö-verkostojen tarjoamista palveluista ovat hyvin hajanaiset. Ongelma jatkuu helposti niin kauan kunnes opettajien koulutusohjelmaan tuodaan lisää yrittäjyyskasvatus- ja yrittäjyysopintoja. Tämä pitäisi huomioida myös tulevissa opetussuunnitelmissa. Tämän tutkimuksen tavoitteena oli tuoda esille Yrittäjyyskasvatuksen mittariston tulosten kautta yrittäjyyskasvatuksen nykytila, tuoda ratkaisuja ehdotusten kautta opetukseen ja herättää keskustelua yrittäjyyskasvatuksen parantamiseksi.

Floristic relationships among inland swamp forests of Southeastern and Central-Western Brazil

We evaluated the floristic relationships among 20 swamp forests of Southeastern and Central-Western Brazil using multivariate analyses. Detrended correspondence analysis (DCA) and TWINSPAN (Two way indicator species analysis) indicated two distinct floristic groups among forests, according to the Phytogeographic Province (Paranaense or Cerrado) and their climate conditions, phytophysiognomies, and species composition. Within the same province, edaphic conditions and geographical distance, among other factors, may be responsible for similarities or dissimilarities among the forests floras. Our results indicated that, despite the low a diversity, γ diversity is high among the forests, as a result of the low floristic similarities among the remnants and the high number of unique species (55% of all species). Although floristically distinct, we concluded that the inland swamp forests of Southeastern Brazil and the gallery swamp forests of Central Brazil are part of the same forest formation. These forests have in common, in addition to the swampy environment, low plant species diversity and species that have high local densities, such as Calophyllum brasiliense Cambess., Cecropia pachystachya Trécul, Dendropanax cuneatus Decne. & Planch., Guarea macrophylla Vahl, Magnolia ovata (A. St.-Hil.) Spreng., Protium spruceanum (Benth.) Engl. and Tapirira guianensis Aubl.

The board of directors as a part of family business governance – multilevel participation and board development

In this study, I examine the board of directors as a part of family business governance. Both boards and governance have increased their attractiveness as a research topic lately. Research on boards has concentrated mostly on the study of different board attributes, like composition, and the relationship of these attributes to the firm’s performance. Family business governance studies are criticized for ignoring the multifaceted needs of companies. More research observing the context and contingencies affecting the governance and board of directors is needed. The objective of this study is to clarify: 1) how the board participates in family business governance, and 2) how the board develops along with the firm’s and family’s development. The study is implemented as qualitative research, and the longitudinal process approach has been used as it provides the opportunity to examine development in context. Selection criteria for the two cases selected for this study are: active board of directors, at least one implemented succession, and interviewees available from two generations and from different positions in the firm. The data consists of interviews and secondary data, and it is collected from different data sources. The analysis was done selecting first some critical events from both cases to closer examination, and analysing them by using content analysis technique. Several conclusions were drawn basing on the findings. First, the family business board participates in the firm’s activities much more widely than it is customary to think. Second, the family business board is not a static part of the business, but it develops and it has to develop for different reasons. Third, ownership is not only the basis for the board’s activities or existence, but the relationship between the board and ownership is two-way. The board contributes to a large extent to the ownership decisions, and in this way to the management of ownership. Fourth, according to the cases, the board has many unrecognized possibilities to facilitate succession in family firms.

Effects of entorhinal cortex lesions on memory in different tasks

Lesions of the entorhinal cortex produce retrograde memory impairment in both animals and humans. Here we report the effects of bilateral entorhinal cortex lesions caused by the stereotaxic infusion of N-methyl-D-aspartate (NMDA) in rats at two different moments, before or after the training session, on memory of different tasks: two-way shuttle avoidance, inhibitory avoidance and habituation to an open field. Pre- or post-training entorhinal cortex lesions caused an impairment of performance in the shuttle avoidance task, which agrees with the previously described role of this area in the processing of memories acquired in successive sessions. In the inhibitory avoidance task, only the post-training lesions had an effect (amnesia). No effect was observed on the open field task. The findings suggest that the role of the entorhinal cortex in memory processing is task-dependent, perhaps related to the complexity of each task

Postnatal development of rats exposed to fluoxetine or venlafaxine during the third week of pregnancy

The aim of the present study was to compare the toxic effects of fluoxetine (F) (8 and 16 mg/kg) and venlafaxine (V) (40 and 80 mg/kg) administered during the third week of pregnancy on early development of rats. Both antidepressants were administered by gavage on pregnancy days 15 to 20 to groups of 10 to 12 animals each. Duration of gestation, food and water consumption, number of live pups and birth weight were recorded. Litters were culled to six pups at birth (day 1) and followed for growth until weaning (day 25). On day 60, a male and a female from each litter were injected with the 5-HT1 agonist, 5-methoxy-N,N-dimethyltryptamine (6 mg/kg, ip) and the serotonergic syndrome was graded. Fluoxetine but not venlafaxine reduced the duration of pregnancy when compared to the control (C) group (F = 21.1 days and C = 21.6 days, mean, P<0.02; maximum = 22 days and minimum = 21 days in both groups). The highest doses of both fluoxetine, 16 mg/kg (F16), and venlafaxine, 80 mg/kg (V80), reduced the food intake of pregnant rats, resulting in different rates of body weight gain during treatment (from pregnancy day 15 to day 20): F16 = 29.0 g, V80 = 28.7 g vs C = 39.5 g (median). Birth weight was influenced by treatment and sex (P<0.05; two-way ANOVA). Both doses of fluoxetine or venlafaxine reduced the body weight of litters; however, the body weight of litters from treated dams was equal to the weight of control litters by the time of weaning. At weaning there was no significant difference in weight between sexes. There was no difference among groups in number of live pups at birth, stillbirths, mortality during the lactation period or in the manifestation of serotonergic syndrome in adult rats. The occurrence of low birth weight among pups born to dams which did not show reduced food ingestion or reduction of body weight gain during treatment with lower doses of fluoxetine or venlafaxine suggests that these drugs may have a deleterious effect on prenatal development when administered during pregnancy. In addition, fluoxetine slightly but significantly affected the duration of pregnancy (about half a day), an effect not observed in the venlafaxine-treated groups.

Effect of repeated restraint stress on memory in different tasks

The present study investigated the effect of repeated stress applied to female rats on memory evaluated by three behavioral tasks: two-way shuttle avoidance, inhibitory avoidance and habituation to an open field. Repeated stress had different effects on rat behavior when different tasks were considered. In the two-way active avoidance test the stressed animals presented memory of the task, but their memory scores were impaired when compared to all other groups. In the habituation to the open field, only the control group showed a significant difference in the number of rearings between training and testing sessions, which is interpreted as an adequate memory of the task. In the handled and chronically stressed animals, on the other hand, no memory was observed, suggesting that even a very mild repeated stress would be enough to alter habituation to this task. The performance in the inhibitory avoidance task presented no significant differences between groups. The findings suggest that repeated restraint stress might induce cognitive impairments that are dependent on the task and on stress intensity.